Systems and methods for generating entangled photons

Abstract

Systems and methods are presented for generating entangled photons. The systems and methods generally utilize dopant molecules in host materials that are contained within a micro¬ cavity. The dopant molecules are generally associated with a ground state triplet (GST) electronic manifold. When the dopant molecules are subjected to light, the electronic state of the dopant molecules is excited to an excited state triplet (EST) electronic manifold. The electronic state then decays via transition pathways that include a zero-phonon line (ZPL) electronic transition. In the presence of the micro-cavity, the decay rate along the ZPL electronic transition is greatly enhanced. Thus, the dopant molecules emit photons with a nearly pure optical state (e.g., a nearly pure wavelength and optical polarization) as they decay from the EST electronic manifold to the GST electronic manifold. As such, the optical state of the emitted photons is correlated with the electronic state of the dopant molecules.

Description

14584.0034-00304 SYSTEMS AND METHODS FOR GENERATING ENTANGLED PHOTONS CROSS-REFERENCE

[0001] The present application claims priority to U.S. Provisional Patent Application No. 63 / 523,376, entitled “SYSTEMS AND METHODS FOR GENERATING ENTANGLED PHOTONS,” filed on June 27, 2023, and to U.S. Provisional Patent Application No. 63 / 552,204, entitled “SYSTEMS AND METHODS FOR GENERATING SPIN-PHOTON ENTANGLEMENT,” filed on February 12, 2024, each of which is incorporated herein by reference in its entirety for all purposes. TECHNICAL FIELD

[0002] The disclosed embodiments generally relate to techniques for generating entangled photons for use in non-classical communications, non-classical information processing, and / or non-classical computing, such as quantum communications, quantum information processing, and / or quantum computing. BACKGROUND

[0003] Non-classical information processing systems such as non-classical computers (e.g., quantum computers) typically exploit quantum mechanical phenomena, such as superposition, entanglement, and interference, to perform computational operations on data. In comparison to classical computers, which utilize binary digits (bits) that always have a defined state (0 or 1), non-classical computers utilize quantum bits (qubits) that can exist in a superposition of basis states (i.e., some linear combination of basis state |0> and basis state |1>, where basis states |0> and |1> are orthonormal). Various qubits of the non-classical computer may be entangled with other qubits (i.e., the quantum states of two or more qubits may be correlated such that operations on one qubit affect the state of an entangled qubit). Quantum operations may be14584.0034-00304 performed to direct the states of the qubits to probabilistically converge on a particular final state, which represents the solution to some problem. For certain classes of problems, the non- classical computer may converge to the solution faster than is possible using any known algorithm on a classical computer. In some cases, this “quantum advantage” may allow the non- classical computer to solve problems that would be intractable using any known classical computer. Such problems include the factoring of large relatively prime numbers (e.g., for breaking modern cryptographic hash functions), searching for particular items in large quantities of data, and simulating the chemical behavior of drugs, materials, or other molecules.

[0004] Similarly, non-classical communications systems (e.g., quantum communications systems) typically exploit quantum mechanical phenomena, such as superposition, entanglement, and interference, to communicate (i.e., transmit and / or receive) information between systems located at two different locations. In comparison to classical communications systems, which transmit a series of bits that always have a defined state (0 or 1), non-classical communications systems utilize qubits that can exist in a superposition of basis states (i.e., some linear combination of basis state |0> and basis state |1>, where basis states |0> and |1> are orthonormal). While the bits of classical communications are generally unentangled (i.e., the state of one bit is not dependent on or correlated with the state of the previous bit, such that operations on one bit does not affect the state of the previous bit), in quantum communications, various qubits may be entangled with other qubits (i.e., the quantum states of two or more qubits may be correlated such that operations on one qubit affect the state of an entangled qubit). Thus, for instance, when a state of one entangled qubit is determined or otherwise manipulated (i.e., collapsed into a particular basis state), a state of a different entangled qubit may be altered (i.e., collapsed into a particular basis state). Thus, unwanted eavesdropping on the content of the information transmitted and / or received by the non-classical communications system may be immediately detected by performing operations on an entangled qubit. This general scheme14584.0034-00304 forms the basis for numerous quantum cryptography applications which aim to create secure communications channels between different locations.

[0005] Numerous non-classical information processing systems and non-classical communications systems require the generation of streams of entangled photons. However, previous attempts to generate such entangled photons have generally been limited to producing small numbers of entangled photons due to materials limitations. Thus, there is a need for systems and methods that allow for the generation of large numbers of entangled photons. SUMMARY

[0006] The systems and methods presented herein allow for the generation of large numbers of entangled photons. The systems and methods generally utilize dopant molecules contained in host materials that are contained within at least one micro-cavity. The dopant molecules are generally associated with a ground state triplet (GST) electronic manifold. When the dopant molecules are subjected to light, the electronic state of the dopant molecules is excited to an excited state triplet (EST) electronic manifold. The electronic state of the dopant molecules then decays via one or more electronic transition pathways, including a zero-phonon line (ZPL) electronic transition.

[0007] In the presence of the micro-cavity, the decay rate along the ZPL electronic transition is greatly enhanced, causing the dopant molecules to act as a nearly pure two-level electronic system. Thus, the dopant molecules emit photons with a nearly pure optical state (e.g., a nearly pure wavelength and optical polarization) as they decay from the EST electronic manifold to the GST electronic manifold. As such, the optical state of the emitted photons is correlated with the electronic state of the dopant molecules.

[0008] Electromagnetic (EM) radiation, such as radio-frequency (RF) and / or microwave (MW) radiation, may be directed to the dopant molecules to alter an electronic spin state of the dopant molecules. The electronic spin state of the at least one dopant molecule is correlated with the14584.0034-00304 polarization of the emitted photons. Thus, the polarization of each emitted photon may be correlated with the electronic spin state of the dopant molecules. By repeatedly subjecting the dopant molecules to EM radiation and light, a stream of photons may be emitted, with each photon having a polarization state that is determined by (i.e., correlated with) the electronic spin state of the dopant molecules at the time that the light is supplied. The stream of photons emitted may thus have polarizations that are correlated with one another. In other words, the stream of photons may be entangled.

[0009] The dopant molecules generally use organic materials. In contrast to previous materials, such as quantum dots, the use of organic materials allows for significant flexibility in molecular design and coupling to the micro-cavity. For instance, the organic materials may be chemically optimized to allow for the emission of photons having a wavelength that is compatible with the fiber optics materials that undergird the modern telecommunications industry or for other useful properties. In contrast to previous materials, which are often fabricated simultaneously with the micro-cavities, the organic materials may be optimized to allow for later deposition on the micro-cavities (e.g., using spin coating, chemical vapor deposition, or the like). Moreover, the micro-cavities may thus be individually optimized to provide the highest achievable ZPL rates without concern for materials limitations. As such, the dopant molecules may provide significant opportunity for optimization to produce long streams of entangled photons, interface with existing microelectronics or fiber optics infrastructure, and the like.

[0010] It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosed embodiments, as claimed.14584.0034-00304 BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The accompanying drawings, which comprise a part of this specification, illustrate several embodiments and, together with the description, serve to explain the principles and features of the disclosed embodiments. In the drawings:

[0012] FIG.1A depicts a top view of an exemplary system for generating entangled photons, in accordance with disclosed embodiments.

[0013] FIG.1B depicts a side view of an exemplary system for generating entangled photons, in accordance with disclosed embodiments.

[0014] FIG.2 depicts an exemplary energy level diagram from a GST molecule, in accordance with various embodiments.

[0015] FIG. 3 depicts an exemplary method for generating entangled photons, in accordance with disclosed embodiments.

[0016] FIG. 4 depicts an exemplary method for rapidly generating streams of entangled photons, in accordance with disclosed embodiments.

[0017] FIG.5 depicts an exemplary system for rapidly generating streams of entangled photons, in accordance with disclosed embodiments.

[0018] FIG. 6A shows exemplary continuous wave (cw) electron paramagnetic resonance (EPR) signals associated with stepwise photoactivation of di(naphthalen-2-yl)carbene in di(naphthalen-2-yl)methanone at a temperature of 25 K using a green laser, in accordance with various embodiments.

[0019] FIG.6B shows the double integral of the cw EPR signals from FIG.6A as a function of the applied light energy, in accordance with various embodiments.

[0020] FIG. 7A shows exemplary cw EPR signals associated with the conversion of freshly photoactivated di(naphthalen-2-yl)carbene in di(naphthalen-2-yl)methanone to an annealed form at a temperature of 140 K, in accordance with various embodiments.14584.0034-00304

[0021] FIG.7B shows the double integral of the cw EPR signals from FIG.7A as a function of the annealing time, in accordance with various embodiments.

[0022] FIG. 7C shows exemplary cw EPR signals after photoactivation of (4-(N- carbazoyl)phenyl)(phenyl)carbene in (4-(N-carbazoyl)phenyl)-(phenyl)methanone at a temperature of 25 K, in accordance with various embodiments.

[0023] FIG.8A shows an exemplary spin-lattice (T1) relaxation decay curve for di(naphthalen- 2-yl)carbene-d14in di(naphthalen-2-yl)methanone-d14at a single temperature, in accordance with various embodiments.

[0024] FIG.8B shows an exemplary plot of the T1 temperature dependence for di(naphthalen- 2-yl)carbene-d14in di(naphthalen-2-yl)methanone-d14, in accordance with various embodiments.

[0025] FIG. 9 shows exemplary spin-spin (T2) relaxation decay curves for protonated and deuterated dilute molecular crystals of di(naphthalen-2-yl)carbene in di(naphthalen-2- yl)methanone, in accordance with various embodiments.

[0026] FIG.10 shows exemplary double electron-electron resonance (DEER) decay curves for partially and fully activated di(naphthalen-2-yl)carbene-d14 in di(naphthalen-2-yl)methanone- d14, in accordance with various embodiments.

[0027] FIG.11A shows exemplary cw EPR signals associated with stepwise photoactivation of 4-nitrenebenzoic acid in 4-iodobenzoic acid at a temperature of 25 K using light with a wavelength of 370 nm, in accordance with various embodiments.

[0028] FIG.11B shows the double integral of the cw EPR signals from FIG.11A as a function of the activation time, in accordance with various embodiments.

[0029] FIG.12 shows an exemplary cw EPR signal associated with the conversion of freshly photoactivated 4-nitrenebenzoic acid in 4-iodobenzoic acid to an annealed form at room temperature, in accordance with various embodiments.14584.0034-00304

[0030] FIG. 13A shows an exemplary 5x magnified microscope image of a thin film di(naphthalen-2-yl)methanone crystal on a dielectric mirror, in accordance with various embodiments.

[0031] FIG. 13B shows an exemplary 100x magnified microscope image of a thin film di(naphthalen-2-yl)methanone crystal on a dielectric mirror, in accordance with various embodiments.

[0032] FIG. 14 shows an exemplary atomic force microscopy (AFM) image of a thin film di(napthalen-2-yl)methanone crystal on a dielectric mirror, in accordance with various embodiments.

[0033] FIG. 15 shows an exemplary image depicting the finesse of a micro-cavity in the presence of a thin film di(naphthalen-2-yl)methanone crystal, in accordance with various embodiments.

[0034] FIG. 16 shows an exemplary two-dimensional (2D) Rabi plot associated with 2,2’- dinaphthylcarbene dopant molecules in a 2,2’-dinaphtylketone host material, in accordance with various embodiments. DETAILED DESCRIPTION

[0035] Reference will now be made in detail to exemplary embodiments, discussed with regards to the accompanying drawings. In some instances, the same reference numbers will be used throughout the drawings and the following description to refer to the same or like parts. Unless otherwise defined, technical and / or scientific terms have the meaning commonly understood by one of ordinary skill in the art. The disclosed embodiments are described in sufficient detail to enable those skilled in the art to practice the disclosed embodiments. It is to be understood that other embodiments may be utilized and that changes may be made without departing from the scope of the disclosed embodiments. Thus, the materials, methods, and examples are illustrative only and are not intended to be necessarily limiting.14584.0034-00304 Definitions

[0036] As used in the present disclosure, the phrase “or” refers to both conjunctive and disjunctive meanings, unless such a definition is impossible in a given context. For instance, the phrase “A or B” refers to A alone, B alone, or A and B, unless any such meaning is impossible. Similarly, the phrase “A, B, or C” refers to A alone, B alone, C alone, A and B but not C, A and C but not B, B and C but not A, or A, B, and C, unless any such meaning is impossible.

[0037] As used herein, the indefinite articles “a” and “an” mean “one or more.” Similarly, the use of a plural term does not necessarily denote a plurality unless it is unambiguous in the given context.

[0038] As used herein, the terms “non-classical computation,” “non-classical procedure,” “non- classical operation,” and “non-classical computer” generally refer to any system or method for performing computational procedures outside of the paradigm of classical computing. A non- classical computation, non-classic procedure, non-classical operation, or non-classical computer may comprise a quantum computation, quantum procedure, quantum operation, or quantum computer.

[0039] As used herein, the terms “quantum computation,” “quantum procedure,” “quantum operation,” and “quantum computer” generally refer to any method or system for performing computations using quantum mechanical operations (such as unitary transformations or completely positive trace-preserving (CPTP) maps on quantum channels) on a Hilbert space represented by a quantum device. As such, quantum and classical (or digital) computation may be similar in the following aspect: both computations may comprise sequences of instructions performed on input information to then provide an output. Various paradigms of quantum computation may break the quantum operations down into sequences of basic quantum operations that affect a subset of qubits of the quantum device simultaneously. The quantum operations may be selected based on, for instance, their locality or their ease of physical14584.0034-00304 implementation. A quantum procedure or computation may then consist of a sequence of such instructions that in various applications may represent different quantum evolutions on the quantum device. For example, procedures to compute or simulate quantum chemistry may represent the quantum states and the annihilation and creation operators of electron spin orbitals by using qubits (such as two-level quantum systems) and a universal quantum gate set (such as the Hadamard, controlled-not (CNOT), and π / 8 rotation) through the so-called Jordan-Wigner transformation or Bravyi-Kitaev transformation.

[0040] Additional examples of quantum procedures or computations may include procedures for optimization such as quantum approximate optimization algorithm (QAOA) or quantum minimum finding. QAOA may comprise performing rotations of single qubits and entangling gates of multiple qubits. In quantum adiabatic computation, the instructions may carry stochastic or non-stochastic paths of evolution of an initial quantum system to a final one. Quantum-inspired procedures may include simulated annealing, parallel tempering, master equation solver, Monte Carlo procedures, quantum algorithms for approximating maximum independent sets, and the like. Quantum-classical or hybrid algorithms or procedures may comprise such procedures as variational quantum eigensolver (VQE) and the variational and adiabatically navigated quantum eigensolver (VanQver).

[0041] In general, examples of quantum procedures or computations may include any procedures or computations described in M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2013), which is incorporated herein by reference in its entirety for all purposes.

[0042] A quantum computer may comprise one or more adiabatic quantum computers, quantum gate arrays, one-way quantum computers, topological quantum computers, quantum Turing machines, quantum annealers, Ising solvers, or gate models of quantum computing.14584.0034-00304

[0043] As used herein, the term “non-classical communication” generally refers to any system or method for performing communications procedures outside of the paradigm of classical communications. A non-classical communication may comprise a quantum communication.

[0044] As used herein, the term “quantum communication” generally refers to any method or system for communicating data using quantum mechanical operations (such as superposition and / or entanglement).

[0045] As recognized herein, there is a need for systems and methods that allow for the generation of large numbers of entangled photons. Thus, provided herein are systems and methods for generating entangled photons. The systems and methods generally utilize dopant molecules contained in organic host materials. The dopant molecules generally function as photon sources and are associated with electronic energy level structures that include a GST electronic manifold and an EST electronic manifold. The GST electronic manifold and the EST electronic manifold each generally comprise three triplet states, which can be linearly combined to form GST basis states and EST basis states (e.g., with respect to a laboratory frame of reference, a rotating frame of reference, or another suitable time-independent or time-dependent frame of reference). The GST basis states generally have long lifetimes at the temperatures obtainable using liquid helium-based cryogenic systems. The quantum states of the various dopant molecules may be individually manipulated using optical, MW, or RF techniques. Systems for Generating Entangled Photons Using GST Molecules

[0046] FIG. 1A shows a top view of a system 100 for generating entangled photons. In the example shown, the system 100 comprises at least one host material 110. In some embodiments, the host material 110 comprises at least one organic molecule. In some embodiments, the host material 110 is referred to herein as a “matrix.”

[0047] In some embodiments, the host material 110 comprises a crystalline host material. In some embodiments, the host material 110 comprises a single crystalline host material. In some embodiments, the host material 110 comprises a polycrystalline host material. In some14584.0034-00304 embodiments, the host material 110 comprises a liquid crystalline host material. In some embodiments, the host material 110 comprises an amorphous host material. In some embodiments, the host material 110 comprises a powder host material. In some embodiments, the host material 110 comprises a frozen solution host material. In some embodiments, the frozen solution host material comprises a solution that is frozen at cryogenic temperatures. For instance, in some embodiments, the frozen solution host material is frozen at a temperature of at least about 1 Kelvin (K), 2 K, 3 K, 4 K, 5 K, 6 K, 7 K, 8 K, 9 K, 10 K, 15 K, 20 K, 25 K, 30 K, 35 K, 40 K, 45 K, 50 K, or more, at most about 50 K, 45 K, 40 K, 35 K, 30 K, 25 K, 20 K, 15 K, 10 K, 9 K, 8 K, 7 K, 6 K, 5 K, 4 K, 3 K, 2 K, 1 K, or less, or a temperature that is between any two of the preceding values.

[0048] In some embodiments, the host material 110 comprises a linear or branched alkane. In some embodiments, the linear or branched alkane comprises a C4-C20 linear or branched alkane. In some embodiments, the linear or branched alkane comprises a C4 linear or branched alkane, a C5 linear or branched alkane, a C6 linear or branched alkane, a C7 linear or branched alkane, a C8 linear or branched alkane, a C9 linear or branched alkane, a C10 linear or branched alkane, a C11 linear or branched alkane, a C12 linear or branched alkane, a C13 linear or branched alkane, a C14 linear or branched alkane, a C15 linear or branched alkane, a C16 linear or branched alkane, a C17 linear or branched alkane, a C18 linear or branched alkane, a C19 linear or branched alkane, or a C20 linear or branched alkane. In some embodiments, the host material 110 comprises an aromatic hydrocarbon. In some embodiments, the host material 110 comprises a polyaromatic hydrocarbon. In some embodiments, the polyaromatic hydrocarbon is optionally substituted with a methylene, nitrile, carbonyl, carboxylate, alkyl, deuterated alkyl, aryl, deuterated aryl, heteroaryl, deuterated heteroaryl, borane, imine, amine, nitro, phosphine, thioether, ether, fluoro, chloro, bromo, iodo, or thiocarbonyl group. In some embodiments, the host material 110 comprises a diarylketone. In some embodiments, the host material 110 comprises octasulfur. In some embodiments, the host material 110 comprises naphthalene,14584.0034-00304 anthracene, benzoic acid, fluorene, biphenyl, benzene, biphenylene, ortho-terphenyl, meta- terphenyl, para-terphenyl, di(phenyl)methanone, phenanthrene, or di(napthalen-2- yl)methanone. In some embodiments, the host material 110 comprises any partially or fully isotopically labeled derivative of any of the foregoing.

[0049] In some embodiments, the host material 110 is at least partially deuterated. That is, in some embodiments, the host material 110 contains one or more deuterium atoms where hydrogen atoms would otherwise be expected. In some embodiments, the host material 110 contains at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, or more deuterium atoms, at most about 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, or one deuterium atoms, or a number of deuterium atoms that is within a range defined by any two of the preceding values. In some embodiments, the host material 110 is fully deuterated. That is, in some embodiments, the host material 110 contains deuterium atoms at every site where hydrogen atoms would otherwise be expected. In some embodiments, the host material 110 is at least partially labeled with carbon-13. That is, in some embodiments, the host material 110 contains one or more carbon-13 atoms where carbon-12 atoms would otherwise be expected. In some embodiments, the host material 110 contains at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, or more carbon-13 atoms, at most about 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, or one carbon-13 atoms, or a number of carbon- 13 atoms that is within a range defined by any two of the preceding values.

[0050] In some embodiments, the host material 110 comprises an isotopically enriched host material. In some embodiments, the host material 110 is isotopically enriched with a particular atomic isotope. In some embodiments, the isotope comprises hydrogen (1H), deuterium (2H), carbon-13 (13C), nitrogen-15 (15N), fluorine-19 (19F), silicon-29 (29Si), or phosphorous-31 (31P). In some embodiments, the host material 110 is isotopically enriched to feature the isotope at an abundance of at least about 1%, 2%, 3%, 4%, 5%, 6%, 7%, 8%, 9%, 10%, 15%, 20%, 25%, 30%, 35%, 40%, 45%, 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, 91%, 92%, 93%,14584.0034-00304 94%, 95%, 96%, 97%, 98%, 99%, or more, at most about 99%, 98%, 97%, 96%, 95%, 94%, 93%, 92%, 91%, 90%, 85%, 80%, 75%, 70%, 65%, 60%, 55%, 50%, 45%, 40%, 35%, 30%, 25%, 20%, 15%, 10%, 9%, 8%, 7%, 6%, 5%, 4%, 3%, 2%, 1%, or less, or an abundance that is within a range defined by any two of the preceding values. In some embodiments, isotopic enrichment allows improved control over the magnetic environment of the dopant molecules 120 described herein.

[0051] In some embodiments, the host material 110 does not include diamond or graphite.

[0052] In some embodiments, the host material 110 is configured to contain at least one dopant molecule 120 described herein.

[0053] In the example shown, the system 100 comprises at least one dopant molecule 120. In some embodiments, the at least one dopant molecule 120 is contained in the host material. The quantum states of the at least one dopant molecule 120 are described in further detail in FIG.2. Although depicted as comprising a single dopant molecule 120 in FIG.1A, the system 100 may comprise a plurality of dopant molecules 120. In some embodiments, the system 100 comprises at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, or more dopant molecules 120, at most about 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 dopant molecules 120, or a number of dopant molecules 120 that is within a range defined by any two of the preceding values.

[0054] In some embodiments, the at least one dopant molecule 120 comprises an organic molecule. In some embodiments, the at least one dopant molecule 120 comprises a GST molecule; that is, in some embodiments, the at least one dopant molecule 120 is associated with a GST electronic manifold, as described herein with respect to FIG.2.

[0055] In some embodiments, the at least one dopant molecule 120 comprises a carbene molecule. In some embodiments, the at least one dopant molecule 120 comprises a nitrene molecule. In some embodiments, the at least one dopant molecule 120 comprises a radical molecule. In some embodiments, the at least one dopant molecule 120 comprises a biradical14584.0034-00304 molecule. In some embodiments, the at least one dopant molecule 120 comprises a diradical molecule. In some embodiments, the at least one dopant molecule 120 comprises a diaryl diazomethane compound, di(naphthalen-2-yl)carbene, or di(phenyl)carbene. In some embodiments, the at least one dopant molecule 120 comprises any partially or fully isotopically labeled derivative of any of the foregoing.

[0056] In some embodiments, the at least one dopant molecule 120 has a high brightness, i.e. it strongly absorbs and emits light at a particular wavelength. In some embodiments, such a high brightness can be achieved by covalently attaching an electron-donating and / or an electron-accepting functional group to a monoarylcarbene or a diarylcarbene or to a diazo precursor thereof. Electron-donating units include substituted alkynes, substituted alkenes, aryl, heteroaryl, amine, phosphine, ether, thioether groups, and the like. Electron-accepting units include substituted alkynes, substituted alkenes, aryl, heteroaryl, cyano, dicyanoethylene, nitro, carbonyl, imine, fluor, chloro, bromo, iodo groups, and the like.

[0057] Molecular design principles for increasing the fluorescent quantum yield of spin-1 / 2 systems are described in M. Arnold et al, “On the Effect of Donor Strength on the Photoluminescence Performance in Mono-substituted N-Donor Triarylmethyl Radicals,” ChemRxiv 2014, doi:10:26434 / chemrxiv-2023-5cbcl-v3, which is incorporated herein by reference in its entirety for all purposes.

[0058] In some embodiments, the at least one dopant molecule 120 is at least partially deuterated. That is, in some embodiments, the at least one dopant molecule 120 contains one or more deuterium atoms where hydrogen atoms would otherwise be expected. In some embodiments, the at least one dopant molecule 120 contains at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, or more deuterium atoms, at most about 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, or one deuterium atoms, or a number of deuterium atoms that is within a range defined by any two of the preceding values. In some embodiments, the at least one dopant molecule 120 is fully deuterated. That is, in some14584.0034-00304 embodiments, the at least one dopant molecule 120 contains deuterium atoms at every site where hydrogen atoms would otherwise be expected. In some embodiments, the at least one dopant molecule 120 is at least partially labeled with carbon-13. That is, in some embodiments, the at least one dopant molecule 120 contains one or more carbon-13 atoms where carbon-12 atoms would otherwise be expected. In some embodiments, the at least one dopant molecule 120 contains at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, or more carbon-13 atoms, at most about 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, or one carbon-13 atoms, or a number of carbon-13 atoms that is within a range defined by any two of the preceding values.

[0059] In some embodiments, the at least one dopant molecule 120 is contained in the host material 110 at a concentration of at most about 1 dopant molecules per cubic micrometer (μm-3), 0.9 μm-3, 0.8 μm-3, 0.7 μm-3, 0.6 μm-3, 0.5 μm-3, 0.4 μm-3, 0.3 μm-3, 0.2 μm-3, 0.1 μm-3, 0.09 μm-3, 0.08 μm-3, 0.07 μm-3, 0.06 μm-3, 0.05 μm-3, 0.04 μm-3, 0.03 μm-3, 0.02 μm-3, 0.01 μm-3, or less, at least about 0.01 μm-3, 0.02 μm-3, 0.03 μm-3, 0.04 μm-3, 0.05 μm-3, 0.06 μm-3, 0.07 μm-3, 0.08 μm-3, 0.09 μm-3, 0.1 μm-3, 0.2 μm-3, 0.3 μm-3, 0.4 μm-3, 0.5 μm-3, 0.6 μm-3, 0.7 μm-3, 0.8 μm-3, 0.9 μm-3, 1 μm-3, or more, or a concentration that is within a range defined by any two of the preceding values. For instance, in some embodiments, the at least one dopant molecule 120 is contained in the host material 110 at a concentration that permits individual optical addressing of each dopant molecule 120. For instance, in some embodiments, the at least one dopant molecule 120 is contained in the host material 110 at a concentration that places one dopant molecule 120 in each of a plurality of confocal light spots. Such an arrangement may permit the individual optical manipulation of each dopant molecule 120.

[0060] In some embodiments, the at least one dopant molecule 120 is generated by cleaving (e.g., by photolyzing) at least one precursor to at least one of the dopant molecules 120. In some embodiments, the at least one precursor comprises at least one cleavable moiety. In some embodiments, the at least one cleavable moiety comprises at least one photocleavable moiety.14584.0034-00304 In some embodiments, the at least one photocleavable moiety comprises at least one diazo moiety. In some embodiments, the precursor comprises a derivative of a carbene molecule. In some embodiments, the precursor comprises a diazo derivative of a carbene molecule or any partially or fully isotopically labeled derivative thereof.

[0061] In some embodiments, the precursor comprises a diazo derivative of a diarylcarbene. In some embodiments, the precursor comprises (diazomethylene)dinaphthalene, (diazomethylene)dibenzene, (4-(diazo(phenyl)methyl)phenyl)N-carbazole, or any partially or fully isotopically labeled derivative thereof.

[0062] In some embodiments, the at least one photocleavable moiety comprises at least one azido moiety, at least one isocyanato moiety, or at least one iminoiodinane moiety. In some embodiments, the precursor comprises an azido derivative of a nitrene molecule, an isocyanato derivative of a nitrene molecule, or an iminoiodinane derivative of a nitrene molecule, or any partially or fully isotopically labeled derivative thereof.

[0063] In some embodiments, the precursor comprises 4-azidobenzoic acid or any partially or fully isotopically labeled derivative thereof.

[0064] In some embodiments, the precursor is at least partially deuterated. That is, in some embodiments, the precursor contains one or more deuterium atoms where hydrogen atoms would otherwise be expected. In some embodiments, the precursor contains at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, or more deuterium atoms, at most about 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, or one deuterium atoms, or a number of deuterium atoms that is within a range defined by any two of the preceding values. In some embodiments, the precursor is fully deuterated. That is, in some embodiments, the precursor contains deuterium atoms at every site where hydrogen atoms would otherwise be expected. In some embodiments, the precursor is at least partially labeled with carbon-13. That is, in some embodiments, the precursor contains one or more carbon-13 atoms where carbon- 13 atoms would otherwise be expected. In some embodiments, the precursor contains at least14584.0034-00304 about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, or more carbon-13 atoms, at most about 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, or one carbon-13 atoms, or a number of carbon-13 atoms that is within a range defined by any two of the preceding values.

[0065] In some embodiments, the at least one photocleavable moiety is susceptible to cleavage from the at least one precursor when exposed to cleavage (e.g., photolysis) light. In some embodiments, the cleavage light has a central wavelength of at least about 200 nanometers (nm), 210 nm, 220 nm, 230 nm, 240 nm, 250 nm, 260 nm, 270 nm, 280 nm, 290 nm, 300 nm, 310 nm, 320 nm, 330 nm, 340 nm, 350 nm, 360 nm, 370 nm, 380 nm, 390 nm, 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, or more. In some embodiments, the cleavage light has a central wavelength of at most about 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm, 440 nm, 430 nm, 420 nm, 410 nm, 400 nm, 390 nm, 380 nm, 370 nm, 360 nm, 350 nm, 340 nm, 330 nm, 320 nm, 310 nm, 300 nm, 290 nm, 280 nm, 270 nm, 260 nm, 250 nm, 240 nm, 230 nm, 220 nm, 210 nm, 200 nm, or less. In some embodiments, the cleavage light has a central wavelength that is within a range defined by any two of the preceding values, such as between about 300 nm and about 500 nm, about 300 nm and about 400 nm, or about 350 nm and about 400 nm.

[0066] In the example shown, the system 100 comprises at least one micro-cavity 130. In some embodiments, the at least one micro-cavity 130 is configured to support a material therein. In some embodiments, the at least one micro-cavity 130 is configured to support the at least one host material 110 and the at least one dopant molecule 120 therein. In some embodiments, the at least one host material 110 and the at least one dopant molecule 120 are supported within the at least one micro-cavity 130.

[0067] In some embodiments, the at least one micro-cavity 130 is configured to enhance radiative decay of the at least one dopant molecule 120 via a ZPL electronic transition following excitation of an electronic state of the at least one dopant molecule from the GST electronic14584.0034-00304 manifold to the at least one EST electronic manifold, as described herein. That is, in some embodiments, the at least one micro-cavity 130 is configured to increase a rate of radiative decay via the ZPL electronic transition when compared to a situation in which the at least one micro-cavity 130 is not present. In some embodiments, the at least one micro-cavity 130 is configured to multiplicatively increase the radiative decay via the ZPL electronic transition by a Purcell factor. In some embodiments, the Purcell factor is at least about 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, or more, at most about 10,000, 9,000, 8,000, 7,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, or less, or a number that is within a range defined by any two of the preceding values.

[0068] In some embodiments, the at least one micro-cavity 130 comprises at least one Fabry- Perot cavity. In some embodiments, the at least one Fabry-Perot cavity comprises a planar mirror and a curved mirror. In some embodiments, the planar mirror and the curved mirror each comprise micro-mirrors. In some embodiments, the planar mirror and the curved mirror each have at least one characteristic dimension (e.g., a length, width, height, radius, major axis, or minor axis). In some embodiments, the at last one characteristic dimension is at least 10 nm, 20 nm, 30 nm, 40 nm, 50 nm, 60 nm, 70 nm, 80 nm, 90 nm, 100 nm, 200 nm, 300 nm, 400 nm, 500 nm, 600 nm, 700 nm, 800 nm, 900 nm, 1 micrometer (µm), 2 µm, 3 µm, 4 µm, 5 µm, 6 µm, 7 µm, 8 µm, 9 µm, 10 µm, or more, at most about 10 µm, 9 µm, 8 µm, 7 µm, 6 µm, 5 µm, 4 µm, 3 µm, 2 µm, 1 µm, 900 nm, 800 nm, 700 nm, 600 nm, 500 nm, 400 nm, 300 nm, 200 nm, 100 nm, 90 nm, 80 nm, 70 nm, 60 nm, 50 nm, 40 nm, 30 nm, 20 nm, 10 nm, or less, or within a range defined by any two of the preceding values.

[0069] In some embodiments, the at least one micro-cavity 130 comprises a mode volume. In some embodiments, the mode volume is at least about 0.1 cubic micrometers (µm3), 0.2 µm3, 0.3 µm3, 0.4 µm3, 0.5 µm3, 0.6 µm3, 0.7 µm3, 0.8 µm3, 0.9 µm3, 1 µm3, 2 µm3, 3 µm3, 4 µm3, 5 µm3, 6 µm3, 7 µm3, 8 µm3, 9 µm3, 10 µm3, or more, at most about 10 µm3, 9 µm3, 8 µm3, 714584.0034-00304 µm3, 6 µm3, 5 µm3, 4 µm3, 3 µm3, 2 µm3, 1 µm3, 0.9 µm3, 0.8 µm3, 0.7 µm3, 0.6 µm3, 0.5 µm3, 0.4 µm3, 0.3 µm3, 0.2 µm3, 0.1 µm3, or less, or within a range defined by any two of the preceding values.

[0070] In some embodiments, the at least one micro-cavity 130 is characterized by a quality (Q) factor. In some embodiments, the Q factor is at least about 10,000, 20,000, 30,000, 40,000, 50,000, 60,000, 70,000, 80,000, 90,000, 100,000, 200,000, 300,000, 400,000, 500,000, 600,000, 700,000, 800,000, 900,000, 1,000,000, 2,000,000, 3,000,000, 4,000,000, 5,000,000, 6,000,000, 7,000,000, 8,000,000, 9,000,000, 10,000,000, or more, at most about 10,000,000,000, 9,000,000, 8,000,000, 7,000,000, 6,000,000, 5,000,000, 4,000,000, 3,000,000, 2,000,000, 1,000,000, 900,000, 800,000, 700,000, 600,000, 500,000, 400,000, 300,000, 200,000, 100,000, 90,000, 80,000, 70,000, 60,000, 50,000, 40,000, 30,000, 20,000, 10,000, or less, or within a range defined by any two of the preceding values.

[0071] In some embodiments, the at least one micro-cavity 130 is characterized by a finesse. In some embodiments, the finesse is at least about 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, 20,000, 30,000, 40,000, 50,000, 60,000, 70,000, 80,000, 90,000, 100,000, or more, at most about 100,000, 90,000, 80,000, 70,000, 60,000, 50,000, 40,000, 30,000, 20,000, 10,000, 9,000, 8,000, 7,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, or less, or within a range defined by any two of the preceding values.

[0072] In some embodiments, the at least one micro-cavity 130 is formed from a microfabrication processing material such as silicon, mono-crystalline silicon, polysilicon, germanium, diamond, silicon carbide, silicon nitride, silicon on insulator, silicon dioxide, boron nitride, boron phosphide, boron arsenide, aluminum nitride, aluminum phosphide, aluminum arsenide, gallium nitride, gallium phosphide, gallium arsenide, indium nitride, indium phosphide, indium arsenide, indium tin oxide, glass, sapphire, or the like. In some embodiments, the at least one micro-cavity 130 is formed using one or more microfabrication14584.0034-00304 techniques such as wet cleaning, Piranha cleaning, RCA cleaning, surface passivation, spin coating, dip coating, chemical vapor deposition (CVD), atmospheric pressure CVD, low- pressure CVD, ultrahigh vacuum CVD, aerosol assisted CVD, direct liquid injection CVD, hot wall CVD, cold wall CVD, microwave plasma-assisted CVD, plasma-enhanced CVD (PECVD), remote PECVD, low-energy PECVD, atomic-layer CVD, combustion CVD, rapid thermal CVD, photo-initiated CVD, laser CVD, vapor phase epitaxy, physical vapor deposition, sputter deposition, evaporative deposition, pulsed laser deposition, pulsed electron deposition, atomic layer deposition, molecular beam epitaxy, etching, wet etching, dry etching, reactive- ion etching (RIE), deep RIE, electron-beam milling, or atomic layer etching.

[0073] FIG. 1B shows a side view of the system 100. In the example shown, the system 100 comprises the at least one host material 110, the at least one dopant molecule 120, and the at least one micro-cavity 130.

[0074] In the example shown, the system 100 comprises at least one optical unit 140. In some embodiments, the at least one optical unit 140 is configured to direct light to the at least one dopant molecule 120. In some embodiments, the light is configured to excite an electronic state of the at least one dopant molecule 120 from the GST electronic manifold to the EST electronic manifold. In some embodiments, following excitation of the electronic state of the at least one dopant molecule 120, the at least one dopant molecule 120 decays via the ZPL electronic transition. In some embodiments, the at least one dopant molecule 120 emits at least one photon following the decay via the ZPL electronic transition, as described herein with respect to FIG. 2. In some embodiments, an optical state of the at least one photon is entangled with an electronic spin state of the at least one dopant molecule 120, as described herein with respect to FIG.2. In some embodiments, the optical state comprises a polarization state of the at least one photon. In some embodiments, the optical state is entangled with the electronic state by time-domain entanglement, time-domain-to-polarization entanglement, multi-photon time-14584.0034-00304 domain entanglement, or multi-photon time-domain-to-polarization entanglement, as described herein.

[0075] In some embodiments, the at least one optical unit 140 comprises at least one laser. In some embodiments, the light comprises laser light. In some embodiments, the light comprises confocal laser light. In some embodiments, the at least one optical unit 140 is configured to condition the light in route to its interaction with the at least one dopant molecule 120. In some embodiments, the at least one optical unit 140 comprises at least one polarizer. In some embodiments, the at least one optical unit 140 comprises at least one collimator, beam expander, telescope, or the like. In some embodiments, the at least one optical unit 140 comprises at least one focusing element, such as a lens, mirror, objective lens, or the like.

[0076] In some embodiments, the light from the at least one optical unit 140 comprises a central wavelength. For instance, in some embodiments, the light comprises laser light comprising a narrow distribution of wavelengths centered around the central wavelength. In some embodiments, the central wavelength is at least about 500 nm, 550 nm, 600 nm, 650 nm, 700 nm, 750 nm, 800 nm, 850 nm, 900 nm, 950 nm, 1,000 nm, 1,050 nm, 1,100 nm, 1,150 nm, 1,200 nm, 1,250 nm, 1,300 nm, 1,350 nm, 1,400 nm, 1,450 nm, 1,500 nm, 1,550 nm, 1,600 nm, 1,650 nm, 1,700 nm, 1,750 nm, 1,800 nm, 1,850 nm, 1,900 nm, 1,950 nm, 2,000 nm, or more, 2,000 nm, 1,950 nm, 1,900 nm, 1,850 nm, 1,800 nm, 1,750 nm, 1,700 nm, 1,650 nm, 1,600 nm, 1,550 nm, 1,500 nm, 1,450 nm, 1,400 nm, 1,350 nm, 1,300 nm, 1,250 nm, 1,200 nm, 1,150 nm, 1,100 nm, 1,050 nm, 1,000 nm, 950 nm, 900 nm, 850 nm, 800 nm, 750 nm, 700 nm, 650 nm, 600 nm, 550 nm, 500 nm, or less, or within a range defined by any two of the preceding values.

[0077] In some embodiments, the light emitted by the at least one dopant molecule (i.e., the at least one photon emitted by the at least one dopant molecule) comprises a central wavelength. In some embodiments, the central wavelength is at least about 500 nm, 550 nm, 600 nm, 650 nm, 700 nm, 750 nm, 800 nm, 850 nm, 900 nm, 950 nm, 1,000 nm, 1,050 nm, 1,100 nm, 1,150 nm, 1,200 nm, 1,250 nm, 1,300 nm, 1,350 nm, 1,400 nm, 1,450 nm, 1,500 nm, 1,550 nm, 1,60014584.0034-00304 nm, 1,650 nm, 1,700 nm, 1,750 nm, 1,800 nm, 1,850 nm, 1,900 nm, 1,950 nm, 2,000 nm, or more, 2,000 nm, 1,950 nm, 1,900 nm, 1,850 nm, 1,800 nm, 1,750 nm, 1,700 nm, 1,650 nm, 1,600 nm, 1,550 nm, 1,500 nm, 1,450 nm, 1,400 nm, 1,350 nm, 1,300 nm, 1,250 nm, 1,200 nm, 1,150 nm, 1,100 nm, 1,050 nm, 1,000 nm, 950 nm, 900 nm, 850 nm, 800 nm, 750 nm, 700 nm, 650 nm, 600 nm, 550 nm, 500 nm, or less, or within a range defined by any two of the preceding values.

[0078] In some embodiments, the light from the at least one optical unit 140 comprises a bandwidth. In some embodiments, the bandwidth is measured as a full width at half maximum (FWHM). In some embodiments, the bandwidth is at least about 1 MHz, 2 MHz, 3 MHz, 4 MHz, 5 MHz, 6 MHz, 7 MHz, 8 MHz, 9 MHz, 10 MHz, 15 MHz, 20 MHz, 25 MHz, 30 MHz, 35 MHz, 40 MHz, 45 MHz, 50 MHz, 55 MHz, 60 MHz, 65 MHz, 70 MHz, 75 MHz, 80 MHz, 85 MHz, 90 MHz, 95 MHz, 100 MHz, or more, at most about 100 MHz, 95 MHz, 90 MHz, 85 MHz, 80 MHz, 75 MHz, 70 MHz, 65 MHz, 60 MHz, 55 MHz, 50 MHz, 45 MHz, 40 MHz, 35 MHz, 30 MHz, 25 MHz, 20 MHz, 15 MHz, 10 MHz, 9 MHz, 8 MHz, 7 MHz, 6 MHz, 5 MHz, 4 MHz, 3 MHz, 2 MHz, 1 MHz, or less, or within a range defined by any two of the preceding values.

[0079] In some embodiments, the light emitted by the at least one dopant molecule 120 comprises a bandwidth. In some embodiments, the bandwidth is measured as a FWHM. In some embodiments, the bandwidth is at least about 1 MHz, 2 MHz, 3 MHz, 4 MHz, 5 MHz, 6 MHz, 7 MHz, 8 MHz, 9 MHz, 10 MHz, 15 MHz, 20 MHz, 25 MHz, 30 MHz, 35 MHz, 40 MHz, 45 MHz, 50 MHz, 55 MHz, 60 MHz, 65 MHz, 70 MHz, 75 MHz, 80 MHz, 85 MHz, 90 MHz, 95 MHz, 100 MHz, 125 MHz, 150 MHz, 175 MHz, 200 MHz, 225 MHz, 250 MHz, 275 MHz, 300 MHz, or more, at most about 300 MHz, 275 MHz, 250 MHz, 225 MHz, 200 MHz, 175 MHz, 150 MHz, 125 MHz, 100 MHz, 95 MHz, 90 MHz, 85 MHz, 80 MHz, 75 MHz, 70 MHz, 65 MHz, 60 MHz, 55 MHz, 50 MHz, 45 MHz, 40 MHz, 35 MHz, 30 MHz, 25 MHz, 20 MHz,14584.0034-00304 15 MHz, 10 MHz, 9 MHz, 8 MHz, 7 MHz, 6 MHz, 5 MHz, 4 MHz, 3 MHz, 2 MHz, 1 MHz, or less, or within a range defined by any two of the preceding values.

[0080] In the example shown, the system 100 comprises an EM unit 150. In some embodiments, the EM unit 150 is configured to direct EM radiation to the at least one dopant molecule 120. In some embodiments, the EM radiation is configured to alter an electronic spin state of the at least one dopant molecule 120. In some embodiments, the electronic spin state of the at least one dopant molecule 120 determines the optical state (e.g., the polarization state) of the photon emitted by the at least one dopant molecule 120 following decay from the EST electronic manifold to the GST electronic manifold. Thus, in some embodiments, the optical state of the photon emitted by the at least one dopant molecule 120 is correlated with or entangled with the electronic spin state of the at least one dopant molecule 120 prior to the decay from the EST electronic manifold to the GST electronic manifold.

[0081] In some embodiments, the EM radiation comprises MW or RF radiation. In some embodiments, the EM radiation is associated with a central frequency. In some embodiments, the central frequency is at least about 1 MHz, 2 MHz, 3 MHz, 4 MHz, 5 MHz, 6 MHz, 7 MHz, 8 MHz, 9 MHz, 10 MHz, 20 MHz, 30 MHz, 40 MHz, 50 MHz, 60 MHz, 70 MHz, 80 MHz, 90 MHz, 100 MHz, 200 MHz, 300 MHz, 400 MHz, 500 MHz, 600 MHz, 700 MHz, 800 MHz, 900 MHz, 1 gigahertz (GHz), 2 GHz, 3 GHz, 4 GHz, 5 GHz, 6 GHz, 7 GHz, 8 GHz, 9 GHz, 10 GHz, 20 GHz, or more, at most about 20 GHz, 10 GHz, 9 GHz, 8 GHz, 7 GHz, 6 GHz, 5 GHz, 4 GHz, 3 GHz, 2 GHz, 1 GHz, 900 MHz, 800 MHz, 700 MHz, 600 MHz, 500 MHz, 400 MHz, 300 MHz, 200 MHz, 100 MHz, 90 MHz, 80 MHz, 70 MHz, 60 MHz, 50 MHz, 40 MHz, 30 MHz, 20 MHz, 10 MHz, 9 MHz, 8 MHz, 7 MHz, 6 MHz, 5 MHz, 4 MHz, 3 MHz, 2 MHz, 1 MHz, or less, or within a range defined by any two of the preceding values.

[0082] In some embodiments, the system 100 comprises at least one cryogenic unit (not shown in FIG.1B). In some embodiments, the cryogenic unit is configured to contain the at least one host material 110, the at least one dopant molecule 120, and the at least one micro-cavity 13014584.0034-00304 therein. In some embodiments, the cryogenic unit is configured to contain the at least one optical unit 140 therein. In some embodiments, the cryogenic unit is configured to contain the at least one EM unit 150 therein. In some embodiments, the cryogenic unit is not configured to contain the at least one optical unit 140 therein. In some embodiments, the cryogenic unit is not configured to contain the at least one EM unit 150 therein.

[0083] In some embodiments, the cryogenic unit is configured to cool the at least one host material 110, the at least one dopant molecule 120, and the at least one micro-cavity 130 to an operating temperature, such as a temperature of at least about 1 K, 2 K, 3 K, 4 K, 5 K, 6 K, 7 K, 8 K, 9 K, 10 K, 15 K, 20 K, 25 K, 30 K, 35 K, 40 K, 45 K, 50 K, or more, at most about 50 K, 45 K, 40 K, 35 K, 30 K, 25 K, 20 K, 15 K, 10 K, 9 K, 8 K, 7 K, 6 K, 5 K, 4 K, 3 K, 2 K, 1 K, or less, or a temperature that is between any two of the preceding values (such as between about 4 K and about 20 K). In some embodiments, the cryogenic unit comprises at least one helium cryocooler. In some embodiments, the cryogenic unit comprises at least one closed- cycle helium cryocooler. In some embodiments, the cryogenic unit comprises at least one window configured to permit EM energy (such as light from the at least one optical unit 140, EM radiation from the at least one EM unit 150, or light emitted by the at least one dopant molecule 120) to pass therethrough. In some embodiments, the cryogenic unit comprises at least one electrical feedthrough configured to permit EM energy (such as RF or MW energy) to pass therethrough.

[0084] In some embodiments, the system 100 comprises one or more magnetic field sources (not shown in FIG. 1B). In some embodiments, the magnetic field sources are configured to generate one or more magnetic fields or magnetic field gradients in a vicinity of the at least one dopant molecule 120. In some embodiments, the magnetic field sources each comprise a permanent magnet, an electromagnet, or a superconducting magnet. In some embodiments, the magnetic field sources comprise one or more solenoids, Helmholtz coils, anti-Helmholtz coils, saddle coils, Halbach arrays, or the like. In some embodiments, one or more of the magnetic14584.0034-00304 field sources are contained within the cryogenic unit. In some embodiments, one or more of the magnetic field sources are contained outside of the cryogenic unit. In some embodiments, one or more of the magnetic field sources is configured to generate a magnetic field strength at the at least one dopant molecule 120 of at least about 1 microtesla (μT), 2 μT, 3 μT, 4 μT, 5 μT, 6 μT, 7 μT, 8 μT, 9 μT, 10 μT, 20 μT, 30 μT, 40 μT, 50 μT, 60 μT, 70 μT, 80 μT, 90 μT, 100 μT, 200 μT, 300 μT, 400 μT, 500 μT, 600 μT, 700 μT, 800 μT, 900 μT, 1 millitesla (mT), 2 mT, 3 mT, 4 mT, 5 mT, 6 mT, 7 mT, 8 mT, 9 mT, 10 mT, 20 mT, 30 mT, 40 mT, 50 mT, 60 mT, 70 mT, 80 mT, 90 mT, 100 mT, 200 mT, 300 mT, 400 mT, 500 mT, 600 mT, 700 mT, 800 mT, 900 mT, 1 Tesla (T), or more, at most about 1 T, 900 mT, 800 mT, 700 mT, 600 mT, 500 mT, 400 mT, 300 mT, 200 mT, 100 mT, 90 mT, 80 mT, 70 mT, 60 mT, 50 mT, 40 mT, 30 mT, 20 mT, 10 mT, 9 mT, 8 mT, 7 mT, 6 mT, 5 mT, 4 mT, 3 mT, 2 mT, 1 mT, 900 μT, 800 μT, 700 μT, 600 μT, 500 μT, 400 μT, 300 μT, 200 μT, 100 μT, 90 μT, 80 μT, 70 μT, 60 μT, 50 μT, 40 μT, 30 μT, 20 μT, 10 μT, 9 μT, 8 μT, 7 μT, 6 μT, 5 μT, 4 μT, 3 μT, 2 μT, 1 μT, or less, or a magnetic field strength that is within a range defined by any two of the preceding values.

[0085] In the example shown, the host material 110 comprises a thickness 160. In some embodiments, the host material 110 comprises a thin film. That is, in some embodiments, the thickness 160 is at least about 0.1 nm, 0.2 nm, 0.3 nm, 0.4 nm, 0.5 nm, 0.6 nm, 0.7 nm, 0.8 nm, 0.9 nm, 1 nm, 2 nm, 3 nm, 4 nm, 5 nm, 6 nm, 7 nm, 8 nm, 9 nm, 10 nm, 20 nm, 30 nm, 40 nm, 50 nm, 60 nm, 70 nm, 80 nm, 90 nm, 100 nm, 200 nm, 300 nm, 400 nm, 500 nm, 600 nm, 700 nm, 800 nm, 900 nm, 1,000 nm, or more, at most about 1,000 nm, 900 nm, 800 nm, 700 nm, 600 nm, 500 nm, 400 nm, 300 nm, 200 nm, 100 nm, 90 nm, 80 nm, 70 nm, 60 nm, 50 nm, 40 nm, 30 nm, 20 nm, 10 nm, 9 nm, 8 nm, 7 nm, 6 nm, 5 nm, 4 nm, 3 nm, 2 nm, 1 nm, 0.9 nm, 0.8 nm, 0.7 nm, 0.6 nm, 0.5 nm, 0.4 nm, 0.3 nm, 0.2 nm, 0.1 nm, or less, or within a range defined by any two of the preceding values. For instance, in some embodiments, the thickness 160 is between about 0.1 nm and about 1 nm, about 0.1 nm and about 10 nm, about 0.1 nm and about 100 nm, about 0.1 nm and about 1,000 nm, about 1 nm and about 10 nm, about 1 nm and about14584.0034-00304 10 nm, about 1 nm and about 100 nm, about 1 nm and about 1,000 nm, about 10 nm and about 100 nm, about 10 nm and about 1,000 nm, or about 100 nm and about 1,000 nm.

[0086] In some embodiments, the thin film is formed within or on top of the at least one micro- cavity 130. In some embodiments, the thin film is formed using one or more microfabrication techniques such as wet cleaning, Piranha cleaning, RCA cleaning, surface passivation, spin coating, dip coating, CVD, atmospheric pressure CVD, low-pressure CVD, ultrahigh vacuum CVD, aerosol assisted CVD, direct liquid injection CVD, hot wall CVD, cold wall CVD, microwave plasma-assisted CVD, PECVD, remote PECVD, low-energy PECVD, atomic-layer CVD, combustion CVD, rapid thermal CVD, photo-initiated CVD, laser CVD, vapor phase epitaxy, physical vapor deposition, sputter deposition, evaporative deposition, pulsed laser deposition, pulsed electron deposition, atomic layer deposition, molecular beam epitaxy, etching, wet etching, dry etching, RIE, deep RIE, electron-beam milling, atomic layer etching, or self-assembly (to form a self-assembled monolayer).

[0087] In some embodiments, the thin film is formed within or on top of the at least one micro- cavity 130 using one or more microfabrication techniques (such as spin coating, CVD, atmospheric pressure CVD, low-pressure CVD, ultrahigh vacuum CVD, aerosol assisted CVD, direct liquid injection CVD, hot wall CVD, cold wall CVD, microwave plasma-assisted CVD, PECVD, remote PECVD, low-energy PECVD, atomic-layer CVD, combustion CVD, rapid thermal CVD, photo-initiated CVD, or laser CVD) that is compatible with microfabrication techniques used to form the at least on micro-cavity 130. Thus, in some embodiments, the thin film is formed as a step in the same microfabrication process (e.g., a wafer manufacturing process) that forms the at least one micro-cavity 130. In some embodiments, forming the thin film and the at least one micro-cavity 130 in the same microfabrication process reduces overall system processing costs, reduces system complexity, reduces the need for optical or electronic interconnects between the host material 110 and the micro-cavity 130 (compared to systems which form qubits and micro-cavities on different substrates), and the like.14584.0034-00304 GST Molecules for Generating Entangled Photons

[0088] FIG.2 shows an example of an electronic energy level diagram 200 for a GST molecule. In the example shown, the GST molecule is associated with a GST electronic manifold 210, a first singlet electronic state 220, a second singlet electronic state 230, and an excited state triplet (EST) electronic manifold 240. In some embodiments, the GST electronic manifold 210 comprises a first ground triplet state 211, a second ground triplet state 212, and a third ground triplet state 213. In some embodiments, the first ground triplet state 211, second ground triplet state 212, and third ground triplet state 213 represent the lowest-energy electronic states of the GST molecule. In some embodiments, the first ground triplet state 211 is denoted by |^^^1^^^^^^, the second ground triplet state 212 is denoted by |^^^^2^^^^^, and the third ground triplet state 213 is denoted by |^^^^3^^^^^. In some embodiments, the EST electronic manifold 240 comprises a first excited triplet state 241, a second excited triplet state 242, and a third excited triplet state 243. In some embodiments, the first excited triplet state 241 is denoted by |^^^^1^^^^^, the second excited triplet state 242 is denoted by |^^^^2^^^^^, and the third excited triplet state 243 is denoted by |^^^^3^^^^^. In some embodiments, the first singlet electronic state 220, second singlet electronic state 230, and EST electronic manifold 240 each represent higher-energy electronic states than the GST electronic manifold. As depicted in FIG.2, in some embodiments, the second singlet electronic state 230 is lower in energy than the EST electronic manifold 240. However, in other embodiments, the second singlet electronic state 230 is higher in energy than the EST electronic manifold 240.

[0089] In some embodiments, at thermal equilibrium, the GST electronic state 210 is highly populated (i.e., the electronic wavefunction of the GST molecule is heavily biased to the GST electronic state 210, with relatively equal contributions to the first ground triplet state 211, second ground triplet state 212, and third ground triplet state 213), while the first singlet electronic state 220, second singlet electronic state 230, first excited triplet state 241, second excited triplet state 242, and third excited triplet state 243 are not highly populated.14584.0034-00304

[0090] In some embodiments, the GST molecule is configured to absorb EM radiation (e.g., MW or RF radiation from the at least one EM unit 150 described herein with respect to FIG. 1B) to drive the population from the first ground triplet state 211, second ground triplet state 212, or third ground triplet state 213, or a linear combination thereof, to the first ground triplet state 211, second ground triplet state 212, or the third ground triplet state 213, or a different linear combination thereof. In this manner, the electronic spin state of the GST molecule may be set prior to optical excitation. Since the electronic spin state of the GST molecule determines the optical state of an emitted photon (as described herein with respect to FIG.1B), this process allows the optical state of each emitted photon to be selected.

[0091] In some embodiments, the GST molecule is configured to absorb light (e.g., light from the at least one optical unit 140 described herein with respect to FIG.1B) to drive the population from the first ground triplet state 211, second ground triplet state 212, or third ground triplet state 213, or a linear combination thereof, to the first excited triplet state 241, second excited triplet state 242, third excited triplet state 243, or a linear combination thereof. In some embodiments, the GST molecule is configured to relax via radiative decay back to the first ground triplet state 211, second ground triplet state 212, or third ground triplet state 213, or a linear combination thereof, via a ZPL electronic transition and to emit a photon having an optical state (e.g., a polarization state) that is correlated or entangled with the electronic spin state (i.e., the state |^^^1^^^^^^, |^^^^2^^^^^, |^^^^3^^^^^, or a linear combination thereof) of the GST molecule prior to absorbing the light.

[0092] In some embodiments, the first ground triplet state 211, second ground triplet state 212, and third ground triplet state 213 described herein are separated by energy differences that are in the RF or MW portion of the EM spectrum. Thus, in some embodiments, manipulation of the electronic spin state of the GST molecule may be performed using RF or MW energy prior to the GST molecule absorbing the light. Methods for Generating Entangled Photons Using GST Molecules14584.0034-00304

[0093] FIG. 3 depicts an exemplary method 300 for generating entangled photons. At 310, at least one micro-cavity supporting at least one host material therein is obtained. In some embodiments, the at least one micro-cavity comprises any micro-cavity 130 described herein with respect to FIG. 1A. In some embodiments, the at least one host material comprises any host material 110 described herein with respect to FIG.1A. In some embodiments, the at least one host material contains at least one dopant molecule therein. In some embodiments, the at least one dopant molecule comprises any dopant molecule 120 described herein with respect to FIG. 1A. In some embodiments, the at least one dopant molecule is associated with a GST electronic manifold and at least one EST electronic manifold, as described herein with respect to FIG.1A or 2.

[0094] At 320, EM radiation is directed to the at least one dopant molecule to thereby alter an electronic spin state of the at least one dopant molecule, as described herein with respect to FIG.1B or 2. In some embodiments, the EM radiation comprises any EM radiation described herein with respect to FIG.1B or 2. In some embodiments, the EM radiation is directed to the at least one dopant molecule by the at least one EM unit 150 described herein with respect to FIG.1B.

[0095] At 330, light is directed to the at least one dopant molecule to thereby excite an electronic state of the at least one dopant molecule from the GST electronic manifold to the at least one EST electronic manifold, as described herein with respect to FIG. 1B or 2. In some embodiments, the light comprises any light described herein with respect to FIG. 1B or 2. In some embodiments, the light is directed to the at least one dopant molecule by the at least one optical unit 140 described herein with respect to FIG.1B.

[0096] At 340, the at least one dopant molecule is permitted to emit at least one photon via enhanced radiative decay via a ZPL electronic transition, as described herein with respect to FIG. 1B or 2. In some embodiments, the at least one photon comprises any emitted photon described herein with respect to FIG.1B or 2.14584.0034-00304

[0097] In some embodiments, the method 300 further comprises cooling the at least one micro- cavity, the at least one host material, and the at least one dopant molecule to any operating temperature described herein with respect to FIG.1B. In some embodiments, the method 300 further comprises cooling the at least one optical unit to the operating temperature. In some embodiments, the method 300 further comprises cooling the at least one EM unit to the operating temperature. In some embodiments, the at least one micro-cavity, the at least one host material, and the at least one dopant molecule (and, optionally, the at least one optical unit or the at least one EM unit) are cooled to the operating temperature using any cryogenic unit described herein with respect to FIG.1B. Time-domain entanglement and time-domain-to-polarization entanglement

[0098] In order to generate streams of entangled photons, the optical state of each photon emitted by the at least one dopant molecule may be controllable by controlling the electronic spin state of the at least one dopant molecule. Thus, the optical state of each photon emitted by the at least one dopant molecule may be entangled with an electronic spin state of the at least one dopant molecule in order to generate streams of entangled photons. In some embodiments, time-domain entanglement or time-domain-to-polarization entanglement are used to generate such entanglements.

[0099] In time-domain entanglement, two of the three electronic spin state sublevels of a triplet spin system (e.g., the triplet spin system of the GST molecules described herein) are chosen asphoton emission states (e.g., any two of the |^^^1^^^^^^, |^^^^2^^^^^, and |^^^^3^^^^^electronic spin state sublevelsof the GST molecules described herein with respect to FIG.2). For illustration, we will choosethe |^^^1^^^^^^and |^^^^2^^^^^sublevels to illustrate the concept. However, any two of the |^^^1^^^^^^, |^^^^2^^^^^, and|^^^^3^^^^^ may be chosen based on, for instance, branching ratios associated with a particular GST molecule.

[0100] In general, the electronic spin state of the GST molecule is some mixed state ^^^^|^^^ ^^^^1^ ^ += 1. Electromagnetic radiation (such as light) that is resonant with14584.0034-00304 |^^^1^^^^^^ will excite the |^^^^1^^^^^ portion of the GST molecule wavefunction but not the |^^^^2^^^^^ portion of the wavefunction. Similarly, electromagnetic radiation that is resonant with |^^^^2^^^^^will excite the |^^^^2^^^^^ portion of the GST molecule wavefunction but not the |^^^1^^^^^^ portion of the wavefunction. Moreover, delivering electromagnetic radiation (such as radiofrequency or microwave radiation) that is resonant with a spin flip transition between the |^^^^1^^^^^and |^^^^2^^^^^sublevels will cause rotation between these two sublevels, transforming a portion of |^^^1^^^^^^ into |^^^^2^^^^^ and vice versa. Delivering a so-called “pi pulse” of radiofrequency or microwave radiation transforms |^^^1^^^^^^ completely into |^^^^2^^^^^ and vice versa.

[0101] Consider the following sequence: i) light pulse resonant with |^^^1^^^^^^, ii) radiofrequency or microwave pi pulse, iii) light pulse resonant with |^^^1^^^^^^. The first light pulse is associated withan optical excitation and decay |^^^^^^^^1 ^|^^^1^^^^^^ and the nearly immediate emission of aphoton (represented as |^^^^^with “e” representing a photon emission that is relatively early in time). However, the first light pulse does not affect the |^^^^2^^^^^portion of the wavefunction. Thus,the first light pulse generates the state ^^^^|^^^1^^^^^^|^^^^^ + ^^^^|^^^^^^^^2 ^. The pi pulse transforms |^^^ ^^^^1^ ^ into|^^^^^^^^^ and vice versa, thereby generating the stateThe second light pulseonce again associated with an optical excitation and decaysince time has passed between the first pulse and the second pulse, the second light pulse is now associated with the nearly immediate emission of a photon (represented as |^^^^^with “l” representing a photon emission that is relatively late in time). Thus, the second light pulsegenerates the state

[0102] Thus, delivering pulses of light and electromagnetic or microwave radiation having the proper frequencies and sequence can be used to generate a photon whose optical state is entangled with the electronic spin state of the GST molecule. The optical state of the photon is generally a mixed state having contributions from a photon emitted early in time and a photon emitted late in time. In order to produce a photon whose polarization state is entangled with the14584.0034-00304 electronic spin state of the GST molecule, the time domain information may be converted into polarization information.

[0103] In time-domain-to-polarization entanglement, the time domain information associated with the emitted photon is simply converted to polarization information. Briefly, following the first optical pulse, the early portion of the photon can be directed to an optical switch that is configured to place photons in a first polarization state. Thus, for instance, the early portion of the photon wavefunction can be horizontally polarized (i.e., has the state |^^^^^). Following the second optical pulse, the polarization state of the optical switch can be changed to place photons in a second polarization state and the late portion of the photon can be directed to the optical switch. Thus, for instance, the late portion of the photon wavefunction can be vertically polarized (i.e., has the state |^^^^^). To account for the differences in emission times between early and late photons, an unbalanced interferometer (e.g., an unbalanced free-space interferometer or an unbalanced fiber interferometer) may be constructed to equalize optical delays between the early and late portions of the photon wavefunction, and a beamsplitter may be used to stitch together the early and late portions of the photon wavefunction. Thus, time-domain-to-polarization entanglement results in a state ^^^^|^^^^^^^^2 ^|^^^^^ + ^^^^|^^^ ^^^^1^ ^|^^^^^.

[0104] Time-domain entanglement and time-domain-to-polarization entanglement may be extended to generate streams of entangled photons by repeating the basic optical pulse- radiofrequency / microwave pi pulse-optical pulse block a plurality of times, with a radiofrequency / microwave pi / 2 pulse separating each pulse block. In some embodiments, the GST molecules described herein may be used to generate streams comprising at least about 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, or more entangled photons, at most about 100, 95, 90, 85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 9, 8, 7, 6, 5, 4, 3, or 2 entangled photons, or a number of entangled photons that is within a range defined by any two of the preceding values.14584.0034-00304

[0105] Time-domain entanglement and time-domain-to-polarization entanglement are described in R. Vasconcelos et al, “Scalable spin-photon entanglement by time-to-polarization conversion,” npj Quantum Inf 6, 9 (2020), https: / / doi.org / 10.1038 / s41534-019-0236-x, which is incorporated herein by reference in its entirety for all purposes. Rapid multi-photon time-domain entanglement and time-domain-to-polarization entanglement

[0106] One problem associated with the existing time-domain entanglement and time-domain- to-polarization entanglement methods described above are that they require the use of multiple radiofrequency or microwave pulses and / or require changing the state of the optical switch multiple times in order to generate multiple photons. For instance, the existing time-domain entanglement methods described above require 2n-1 radiofrequency or microwave pulses to generate n entangled photons (i.e., a radiofrequency / microwave pi pulse for each photon and n- 1 pi / 2 pulses between each optical pulse-radiofrequency / microwave pi pulse-optical pulse block). In addition to these 2n-1 radiofrequency or microwave pulses, the existing time-domain- to-polarization entanglement methods described above also require changing the state of the optical switch n times (i.e., once for each photon) to generate n entangled photons. In many cases, the radiofrequency or microwave pulses or changing the state of the optical switch take a substantially longer time than the time required for each optical excitation and decay process. For instance, a GST molecule might complete an optical excitation and decay process on a multi-gigahertz (GHz) timescale, while radiofrequency or microwave pulses and optical switching might be performed only on a sub-GHz timescale (e.g., 10s or 100s of MHz). Thus, the use of multiple radiofrequency or microwave pulses or multiple state changes on an optical switch may drastically limit the rate at which entangled photons are generated using the existing time-domain entanglement or time-domain-to-polarization entanglement methods described above. Since the quantum systems used to generate the photons (such as the GST molecules14584.0034-00304 described herein) maintain coherent quantum states for only limited periods of time, slow photon emissions limit the number of entangled photons that can be generated.

[0107] Thus, provided herein are methods and systems for rapid multi-photon time-domain entanglement and time-domain-to-polarization entanglement. In some embodiments, such methods and systems increase the rate of entangled photon emission (and thus the number of entangled photons that can be generated) by greatly reducing the number of radiofrequency or microwave pulses or the number of optical switch state changes required to generate the entangle photons. The description that follows uses the GST molecules described herein as an example. However, the methods and systems are generally applicable to any quantum system that is capable of emitting photons and has a controllable quantum state. Moreover, for GST molecules, the |^^^1^^^^^^ and |^^^^2^^^^^ sublevels are once again chosen to illustrate the concept.However, any two of the |^^^1^^^^^^, |^^^^2^^^^^, and |^^^^3^^^^^may be chosen based on, for instance, branchingratios associated with a particular GST molecule.

[0108] Consider the following sequence: i) n light pulses resonant with |^^^1^^^^^^, ii) radiofrequency or microwave pi pulse, iii) n light pulses resonant with |^^^1^^^^^^. Each light pulse during (i) isassociated with an optical excitation and decayand the nearly immediateemission of a photon (represented as |^^^^^). However, the light pulses during (i) do not affect the |^^^^2^^^^^portion of the wavefunction. Thus, the first set of light pulses during (i) generates the stateoptical excitation and decay |^^^^^^^^|^^^1^ ^. However, since time has passed betweenfirst set of light pulses and the second set of light pulses, each of the second set of light pulses is now associated with the nearly immediate emission of a photon represented as |^^^^^. Thus, thesecond set of light pulses generates the state14584.0034-00304

[0109] In multi-photon time-domain-to-polarization entanglement, the time domain information associated with each emitted photon is simply converted to polarization information. Briefly, following each of the first set of optical pulses, the early portion of each photon can be directed to an optical switch that is configured to place photons in a first polarization state. Thus, for instance, the early portion of each photon wavefunction can behorizontally polarized (i.e., has the state |^^^^^^^^^ for each photon i, with 1 ≤ ^^^^ ≤ ^^^^). After the firstset of optical pulses, the polarization state of the optical switch can be changed to place photons in a second polarization state and the late portion of each photon can be directed to the optical switch. Thus, for instance, the late portion of each photon wavefunction can be vertically polarized (i.e., has the state |^^^^^^^^^). To account for the differences in emission times between early and late photons, an unbalanced interferometer (e.g., an unbalanced free-space interferometer or an unbalanced fiber interferometer) may be constructed to equalize optical delays between the early and late portions of the photon wavefunction, and a beamsplitter may be used to stitch together the early and late portions of the photon wavefunction. Thus, time-domain-to-polarization entanglement results in a state

[0110] Of course, the quantum state of the GST molecule may be placed into different initial states (e.g., using radiofrequency or microwave pulses) between optical excitations in order to create different optical states for each of the n entangled photons.

[0111] FIG. 4 depicts an exemplary method 400 for rapidly generating streams of entangled photons. In some embodiments, the method 400 encompasses the rapid multi-photon time- domain entanglement or time-domain-to-polarization entanglement processes described above.

[0112] At 410, at least one quantum system is obtained. In some embodiments, the at least one quantum system comprises at least a first ground state, a second ground state, and a first excited state. In some embodiments, the at least one quantum system comprises at least one micro- cavity supporting at least one host material therein. In some embodiments, the at least one micro-cavity comprises any micro-cavity 130 described herein with respect to FIG.1A. In some14584.0034-00304 embodiments, the at least one host material comprises any host material 110 described herein with respect to FIG.1A. In some embodiments, the at least one host material contains at least one dopant molecule therein. In some embodiments, the at least one dopant molecule comprises any dopant molecule 120 described herein with respect to FIG.1A. In some embodiments, the at least one dopant molecule is associated with a GST electronic manifold and at least one EST electronic manifold, as described herein with respect to FIG. 1A or 2. In some embodiments, the GST electronic manifold comprises the first ground state and the second ground state. In some embodiments, the EST electronic manifold comprises the first excited state. That is in some, embodiments, the first and second ground states comprise any two of the |^^^1^^^^^^, |^^^^2^^^^^, and |^^^^3^^^^^electronic spin state sublevels of the GST molecules described herein with respect to FIG. 2 and the first excited state comprises any of the |^^^1^^^^^^, |^^^^2^^^^^, and |^^^^3^^^^^ electronic spin state sublevels of the GST molecules described herein with respect to FIG.2.

[0113] At 420, first electromagnetic energy is directed to the at least one quantum system. In some embodiments, the first electromagnetic energy induces a first quantum transition between the first ground state and the first excited state. In some embodiments, the first electromagnetic energy comprises optical energy. In some embodiments, the first electromagnetic energy is substantially resonant with the first quantum transition. For instance, in the example describedabove, the first electromagnetic energy comprises an optical pulse resonant with aexcitation and the first quantum transition comprises aexcitation anddecay cycle between the |^^^1^^^^^^ and |^^^1^^^^^^ sublevels of a GST molecule.

[0114] At 430, step 420 is repeated for n iterations, as described herein. In some embodiments, n is an integer equal to or greater than about 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, or more, an integer equal to or lesser than about 100, 95, 90, 85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 9, 8, 7, 6, 5, 4, 3, or 2, or an integer that is within a range defined by any two of the preceding values. In some embodiments, step 430 generates an entangled quantum state associated with the early emission of n photons.14584.0034-00304 For instance, in the example described above, step 430 generates the state

[0115] At 440, second electromagnetic energy is directed to the at least one quantum system. In some embodiments, the second electromagnetic energy induces a second quantum transition between the first ground state and the second ground state. In some embodiments, the second electromagnetic energy converts the first ground state into the second ground state and vice versa. In some embodiments, the second electromagnetic energy comprises radiofrequency or microwave energy. In some embodiments, the second electromagnetic energy comprises a radiofrequency or microwave pi pulse. For instance, in the example described above, the secondelectromagnetic energy generates the state

[0116] At 450, the first electromagnetic energy is again directed to the at least one quantum system. In some embodiments, the first electromagnetic energy again induces the first quantum transition between the first ground state and the first excited state. For instance, in the example described above, the first electromagnetic energy comprises an optical pulse resonant with aexcitation and the first quantum transition comprises a |^^^^^^^^1 ^ →excitation and decay cycle between the |^^^1^^^^^^ and |^^^1^^^^^^ sublevels of a GST molecule.

[0117] At 460, step 450 is repeated for n iterations, as described herein. In some embodiments, step 460 generates an entangled quantum state associated with the late emission of n photons. For instance, in the example described above, step 460 generates the stateIn some embodiments, n entangled photonsgenerating subsequent to step 460.

[0118] The bare combination of steps 410, 420, 430, 440, 450, and 460 imparts the rapid multi- photon time-domain entanglement scheme described above. In order to impart the rapid multi- photon time-domain-to-polarization entanglement scheme, at least one optical switch may be maintained in a first configuration associated with a first polarization state during at least steps 420 and 430. For instance, in the example described above, the first configuration may be14584.0034-00304 chosen such that the early portion of each photon wavefunction is horizontally polarized during steps 420 and 430, as described above. During at least steps 450 and 460, the at least one optical switch may be maintained in a second configuration associated with a second polarization state. In some embodiments, the second polarization state is substantially orthogonal to the first polarization state. For instance, in the example described above, the second configuration may be chosen such that the late portion of each photon wavefunction is vertically polarized during steps 450 and 460, as described above. Thus, in some embodiments, the at least one optical switch is configured to convert time domain information associated with the n entangled photons to polarization information associated with the n entangled photons. In some embodiments, the n entangled photons are directed to a polarizing beamsplitter to thereby generate n entangled photons each having a mixed polarization state.

[0119] Although the description of rapid multi-photon time-domain entanglement and rapid multi-photon time-domain-to-polarization entanglement is described herein with respect to GST molecules, the disclosure is not intended to be so limiting. For instance, the rapid multi- photon time-domain entanglement and rapid multi-photon time-domain-to-polarization entanglement methods described herein may be applied to other molecular systems, such as spin-1 / 2 or spin-1 molecular systems, or other molecular systems with higher spin multiplicities. As an example, a spin-1 / 2 system may have ground state sublevels having spinquantum numbers ^^^^^^^^ = −1 / 2 (denoted herein as | − 1 / 2^^^^^) and ^^^^^^^^ = +1 / 2 (denoted hereinas | + 1 / 2^^^^^) and at least one excited state sublevel (e.g., | − 1 / 2^^^^^). In general, the electronicstate of such a system may be placed in a superposition ^^^^| − 1 / 2^^^^^ + ^^^^| + 1 / 2^^^^^. Applying aseries of n optical pulses that are substantially resonant with a | − 1 / 2^^^^^ → | − 1 / 2^^^^^ → | −1 / 2^^^^^ transition generates the state ^^^^| − 1 / 2^^^^^|^^^^1^|^^^^2^… |^^^^^^^^^ + ^^^^+ 1 / 2 ^. Applying aradiofrequency or microwave pi pulse to induce a transition between the | − 1 / 2^^^^^ and | +1 / 2^^^^^ sublevels generates the state ^^^^| + 1 / 2^^^^^|^^^^1^|^^^^2^… |^^^^^^^^^ + ^^^^| − 1 / 2^^^^^. Applying a seriesof n optical pulses that are substantially resonant with the | − 1 / 2^^^^^ → | − 1 / 2^^^^^ → | − 1 / 2^^^^^14584.0034-00304transition generates the state ^^^^| + 1 / 2^^^^^|^^^^1^|^^^^2^… |^^^^^^^^^ + ^^^^| − 1 / 2^^^^^|^^^^1^|^^^^2^… |^^^^^^^^^,completing the rapid multi-photon time-domain entanglement method for a spin-1 / 2 molecular system. The optical switch procedures described herein may be utilized to complete the rapid multi-photon time-domain-to-polarization entanglement method for a spin-1 / 2 molecularsystem, generating, for instance, the state ^^^^| + 1 / 2^^^^^|^^^^1^|^^^^2^… |^^^^^^^^^ + ^^^^| − 1 / 2^^^^^|^^^1^ ^|^^^^2^… |^^^^^^^^^. Similar procedures may be implemented with any two of the ^^^^^^^^ = −1,^^^^^^^^ = 0, and ^^^^^^^^ = +1 ground state sublevels of a spin-1 molecular system. Examples of spin-1 / 2 molecular systems suitable for the rapid multi-photon time-domain entanglement and rapid multi-photon time-domain-to-polarization entanglement schemes described herein include fluorescent radical, biradical, or diradical molecules. Examples of spin-1 molecular systems suitable for the rapid multi-photon time-domain entanglement and rapid multi-photon time- domain-to-polarization entanglement schemes described herein include fluorescent biradical molecules.

[0120] Regardless of which entanglement scheme is employed (e.g., time-domain entanglement, time-domain-to-polarization entanglement, rapid multi-photon time-domain entanglement, or rapid multi-photon time-domain-to-polarization entanglement), the quantum system may be initialized into a defined quantum state before a string of entangled photons can be generated. Thus, the entanglement schemes described herein can be combined with any of a variety of initialization schemes. For instance, any of the three following initialization schemes can be applied: 1) Following reports of e.g. Qiu et al. (Y. Qiu et al, Angew. Chem. Int. Ed.2022, e202214668 https: / / onlinelibrary.wiley.com / doi / full / 10.1002 / anie.202214668, which is incorporated herein by reference it its entirety for all purposes), an optical pumping scheme can be realized by covalently attaching a suitable chromophore to a spin-1 / 2 system (e.g., a perylene-3,4:9,10-bis(dicarboximide)). Other functional groups that may be used in this context are acenes, rylenes, or any polycyclic aromatic hydrocarbon that is able to undergo intersystem crossing to a high multiplicity excited state. Within this scheme, a photoexcitation of the14584.0034-00304 chromophore-radical dyad results in radical-enhanced intersystem crossing to produce a high multiplicity state followed by formation of a spin polarized doublet ground state via spin selective relaxation pathways.2) The quantum state can be initialized by direct read out. That is, repeated resonant excitation of a specific transition and subsequent nearly immediate verticalemission of a photon (e.g., | − 1 / 2^^^^^ → | − 1 / 2^^^^^ → | − 1 / 2^^^^^_ can be used to collapse thesuperposition of the ms= -1 / 2 and +1 / 2 sublevels into a specific quantum state. In such a scheme, photon losses due to sub-unity extraction efficiencies and other non-idealities may be taken into account by performing repeated measurements.3) In case the emission is not vertical(e.g., has a certain chance to cross to ms = -1 / 2 (i.e., | − 1 / 2^^^^^ → | + 1 / 2^^^^^)), resonant opticalpumping can be used to initialize the quantum system into the | + 1 / 2^^^^^ state.

[0121] Regardless of whether the dopant molecule comprises a GST molecule, spin-1 / 2 molecule, or possess some other ground state electron spin characteristics, the dopant molecule may generally possess the following features: (1) a high brightness (e.g., quantum yield >80% and extinction coefficient > 5000 M-1cm-1), (2) a high photostability (e.g., at least 1 hour under resonant excitation of the ZPL), (3) negligible spectral diffusion (e.g., no dark states), long coherence times (e.g., T2 > 10 µs), (4) high emission rates into the ZPL (e.g., > 100 MHz), (5) two ZPL spin selective transitions that are separated by, e.g., > 1 GHz, (6) high branching ratio between the ZPL and the phonon side bands (i.e., strong transition probability into the ZPL and small Stokes shift), (7) emission of polarized photons, and (8) Fourier transform limited linewidth of ZPL of, e.g., < 200 MHz.

[0122] FIG. 5 depicts an exemplary system 500 for rapidly generating streams of entangled photons. In some embodiments, the system 500 implements the rapid multi-photon time- domain entanglement or time-domain-to-polarization entanglement processes described above. In some embodiments, the system 500 implements the method 400 described herein with respect to FIG.4.14584.0034-00304

[0123] In the example shown, the system 500 comprises at least one quantum system 510. In some embodiments, the at least one quantum system 510 comprises any quantum system described herein with respect to method 400 of FIG.4. In some embodiments, the at least one quantum system 510 comprises at least a first ground state, a second ground state, and a first excited state. In some embodiments, the In some embodiments, the at least one quantum system 510 comprises at least one micro-cavity supporting at least one host material therein. In some embodiments, the at least one micro-cavity comprises any micro-cavity 130 described herein with respect to FIG. 1A. In some embodiments, the at least one host material comprises any host material 110 described herein with respect to FIG.1A. In some embodiments, the at least one host material contains at least one dopant molecule therein. In some embodiments, the at least one dopant molecule comprises any dopant molecule 120 described herein with respect to FIG. 1A. In some embodiments, the at least one dopant molecule is associated with a GST electronic manifold and at least one EST electronic manifold, as described herein with respect to FIG.1A or 2. In some embodiments, the GST electronic manifold comprises the first ground state and the second ground state. In some embodiments, the EST electronic manifold comprises the first excited state.

[0124] In the example shown, the system 500 comprises an electromagnetic energy module 520. In some embodiments, the electromagnetic energy module is configured to: (a) direct first electromagnetic energy to the at least one quantum system 510, wherein the first electromagnetic energy induces a first quantum transition between the first ground state and the first excited state; (b) repeat (a) for n iterations; (c) direct second electromagnetic energy to the at least one quantum system, wherein the second electromagnetic energy induces a second quantum transition between the first ground state and the second ground state to thereby convert the first ground state into the second ground state and vice versa; (d) direct the first electromagnetic energy to the at least one quantum system; and (e) repeat (d) for n iterations, thereby generating n entangled photons. That is, in some embodiments, the electromagnetic14584.0034-00304 energy module 520 is configured to implement steps 420, 430, 440, 450, and 460 of method 400 described herein with respect to FIG.4. In some embodiments, the electromagnetic energy module 520 comprises one or more optical sources, laser sources, confocal light sources, radio- frequency (RF) sources, or microwave (MW) sources. In some embodiments, the first electromagnetic energy comprises optical energy. In some embodiments, the first electromagnetic energy is substantially resonant with the first quantum transition. In some embodiments, the second electromagnetic energy comprises RF or MW energy. In some embodiments, wherein the second electromagnetic energy comprises an RF or MW pi pulse. In some embodiments, n is an integer equal to or greater than about 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, or more, an integer equal to or lesser than about 100, 95, 90, 85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 9, 8, 7, 6, 5, 4, 3, or 2, or an integer that is within a range defined by any two of the preceding values

[0125] In the example shown, the system 500 comprises at least one optical switch 530. In some embodiments, the at least one optical switch 530 permits implementation of the rapid multi- photon time-domain-to-polarization entanglement scheme described herein. In some embodiments, the at least one optical switch is configured to: for (a) and (b), remain in a first configuration associated with a first polarization state. For instance, in the example described above, the first configuration may be chosen such that the early portion of each photon wavefunction is horizontally polarized, as described above. In some embodiments, the at least one optical switch is configured to: for (d) and (e), remain in a second configuration associated with a second polarization state. In some embodiments, the second polarization state is substantially orthogonal to the first polarization state. For instance, in the example described above, the second configuration may be chosen such that the late portion of each photon wavefunction is vertically polarized, as described above. Thus, in some embodiments, the at least one optical switch 530 is configured to convert time domain information associated with the n entangled photons to polarization information associated with the n entangled photons.14584.0034-00304

[0126] In the example shown, the system 500 comprises a polarizing beamsplitter 540. In some embodiments, the polarizing beamsplitter 540 is configured to receive the n entangled photons and to generate n entangled photons each having a mixed polarization state therefrom. RECITATION OF EMBODIMENTS

[0127] Embodiment 1. A system for generating entangled photons, the system comprising: at least one micro-cavity configured to support a material therein; at least one host material supported within the at least one micro-cavity, the host material comprising at least one organic molecule; and at least one dopant molecule contained in the host material, wherein: the at least one dopant molecule is associated with an electronic energy level structure that includes a ground state triplet (GST) electronic manifold and at least one excited state triplet (EST) electronic manifold.

[0128] Embodiment 2. The system of Embodiment 1, wherein the at least one micro-cavity comprises a mode volume of at least 0.1 cubic micrometers (µm3).

[0129] Embodiment 3. The system of Embodiment 1 or 2, wherein the at least one micro-cavity comprises a mode volume of at most 10 µm3.

[0130] Embodiment 4. The system of any one of Embodiments 1-3, wherein the at least one micro-cavity is characterized by a quality (Q) factor of at least 100,000.

[0131] Embodiment 5. The system of any one of Embodiments 1-4, wherein the at least one micro-cavity is characterized by a Q factor of at most 10,000,000.

[0132] Embodiment 6. The system of any one of Embodiments 1-5, wherein the at least one micro-cavity is characterized by a finesse of at least 10,000.

[0133] Embodiment 7. The system of any one of Embodiments 1-6, wherein the at least one micro-cavity is characterized by a finesse of at most 100,000.14584.0034-00304

[0134] Embodiment 8. The system of any one of Embodiments 1-7, wherein the at least one micro-cavity is configured to enhance radiative decay via a zero-phonon line (ZPL) electronic transition following excitation of an electronic state of the at least one dopant molecule from the GST electronic manifold to the at least one EST electronic manifold.

[0135] Embodiment 9. The system of Embodiment 8, wherein the enhanced radiative decay via the ZPL electronic transition is increased by a Purcell factor of at least 100 in comparison to a radiative decay via the ZPL electronic transition in the absence of the at least one micro-cavity.

[0136] Embodiment 10. The system of Embodiment 8 or 9, wherein the enhanced radiative decay via the ZPL electronic transition is increased by a Purcell factor of at most 10,000 in comparison to a radiative decay via the ZPL electronic transition in the absence of the at least one micro-cavity.

[0137] Embodiment 11. The system of any one of Embodiments 8-10, wherein the at least one dopant molecule is configured to emit at least one photon following the enhanced radioactive decay via the ZPL electronic transition.

[0138] Embodiment 12. The system of Embodiment 11, wherein an optical state of the at least one photon is entangled with an electronic spin state of the at least one dopant molecule.

[0139] Embodiment 13. The system of Embodiment 12, wherein the optical state comprises a polarization state of the at least one photon.

[0140] Embodiment 14. The system of Embodiment 12 or 13, wherein the optical state is entangled with the electronic state by time-domain entanglement, time-domain-to-polarization entanglement, multi-photon time-domain entanglement, or multi-photon time-domain-to- polarization entanglement.

[0141] Embodiment 15. The system of any one of Embodiments 1-14, wherein the host material comprises a crystalline host material, a single crystalline host material, a polycrystalline host material, a liquid crystalline host material, a powder host material, an amorphous host material, or a frozen solution host material.14584.0034-00304

[0142] Embodiment 16. The system of any one of Embodiments 1-15, wherein the host material comprises a C4-C20 linear or branched alkane; an aromatic hydrocarbon; a polyaromatic hydrocarbon optionally substituted with a methylene, nitrile, carbonyl, carboxylate, alkyl, deuterated alkyl, aryl, deuterated aryl, heteroaryl, deuterated heteroaryl, borane, imine, amine, nitro, phosphine, thioether, ether, fluoro, chloro, bromo, iodo, or thiocarbonyl group; a diarylketone; naphthalene; anthracene; benzoic acid; fluorene; biphenyl; benzene; biphenylene; ortho-terphenyl; meta-terphenyl; para-terphenyl; di(phenyl)methanone; phenanthrene; di(naphthalen-2-yl)methanone; or any partially or fully isotopically labeled derivative thereof.

[0143] Embodiment 17. The system of any one of Embodiments 1-16, wherein the host material and the at least one dopant molecule comprise a thin film having a thickness of at most 100 nanometers (nm).

[0144] Embodiment 18. The system of any one of Embodiments 1-17, wherein the host material and the at least one dopant molecule are deposited on the at least one micro-cavity using spin coating or chemical vapor deposition.

[0145] Embodiment 19. The system of any one of Embodiments 1-18, wherein the at least one micro-cavity is formed from a substrate selected from the group consisting of silicon, mono- crystalline silicon, polysilicon, silicon on insulator, silicon carbide, and silicon nitride.

[0146] Embodiment 20. The system of any one of Embodiments 1-19, wherein the at least one dopant molecule comprises an organic molecule.

[0147] Embodiment 21. The system of any one of Embodiments 1-20, wherein the at least one dopant molecule comprises a carbene molecule; a nitrene molecule; a radical molecule; a biradical molecule; a diradical molecule; a diaryl diazomethane molecule; a di(napthalen-2- yl)carbene molecule; a di(phenyl)carbene molecule; or any partially or fully isotopically labeled derivative thereof.14584.0034-00304

[0148] Embodiment 22. The system of any one of Embodiments 1-21, wherein the at least one dopant molecule is contained in the at least one host material at a concentration of at most 106dopant molecules per cubic micrometer (µm3).

[0149] Embodiment 23. The system of any one of Embodiments 1-22, further comprising at least one optical unit configured to direct light to the at least one dopant molecule to thereby excite an electronic state of the at least one dopant molecule from the GST electronic manifold to the at least one EST electronic manifold.

[0150] Embodiment 24. The system of Embodiment 23, wherein the light comprises laser light.

[0151] Embodiment 25. The system of Embodiment 24, wherein the laser light comprises a central wavelength of at least 500 nm.

[0152] Embodiment 26. The system of Embodiment 24 or 25, wherein the laser light comprises a central wavelength of at most 2,000 nm.

[0153] Embodiment 27. The system of any one of Embodiments 1-26, further comprising at least one electromagnetic (EM) unit configured to direct EM radiation to the at least one dopant molecule to thereby alter an electronic spin state of the at least one dopant molecule.

[0154] Embodiment 28. The system of Embodiment 27, wherein the EM radiation comprises microwave (MW) radiation or radio-frequency (RF) radiation.

[0155] Embodiment 29. A system for generating entangled photons, the system comprising: at least one optical unit configured to direct light to at least one dopant molecule; and at least one EM unit configured to direct EM radiation to the at least one dopant molecule, wherein: the at least one dopant molecule is contained within at least one host material comprising at least one organic molecule; the at least one host material is supported within at least one micro-cavity; and14584.0034-00304 the at least one dopant molecule is associated with an electronic energy level structure that includes a ground state triplet (GST) electronic manifold and at least one excited state triplet (EST) electronic manifold.

[0156] Embodiment 30. The system of Embodiment 29, further comprising the at least one dopant molecule, the at least one host material, and the at least one micro-cavity.

[0157] Embodiment 31. The system of Embodiment 29 or 30, wherein the at least one micro- cavity comprises a mode volume of at least 0.1 cubic micrometers (µm3).

[0158] Embodiment 32. The system of any one of Embodiments 29-31, wherein the at least one micro-cavity comprises a mode volume of at most 10 µm3.

[0159] Embodiment 33. The system of any one of Embodiments 29-32, wherein the at least one micro-cavity is characterized by a quality (Q) factor of at least 100,000.

[0160] Embodiment 34. The system of any one of Embodiments 29-33, wherein the at least one micro-cavity is characterized by a Q factor of at most 10,000,000.

[0161] Embodiment 35. The system of any one of Embodiments 29-34, wherein the at least one micro-cavity is characterized by a finesse of at least 10,000.

[0162] Embodiment 36. The system of any one of Embodiments 29-35, wherein the at least one micro-cavity is characterized by a finesse of at most 100,000.

[0163] Embodiment 37. The system of any one of Embodiments 29-36, wherein the at least one micro-cavity is configured to enhance radiative decay via a zero-phonon line (ZPL) electronic transition following excitation of an electronic state of the at least one dopant molecule from the GST electronic manifold to the at least one EST electronic manifold.

[0164] Embodiment 38. The system of Embodiment 37, wherein the enhanced radiative decay via the ZPL electronic transition is increased by a Purcell factor of at least 100 in comparison to a radiative decay via the ZPL electronic transition in the absence of the at least one micro- cavity.14584.0034-00304

[0165] Embodiment 39. The system of Embodiment 37 or 38, wherein the enhanced radiative decay via the ZPL electronic transition is increased by a Purcell factor of at most 10,000 in comparison to a radiative decay via the ZPL electronic transition in the absence of the at least one micro-cavity.

[0166] Embodiment 40. The system of any one of Embodiments 37-39, wherein the at least one dopant molecule is configured to emit at least one photon following the enhanced radioactive decay via the ZPL electronic transition.

[0167] Embodiment 41. The system of Embodiment 40, wherein an optical state of the at least one photon is entangled with an electronic spin state of the at least one dopant molecule.

[0168] Embodiment 42. The system of Embodiment 41, wherein the optical state comprises a polarization state of the at least one photon.

[0169] Embodiment 43. The system of Embodiment 41 or 42, wherein the optical state is entangled with the electronic state by time-domain entanglement, time-domain-to-polarization entanglement, multi-photon time-domain entanglement, or multi-photon time-domain-to- polarization entanglement.

[0170] Embodiment 44. The system of any one of Embodiments 29-43, wherein the host material comprises a crystalline host material, a single crystalline host material, a polycrystalline host material, a liquid crystalline host material, a powder host material, an amorphous host material, or a frozen solution host material.

[0171] Embodiment 45. The system of any one of Embodiments 29-44, wherein the host material comprises a C4-C20 linear or branched alkane; an aromatic hydrocarbon; a polyaromatic hydrocarbon optionally substituted with a methylene, nitrile, carbonyl, carboxylate, alkyl, deuterated alkyl, aryl, deuterated aryl, heteroaryl, deuterated heteroaryl, borane, imine, amine, nitro, phosphine, thioether, ether, fluoro, chloro, bromo, iodo, or thiocarbonyl group; a diarylketone; naphthalene; anthracene; benzoic acid; fluorene; biphenyl; benzene; biphenylene; ortho-terphenyl; meta-terphenyl; para-terphenyl; di(phenyl)methanone;14584.0034-00304 phenanthrene; di(naphthalen-2-yl)methanone; or any partially or fully isotopically labeled derivative thereof.

[0172] Embodiment 46. The system of any one of Embodiments 29-45, wherein the host material and the at least one dopant molecule comprise a thin film having a thickness of at most 100 nanometers (nm).

[0173] Embodiment 47. The system of any one of Embodiments 29-46, wherein the host material and the at least one dopant molecule are deposited on the at least one micro-cavity using spin coating or chemical vapor deposition.

[0174] Embodiment 48. The system of any one of Embodiments 29-47, wherein the at least one micro-cavity is formed from a substrate selected from the group consisting of silicon, mono- crystalline silicon, polysilicon, silicon on insulator, silicon carbide, and silicon nitride.

[0175] Embodiment 49. The system of any one of Embodiments 29-48, wherein the at least one dopant molecule comprises an organic molecule.

[0176] Embodiment 50. The system of any one of Embodiments 29-49, wherein the at least one dopant molecule comprises a carbene molecule; a nitrene molecule; a radical molecule; a biradical molecule; a diradical molecule; a diaryl diazomethane molecule; a di(napthalen-2- yl)carbene molecule; a di(phenyl)carbene molecule; or any partially or fully isotopically labeled derivative thereof.

[0177] Embodiment 51. The system of any one of Embodiments 29-50, wherein the at least one dopant molecule is contained in the at least one host material at a concentration of at most 106dopant molecules per cubic micrometer (µm3).

[0178] Embodiment 52. The system of any one of Embodiments 29-51, wherein the light comprises laser light.

[0179] Embodiment 53. The system of Embodiment 52, wherein the laser light comprises a central wavelength of at least 500 nm.14584.0034-00304

[0180] Embodiment 54. The system of Embodiment 52 or 53, wherein the laser light comprises a central wavelength of at most 2,000 nm.

[0181] Embodiment 55. The system of any one of Embodiments 29-54, wherein the EM radiation comprises microwave (MW) radiation or radio-frequency (RF) radiation.

[0182] Embodiment 56. A method for generating entangled photons, the method comprising: (a) obtaining at least one micro-cavity supporting at least one host material therein; wherein: the at least one host material comprises at least one organic molecule; at least one dopant molecule is contained in the host material; and the at least one dopant molecule is associated with an electronic energy level structure that includes a ground state triplet (GST) electronic manifold and at least one excited state triplet (EST) electronic manifold; (b) directing electromagnetic (EM) radiation to the at least one dopant molecule to thereby alter an electronic spin state of the at least one dopant molecule; (c) directing light to the at least one dopant molecule to thereby excite an electronic state of the at least one dopant molecule from the GST electronic manifold to the at least one EST electronic manifold; and (d) permitting the at least one dopant molecule to emit at least one photon via enhanced radiative decay via a zero-phonon line (ZPL) electronic transition.

[0183] Embodiment 57. The method of Embodiment 56, wherein the at least one micro-cavity comprises a mode volume of at least 0.1 cubic micrometers (µm3).

[0184] Embodiment 58. The method of Embodiment 56 or 57, wherein the at least one micro- cavity comprises a mode volume of at most 10 µm3.

[0185] Embodiment 59. The method of any one of Embodiments 56-58, wherein the at least one micro-cavity is characterized by a quality (Q) factor of at least 100,000.14584.0034-00304

[0186] Embodiment 60. The method of any one of Embodiments 56-59, wherein the at least one micro-cavity is characterized by a Q factor of at most 10,000,000.

[0187] Embodiment 61. The method of any one of Embodiments 56-60, wherein the at least one micro-cavity is characterized by a finesse of at least 10,000.

[0188] Embodiment 62. The method of any one of Embodiments 56-61, wherein the at least one micro-cavity is characterized by a finesse of at most 100,000.

[0189] Embodiment 63. The method of any one of Embodiments 56-62, wherein the at least one micro-cavity is configured to enhance radiative decay via a zero-phonon line (ZPL) electronic transition following excitation of an electronic state of the at least one dopant molecule from the GST electronic manifold to the at least one EST electronic manifold.

[0190] Embodiment 64. The method of Embodiment 63, wherein the enhanced radiative decay via the ZPL electronic transition is increased by a Purcell factor of at least 100 in comparison to a radiative decay via the ZPL electronic transition in the absence of the at least one micro- cavity.

[0191] Embodiment 65. The method of Embodiment 63 or 64, wherein the enhanced radiative decay via the ZPL electronic transition is increased by a Purcell factor of at most 10,000 in comparison to a radiative decay via the ZPL electronic transition in the absence of the at least one micro-cavity.

[0192] Embodiment 66. The method of any one of Embodiments 56-65, wherein the at least one dopant molecule is configured to emit at least one photon following the enhanced radioactive decay via the ZPL electronic transition.

[0193] Embodiment 67. The method of Embodiment 66, wherein an optical state of the at least one photon is entangled with an electronic spin state of the at least one dopant molecule.

[0194] Embodiment 68. The method of Embodiment 67, wherein the optical state comprises a polarization state of the at least one photon.14584.0034-00304

[0195] Embodiment 69. The method of Embodiment 67 or 68, wherein the optical state is entangled with the electronic state by time-domain entanglement, time-domain-to-polarization entanglement, multi-photon time-domain entanglement, or multi-photon time-domain-to- polarization entanglement.

[0196] Embodiment 70. The method of any one of Embodiments 56-69, wherein the host material comprises a crystalline host material, a single crystalline host material, a polycrystalline host material, a liquid crystalline host material, a powder host material, an amorphous host material, or a frozen solution host material.

[0197] Embodiment 71. The method of any one of Embodiments 56-70, wherein the host material comprises a C4-C20 linear or branched alkane; an aromatic hydrocarbon; a polyaromatic hydrocarbon optionally substituted with a methylene, nitrile, carbonyl, carboxylate, alkyl, deuterated alkyl, aryl, deuterated aryl, heteroaryl, deuterated heteroaryl, borane, imine, amine, nitro, phosphine, thioether, ether, fluoro, chloro, bromo, iodo, or thiocarbonyl group; a diarylketone; naphthalene; anthracene; benzoic acid; fluorene; biphenyl; benzene; biphenylene; ortho-terphenyl; meta-terphenyl; para-terphenyl; di(phenyl)methanone; phenanthrene; di(naphthalen-2-yl)methanone; or any partially or fully isotopically labeled derivative thereof.

[0198] Embodiment 72. The method of any one of Embodiments 56-71, wherein the host material and the at least one dopant comprise a thin film having a thickness of at most 100 nanometers (nm).

[0199] Embodiment 73. The method of any one of Embodiments 56-72, wherein the host material and the at least one dopant molecule are deposited on the at least one micro-cavity using spin coating or chemical vapor deposition.

[0200] Embodiment 74. The method of any one of Embodiments 56-73, wherein the at least one micro-cavity is formed from a substrate selected from the group consisting of silicon, mono-crystalline silicon, polysilicon, silicon on insulator, silicon carbide, and silicon nitride.14584.0034-00304

[0201] Embodiment 75. The method of any one of Embodiments 56-74, wherein the at least one dopant molecule comprises an organic molecule.

[0202] Embodiment 76. The method of any one of Embodiments 56-75, wherein the at least one dopant molecule comprises a carbene molecule; a nitrene molecule; a radical molecule; a biradical molecule; a diradical molecule; a diaryl diazomethane molecule; a di(napthalen-2- yl)carbene molecule; a di(phenyl)carbene molecule; or any partially or fully isotopically labeled derivative thereof.

[0203] Embodiment 77. The method of any one of Embodiments 56-76, wherein the at least one dopant molecule is contained in the at least one host material at a concentration of at most 106dopant molecules per cubic micrometer (µm3).

[0204] Embodiment 78. The method of any one of Embodiments 56-77, wherein the light comprises laser light.

[0205] Embodiment 79. The method of Embodiment 78, wherein the laser light comprises a central wavelength of at least 500 nm.

[0206] Embodiment 80. The method of Embodiment 78 or 79, wherein the laser light comprises a central wavelength of at most 2,000 nm.

[0207] Embodiment 81. The method of any one of Embodiments 56-80, wherein the EM radiation comprises microwave (MW) radiation or radio-frequency (RF) radiation.

[0208] Embodiment 82. A method for generating a plurality of entangled photons, the method comprising: (a) obtaining at least one quantum system comprising at least a first ground state, a second ground state, and a first excited state; (b) directing first electromagnetic energy to the at least one quantum system, wherein the first electromagnetic energy induces a first quantum transition between the first ground state and the first excited state; (c) repeating (b) for n iterations, wherein n is an integer equal to or greater than 2;14584.0034-00304 (d) directing second electromagnetic energy to the at least one quantum system, wherein the second electromagnetic energy induces a second quantum transition between the first ground state and the second ground state to thereby convert the first ground state into the second ground state and vice versa; (e) directing the first electromagnetic energy to the at least one quantum system; and (f) repeating (e) for n iterations, thereby generating n entangled photons.

[0209] Embodiment 83. The method of Embodiment 82, wherein the at least one quantum system comprises: at least one micro-cavity configured to support a material therein; at least one host material supported within the at least one micro-cavity, the host material comprising at least one organic molecule; and at least one dopant molecule contained in the host material, wherein: the at least one dopant molecule is associated with an electronic energy level structure that includes a ground state triplet (GST) electronic manifold and at least one excited state triplet (EST) electronic manifold.

[0210] Embodiment 84. The method of Embodiment 83, wherein the GST electronic manifold comprises the first ground state and the second ground state.

[0211] Embodiment 85. The method of Embodiment 83 or 84, wherein the EST electronic manifold comprises the first excited state.

[0212] Embodiment 86. The method of any one of Embodiments 82-85, wherein the first electromagnetic energy comprises optical energy.

[0213] Embodiment 87. The method of any one of Embodiments 82-86, wherein the first electromagnetic energy is substantially resonant with the first quantum transition.

[0214] Embodiment 88. The method of any one of Embodiments 82-87, wherein the second electromagnetic energy comprises radiofrequency or microwave energy.14584.0034-00304

[0215] Embodiment 89. The method of Embodiment 88, wherein the second electromagnetic energy comprises a radiofrequency or microwave pi pulse.

[0216] Embodiment 90. The method of any one of Embodiments 82-89, wherein the method further comprises: for (b) and (c), maintaining at least one optical switch in a first configuration associated with a first polarization state and, for (e) and (f), maintaining the optical switch in a second configuration associated with a second polarization state that is substantially orthogonal to the first polarization state.

[0217] Embodiment 91. The method of Embodiment 90, wherein the at least one optical switch is configured to convert time domain information associated with the n entangled photons to polarization information associated with the n entangled photons.

[0218] Embodiment 92. The method of Embodiment 90 or 91, further comprising directing the n entangled photons to a polarizing beamsplitter to thereby generate n entangled photons each having a mixed polarization state.

[0219] Embodiment 93. The method of any one of Embodiments 82-92, wherein n is at least 4.

[0220] Embodiment 94. A system for generating a plurality of entangled photons, the system comprising: at least one quantum system comprising at least a first ground state, a second ground state, and a first excited state; and electromagnetic energy module configured to: (a) direct first electromagnetic energy to the at least one quantum system, wherein the first electromagnetic energy induces a first quantum transition between the first ground state and the first excited state; (b) repeat (a) for n iterations, wherein n is an integer equal to or greater than 2; (c) direct second electromagnetic energy to the at least one quantum system, wherein the second electromagnetic energy induces a second quantum transition between the first ground state and the second ground state to14584.0034-00304 thereby convert the first ground state into the second ground state and vice versa; (d) direct the first electromagnetic energy to the at least one quantum system; and (e) repeat (d) for n iterations, thereby generating n entangled photons.

[0221] Embodiment 95. The system of Embodiment 94, wherein the at least one quantum system comprises: at least one micro-cavity configured to support a material therein; at least one host material supported within the at least one micro-cavity, the host material comprising at least one organic molecule; and at least one dopant molecule contained in the host material, wherein: the at least one dopant molecule is associated with an electronic energy level structure that includes a ground state triplet (GST) electronic manifold and at least one excited state triplet (EST) electronic manifold.

[0222] Embodiment 96. The system of Embodiment 95, wherein the GST electronic manifold comprises the first ground state and the second ground state.

[0223] Embodiment 97. The system of Embodiment 95 or 96, wherein the EST electronic manifold comprises the first excited state.

[0224] Embodiment 98. The system of any one of Embodiments 94-97, wherein the first electromagnetic energy comprises optical energy.

[0225] Embodiment 99. The system of any one of Embodiments 94-98, wherein the first electromagnetic energy is substantially resonant with the first quantum transition.

[0226] Embodiment 100. The system of any one of Embodiments 94-99, wherein the second electromagnetic energy comprises radiofrequency or microwave energy.

[0227] Embodiment 101. The system of Embodiment 100, wherein the second electromagnetic energy comprises a radiofrequency or microwave pi pulse.14584.0034-00304

[0228] Embodiment 102. The system of any one of Embodiments 94-101, further comprising at least one optical switch configured to: for (a) and (b), remain in a first configuration associated with a first polarization state and, for (d) and (e), remain in a second configuration associated with a second polarization state that is substantially orthogonal to the first polarization state.

[0229] Embodiment 103. The system of Embodiment 102, wherein the at least one optical switch is configured to convert time domain information associated with the n entangled photons to polarization information associated with the n entangled photons.

[0230] Embodiment 104. The system of Embodiment 102 or 103, further comprising a polarizing beamsplitter configured to receive the n entangled photons and to generate n entangled photons each having a mixed polarization state therefrom.

[0231] Embodiment 105. The system of any one of Embodiments 94-104, wherein n is at least 4. EXAMPLES Example 1: General synthesis and characterization procedures

[0232] Unless otherwise noted, commercially available materials were used without purification. Moisture- and oxygen-sensitive reactions were carried out in flame-dried glassware and under an inert atmosphere of purified argon using a syringe / septa technique. Thin-layer chromatography (TLC) was performed on aluminium plates coated with 0.20 mm thickness of Silica Gel 60 F254. Developing plates were visualized using ultraviolet (UV) light at wavelength of 254 and 365 nm. NMR spectra were recorded on a Bruker Avance Neo 400 MHz or a Bruker Avance Neo 600 MHz spectrometer operating at 400.13 MHz for1H and 100.61 MHz for13C or 600.15 MHz for1H and 150.94 MHz for13C, respectively. NMR chemical shifts (δ) are reported in parts-per-million (ppm). For the1H and13C spectra, the solvent signal served for internal calibration (1H NMR: δ(CHCl3)=7.26;13C NMR:14584.0034-00304 δ(CDCl3)=77.16].13C NMR spectra were recorded in the proton-decoupled mode. Coupling constants (J) are given in Hz and the apparent resonance multiplicity is reported as s (singlet), d (doublet), t (triplet), q (quartet), quint (quintet) or m (multiplet). Flash chromatography was carried out with a Biotage® Selekt Flash Purification System using a Biotage® Sfär HC Duo column as the solid phase. Electron paramagnetic resonance (EPR) spectra were recorded on an X-band EPR spectrometer (Bruker ELEXSYS E580) with the software xEPR for data acquisition. Measurements were performed using a dielectric ring resonance (Bruker model 4118X-MD5, typical microwave frequency about 9.7 GHz) which was mounted in a helium- flow cryostat (Oxford CF935) with optical access. When operated in continuous-wave (cw) mode, a typical quality factor of about 10,000 was achieved and typical modulation amplitude and frequencies were 1 gauss (G) and 100 kHz, respectively. In pulsed model, a Bruker SpinJet arbitrary waveform generator with a 1 kW traveling-wave tube (TWT) amplifier (Applied Systems Engineering model 117) was used. Prior the measurements, samples were inserted into EPR tubers (Wilmad Quartz CFQ) having an outer diameter (OD) of 4 millimeters (mm) and aligned on a homemade Teflon sample stage. The sample could be rotated with a one-axis goniometer stage (Bruker E218G1). Example 2: Generic synthetic route for the formation of carbene dopant molecules

[0233] The general synthetic route for formation of carbene dopant molecules in organic host materials is shown below.14584.0034-00304

[0234] The carbenes are designed to possess a triplet ground state in which the two unpaired electrons are confined to close-by molecular orbitals. As such, electron coupling is maximized and the zero-field splitting parameters D and E of the electronic spin are large. Moreover, spin lattice relaxation times benefit from the weak spin orbit couplings typically present in purely organic materials. The carbenes may be included in a cyclic structure (1) and comprise two (2) or one (3) aryl or heteroaryl group π1-3that can be substituted by one or more nitrile groups, carbonyl groups, carboxylic acid groups, ester groups, alkyl groups, aryl groups, heteroaryl groups, amine groups, nitro groups, phosphine groups, alcohol groups, ether groups, thioether groups, or halogen groups. Such groups may be selected (e.g., using computational molecular modeling, high-throughput synthesis and screening, or the like) to increase brightness, fine tune the electronic properties such as the ZFS, zero-phonon lines, spectral stability, and / or thermodynamic / kinetic stability.

[0235] Since the carbenes are typically not stable enough to prepare dilute molecular crystals directly, a stable carbene precursor is instead embedded into the molecular matrix (compounds 4–6) and later activated (i.e., converted from carbene precursor form to activated carbene form). Carbene precursors typically comprise a diaryl diazo group (R2C=N--=N), which can be photoactivated with light (λ = 200 to 500 nm or higher) to generate a molecule of dinitrogen N2and a molecule of carbene. An example of such activation is shown below.14584.0034-00304

[0236] The host materials in which the carbenes are embedded (compounds 7–9) are typically designed such that they structurally resemble the carbene precursors 1–3, respectively, and enable the formation of dilute molecular crystals by substitutional replacement of host material (i.e., matrix) molecules by the carbene precursors. This isostructural relationship allows the preparation of high-quality dilute molecular crystals by reducing the amount of strain imparted by the dopant molecules (i.e., the carbenes). Both the carbene and the host material can be partially or fully deuterated to reduce the magnetic noise in the dilute molecular crystals and thus enhance the spin-spin coherence time T2. Using bottom-up synthetic chemistry, the molecules can also be selectively labeled with13C (e.g., at the carbene carbon), adding a nuclear spin manifold that may be used for quantum state preparation or quantum error correction. Close packing of the molecules in the supramolecular arrangement helps to stabilize the carbene by trapping the inert N2 molecule in close proximity to the reactive carbene center and thereby shielding it from any nearby reaction partners. Example 3: Synthesis of the compounds required to embed di(napthalen-2-yl)carbene in di(naphthalen-2-yl)methanone

[0237] The synthetic route for formation of di(napthalen-2-yl)carbene dopant molecules in a di(napthalen-2-yl)methanone host material is shown below.14584.0034-00304di(naphthalen-2-yl)methanone (di(naphthalen-2-yl)methylene)hydrazinecrystal di(naphthalen-2-yl)carbene 2,2'-(diazomethylene)dinaphthalene (carbene precursor) a) Formation of di(naphthalen-2-yl)methanone

[0238] Di(naphthalen-2-yl)methanone was prepared by modifying the procedure described in B. Kozankiewicz, M. Aloshyna, A. D. Gudmundsdottir, M. S. Platz, M. Orrit, P. Tamarat, J. Phys. Chem. A 1999, 103, 3155. A solution of 2-bromonaphthalene (25.0 grams, g, 0.12 moles, mol) in diethyl ether (anhydrous, 400 milliliters, mL, 0.3 molar, M) was cooled to –78 degrees Celsius (°C) and n-butyllithium (2.5 M in hexanes, 48.3 mL, 1.00 equiv.) was added via dropping funnel within 10 minutes (min). The solution was stirred for 1 hour (h) at –78 °C. To the resulting yellowish dispersion, a solution of N-carboethoxypiperidine (9.49 g, 0.12 mol, 1.00 equiv.) in diethyl ether (anhydrous, 50 mL) was added at –78 °C within 5 min after the addition was complete the cooling bath was removed. The reaction mixture was allowed to warm to room temperature (RT) within 1 h. The reaction was quenched by addition of 10% aqueous HCl (150 mL). The organic phase was separated, and the aqueous phase extracted with diethyl ether (2 × 100 mL). The combined organic phases were washed with water (200 mL) and brine (100 mL), and then dried over MgSO4. To the ethereal solution methanol (80 mL) was added and most of the diethyl ether was removed under reduced pressure to give a white14584.0034-00304 precipitate. Nearly quantitative precipitation occurred upon storage at 7 °C for 3 h. The precipitate was filtered off, washed with cold methanol (2 × 50 mL) and dried under vacuum to give the product as a white solid (15.5 g, 91%). The following physical, chemical, and spectroscopic parameters were obtained. Rf (SiO2, CH2Cl2) = 0.81. Melting point (Mp).168.1 – 170.3 °C;1H NMR (400 MHz, CDCl3): δ 8.34 (d, J = 1.3 Hz, 2H), 8.06 – 7.97 (m, 4H), 7.97 – 7.90 (m, 4H), 7.64 (ddd, J = 8.3, 6.9, 1.3 Hz, 2H), 7.57 (ddd, J = 8.3, 6.9, 1.3 Hz, 2H) ppm;13C NMR (101 MHz, CDCl3): δ 196.6, 135.4, 135.3, 132.4, 131.9, 129.5, 128.5, 128.4, 128.0, 126.9, 126.0 ppm. IR (ATR): ^^�^^ 3051 (w), 1650 (m), 1618 (m), 1355 (m), 1272 (m), 954 (m), 918 (m), 871 (m), 830 (m), 776 (m) 748 (s) cm-1. b) Formation of (di(naphthalen-2-yl)methylene)hydrazine

[0239] (Di(naphthalen-2-yl)methylene)hydrazine was prepared by modifying the procedure described in E. Schmitt, G. Landelle, J.-P. Vors, N. Lui, S. Pazenok, F. R. Leroux, Eur. J. Org. Chem. 2015, 2015, 6052. A mixture of di(naphthalen-2-yl)methanone (4.9 g, 17.3 mmol), hydrazine hydrate (1.18 mL, 24.3 mmol, 1.40 equiv.) and EtOH (anhydrous, 6.00 mL, 4.0 M) was heated to 160 °C for 16 h in a high pressure vessel that was sealed with a polytetrafluoroethylene (PTFE)-lined screw cap. The mixture was left to cool to RT for over 1 h and stored at 7 °C for another 2 h. The colorless needles formed were recrystallized from anhydrous EtOH, filtered, and dried in vacuo, to yield the product (4.77 g, 93%). The following physical, chemical, and spectroscopic parameters were obtained. Rf (SiO2, CH2Cl2 / ) = 0.14; Mp. 151.2 – 152.7 °C;1H NMR (400 MHz, CDCl3): δ 8.11 – 8.03 (m, 2H), 8.00 – 7.87 (m, 3H), 7.86 – 7.79 (m, 2H), 7.68 – 7.53 (m, 4H), 7.48 – 7.35 (m, 3H), 5.58 (s, 2H) ppm;13C NMR (101 MHz, CDCl3): δ 149.2, 136.2, 133.7, 133.5, 133.4, 133.3, 130.5, 129.6, 128.6, 128.5, 128.4, 128.1, 128.0, 127.7, 127.1, 126.8, 126.4, 126.3, 126.2, 123.8 ppm; IR (ATR): ^^�^^ 332514584.0034-00304 (m), 3189 (w), 3044 (w), 1622 (w), 1580 (m), 1499 (m), 1323 (w), 1270 (w), 1188 (w), 1151 (w), 1113 (w), 1074 (w), 927 (m), 867 (m) 744 (s) cm-1. c) Formation of 2,2’-(diazomethylene)dinaphthalene

[0240] 2,2’-(diazomethylene)dinaphthalene was prepared by modifying the procedure described in M. I. Javed and M. Brewer, Org. Synth.2008, 85, 189. Handling and isolation of the product was done under exclusion of daylight. To a solution of dimethylsulfoxide (0.19 mL, 0.21 g, 2.73 mmol, 1.10 equiv.) and tetrahydrofuran (anhydrous, 22 mL, 0.13 M) was added oxalyl chloride (0.22 mL, 0.33 g, 2.61 mmol, 1.05 equiv.) in tetrahydrofuran (4 mL) at –55 °C over 5 min. The solution was maintained between –55 °C and –50 °C for 30 min while stirring and then cooled to –78 °C. A mixture of (di(naphthalen-2-yl)methylene)hydrazine (0.74 g, 2.48 mmol, 1.00 equiv.) and triethylamine (0.72 mL, 0.53 g, 5.22 mmol, 2.10 equiv.) in tetrahydrofuran (10 mL) was added to the reaction solution over 5 min to provide a deep-red solution containing a copious white precipitate. The reaction mixture was maintained at –78 °C for 30 min, and then filtered while cold through a medium porosity sintered-glass funnel into round-bottom flask and the solid was rinsed with tetrahydrofuran (2 × 50 mL). The filtrate was concentrated at RT by rotary evaporation. The red residue was redissolved in n-hexane (200 mL) and rapidly filtered through a plug of activated basic alumina supported in a medium porosity sintered glass funnel and the solids were rinsed with n-hexane (~100 mL) until the filtrate was colorless. The filtrate was concentrated at RT by rotary evaporation (to ca.50 mL) and stored at 7 °C overnight. The formed precipitate was filtered off and dried under vacuum to give the product as purple crystalline solid (0.63 g, 87%). The following physical, chemical, and spectroscopic parameters were obtained. Rf(Al2O3basic, hexane) = 0.52; Mp.137.3 – 138.0 °C;1H NMR (400 MHz, CDCl3): δ 7.89 (d, J = 8.6 Hz, 1H), 7.84 (dd, J = 7.6, 1.8 Hz, 1H), 7.80 (d, J = 2.0 Hz, 1H), 7.76 (dd, J = 7.6, 1.7 Hz, 1H), 7.54 – 7.42 (m, 3H) ppm;13C NMR (101 MHz, CDCl3): δ 134.1, 131.9, 129.1, 127.9, 127.5, 127.1, 126.8, 125.8, 123.8, 123.5, 77.5, 77.2,14584.0034-00304 76.8, 63.5 ppm; IR (ATR): ^^�^^ 3053 (w), 2011 (s), 1622 (m), 1590 (m), 1500 (m), 1465 (m) 1385 (m), 1366 (m), 1226 (m), 852 (s), 806 (s), 742 (s) cm-1. d) Formation of dilute molecular crystals of 2,2’-(diazomethylene)dinaphthalene in di(napthalen-2-yl)methanone

[0241] Di(naphthalen-2-yl)methanone (0.85 grams) was dissolved in hot ethyl acetate (HPLC grade, 100 mL, 0.030 M) and the solution was allowed to cool to RT. In the dark, to this solution, 2,2’-(diazomethylene)dinaphthalene (0.91 milligrams, 1025 ppm) was added. Aliquots (5 milliliters, mL) of this resulting parent solution were added into 10 mL vials using a syringe equipped with a 0.45 µm pore size syringe filter and the vials were placed in a screw top jar filled with ethanol (HPLC grade). Dilute molecular crystals (parallelepiped ca.5 × 4 × 4 mm) formed within storage in the dark at RT for 7 days. The crystals were isolated in the dark, washed with ethanol (HPLC grade) and dried in vacuum. The dilute molecular crystals could be stored in the freezer (T = -22 °C) in the dark for several months without detectable degradation.

[0242] To generate the di(napthalen-2-yl)carbene dopant molecules in the di(naphthalen-2- yl)methanone host material, the dilute molecular crystals of 2,2’- (diazomethylene)dinaphthalene in di(napthalen-2-yl)methanone need only be exposed to light of the correct wavelength, as described herein. Example 4: Synthesis of the compounds required to embed di(phenyl)carbene in di(phenyl)methanone

[0243] The synthetic route for formation of di(phenyl)carbene dopant molecules in a di(phenyl)methanone host material is shown below.14584.0034-00304di(phenyl)methanone(diphenylmethylene)hydrazine (diazomethylene)dibenzene(matrix) (carbene precursor)in dilutemolecular crystal di(phenyl)carbenea) Formation of (diphenylmethylene)hydrazine

[0244] (Diphenylmethylene)hydrazine was prepared according to the procedure described in E. Schmitt, G. Landelle, J.-P. Vors, N. Lui, S. Pazenok, F. R. Leroux, Eur. J. Org. Chem.2015, 2015, 6052. b) Formation of (diazomethylene)dibenzene

[0245] (Diazomethylene)dibenzene was prepared according to the procedure described in M. I. Javed and M. Brewer, Org. Synth.2008, 85, 189. c) Formation of dilute molecular crystals of (diazomethylene)dibenzene in di(phenyl)methanone

[0246] Di(phenyl)methanone (0.30 grams, purified by sublimation) was dissolved in hot n- hexane (HPLC grade, 4.1 milliliter, 0.40 M) and the solution was allowed to cool to RT. In the dark, to this solution (diazomethylene)dibenzene (0.08 mg, 247 ppm) was added. Aliquots (1.014584.0034-00304 milliliters, mL) of this resulting parent solution were added into 3.0 mL vials, which were sealed via a punctuated screw cap. Dilute molecular crystals (ca.6 × 4 × 3 mm) formed upon storage in the dark at RT for 6 days. The crystals were isolated in the dark, washed with cold n-hexane (HPLC grade) and dried in vacuum. The dilute molecular crystals could be stored in the freezer (T = -22 °C) in the dark for several months without detectable degradation.

[0247] To generate the di(phenyl)carbene dopant molecules in the di(phenyl)methanone host material, the dilute molecular crystals of (diazomethylene)dibenzene in di(phenyl)methanone need only be exposed to light of the correct wavelength, as described herein. Example 5: Synthesis of the compounds required to embed di(naphthalen-2-yl)carbene- d14in di(naphthalen-2-yl)methanone-d14

[0248] The synthetic route for formation of di(naphthalen-2-yl)carbene-d14 dopant molecules in a di(napthalen-2-yl)methanone-d14host material is shown below.14584.0034-00304 a) Formation of di(naphthalen-2-yl)methane

[0249] Di(naphthalen-2-yl)methane was prepared by modifying the procedure described in T. K. Wood, W. E. Piers, B. A. Keay, M. Parvez, Chem. Eur. J.2010, 16, 12199. To a solution of di(naphthalen-2-yl)methanol (3.80 g, 13,4 mmol) in AcOH (89.0 mL, 0.15 M) at RT was added HI (7.31 mL, 55% in H2O, 53.5 mmol, 4.00 equiv.) and the reaction mixture was heated to reflux (130 °C) for 2 h. The reaction mixture was allowed to cool to RT and an aqueous saturated solution of Na2SO3 (80 mL) was slowly added under vigorous stirring until no further color change from dark to yellow was observed. The mixture was diluted with H2O (80 mL) and extracted with Et2O (3 x 100 mL). The combined organic phases were cooled to 0 °C and an aqueous solution of NaOH (50%, 105 mL) was slowly added until a pH of at least 12 was reached. The aqueous phase was extracted with Et2O (50 mL), the combined organic phases were washed with brine (80 mL), dried over Na2SO4, and the solvent was removed in vacuo. The residue was recrystallized from hot n-hexane / toluene 5:1 (100 mL) to give white crystals (0.99 g, 87%). The following physical, chemical, and spectroscopic parameters were obtained. Rf(SiO2, 30% CH2Cl2 / hexane) = 0.68; Mp.91.7–93.9 °C;1H NMR (400 MHz, CDCl3): δ 7.85 – 7.73 (m, 3H), 7.68 (d, J = 1.7 Hz, 1H), 7.45 (tt, J = 6.9, 5.1 Hz, 2H), 7.36 (dd, J = 8.4, 1.8 Hz, 1H), 4.32 (s, 1H) ppm;13C NMR (101 MHz, CDCl3): δ 138.6, 133.8, 132.3, 128.3, 127.9, 127.8, 127.7, 127.4, 126.2, 125.5, 42.4 ppm; IR (ATR): ^^�^^ 3080 (w), 3051 (w), 2815 (w) 1625 (w), 1596 (m), 1499 (m), 1409 (w), 1361 (m), 1270 (w), 954 (m), 806 (s), 757 (s), 730 (s) cm-1. b) Formation of di(naphthalen-2-yl)methane-d1414584.0034-00304

[0250] Di(naphthalen-2-yl)methane-d14 was prepared by modifying the procedure described in X. Liang, S. Duttwyler, Asian J. Org. Chem. 2017, 6, 1063. A flame dried 100 mL glass vial was charged with non-deuterated di(naphthalen-2-yl)methane (2.5 g, 9.32 mmol), C6D6 (99.5%D, 37.3 mL, 0.25 M), and perfluorobutanesulfonic acid (0.15 mL, 0.93 mmol, 10mol%). The mixture was cooled to 0 °C and sparged with argon for 5 min. The vial was sealed with a PTFE-lined screw cap and the reaction mixture was stirred at 70 °C for 2 days. The reaction was allowed to cool to RT and quenched with D2O (4 mL). Saturated aqueous NaHCO3solution (50 mL) was added, and the mixture was transferred to a separation funnel. The organic layer was separated, and the aqueous layer was extracted with Et2O (3×5 mL). The combined organic layers were dried over Na2SO4, and the solvent was removed under reduced pressure. The as obtained crude product (2.38 g, 91%, 93-94%D determined by internal standard mesitylene) was resubjected to a second deuteration cycle using the same reaction conditions as described above. The crude product resulting from the second cycle was recrystallized from hot n-hexane (20 mL) to give the product as colorless crystals (2.15 g, 82%, 98.5%D determined by internal standard mesitylene). The following physical, chemical, and spectroscopic parameters were obtained. Rf (SiO2, 10% CH2Cl2 / hexane) = 0.43; Mp. 92.4 – 93.7 °C;1H NMR (400 MHz, CDCl3): δ 7.87 (s, residual H), 7.84 (s, residual H), 7.83 (s, residual H), 7.75 (s, residual H), 7.51 (s, residual H), 7.49 (s, residual H), 7.42 (s, residual H) ppm;13C UDEFT NMR (151 MHz, CDCl3): δ 138.4 (s), 133.6 (s), 132.1 (s), 128.1 (s, residual C-H), 127.77 (t, J1C-D= 24.3 Hz), 127.71 (s, residual C-H), 127.4 (t, J1C-D= 24.1 Hz), 127.3 (t, J1C-D= 24.3 Hz), 127.2 (t, J1C-D= 25.2 Hz), 127.0 (t, J1C-D = 23.9 Hz), 125.9 (s, residual C-H), 125.6 (t, J1C-D = 24.0 Hz), 125.3 (s, residual C-H), 125.0 (t, J1C-D= 24.3 Hz) ppm, 42.2 ppm (three residual C-H signals not observed due to overlap); IR (ATR): ^^�^^ 2901 (w), 2271 (w), 1604 (w), 1555 (w), 1438 (m), 1410 (m), 1251 (m) 905, m), 837 (m), 738 (m), 702 (m), 651 (m), 584 (s) cm-1. c) Formation of di(naphthalen-2-yl)methanone-d1414584.0034-00304

[0251] Di(naphthalen-2-yl)methanone-d14 was prepared by modifying the procedure described in J. Zhang, Z. Wang, Y. Wang, C. Wan, X. Zheng, Z. Wang, Green Chem. 2009, 11, 1973. Di(naphthalen-2-yl)methane-d14(1.33 g, 4.73 mmol), iodine (60.0 mg, 0.24 mmol.0.05 equiv.), pyridine (20.0 µL, 24.0 mmol, 0,05 equiv.), aqueous tert-butylhydroperoxide (70% in H2O, 3.48 mL, 18.9 mmol, 4 equiv.), and acetonitrile (23.7 mL, 0.2 M) were sealed in a 15 mL high pressure tube and stirred at 80 °C for 16 h. After cooling to RT, water (20 mL) and the tan precipitate was filtered off and washed with water and small amounts of cold methanol. The crude product was purified by flash chromatography (Si2O, 20%-80% CH2Cl2 / cyclohexane) to obtain a colorless microcrystalline solid (1.15 g, 83%). The following physical, chemical, and spectroscopic parameters were obtained. Rf(SiO2, CH2Cl2) = 0.82; Mp. 167.3-167.5 °C;1H NMR (400 MHz, CDCl3): δ 8.34 (s, residual H), 8.01 (s, residual H), 8.00 (s, residual H), 7.95 (s, residual H), 7.94 (s, residual H), 7.64 (s, residual H), 7.58 (s, residual H) ppm;13C UDEFT NMR (151 MHz, CDCl3): δ 196.9 (s), 135.3 (s), 135.1 (s), 132.3 (s), 131.9 (s, residual C-H), 131.6 (t, J1C-D = 24.5 Hz), 129.4 (s, residual C-H), 129.1 (t, J1C-D = 24.3 Hz), 128.22 (s, residual C-H), 128.16 (s, residual C-H), 128.0 (t, J1C-D= 24.5 Hz), 127.9 (t, J1C-D= 24.3 Hz), 127.5 (t, J1C-D = 24.3 Hz), 126.7 (s, residual C-H), 126.5 (t, J1C-D = 24.3 Hz), 125.9 (s, residual C-H), 125.6 (t, J1C-D = 24.8 Hz) ppm; IR (ATR): ^^�^^ 2271 (w), 1648 (s), 1597 (m), 1541 (m), 1388 (m), 1213 (m), 1068 (m), 1009 (m), 919 (w), 779 (s), 733 (m), 705 (m), 684 (m), 650 (m), 637 (s), 605 (m), 573 (m) cm-1. d) Formation of (di(naphthalen-2-yl)methylene)hydrazine-d1414584.0034-00304

[0252] (Di(naphthalen-2-yl)methylene)hydrazine-d14 was prepared by modifying the procedure described in E. Schmitt, G. Landelle, J.-P. Vors, N. Lui, S. Pazenok, F. R. Leroux, Eur. J. Org. Chem.2015, 2015, 6052. A mixture of di(naphthalen-2-yl)methanone-d14(0.30 g, 1.01 mmol), hydrazine hydrate (69.0 µL, 1.41 mmol, 1.40 equiv.), and EtOH (anhydrous, 0.94 mL, 1.5 M) was heated to 160 °C for 12 h in a high pressure vessel that was sealed with a PTFE- lined screw cap. The mixture was left to cool to RT over 1 h and stored at 7 °C for another 2 h. The colorless needles formed were filtered off and washed with cold EtOH to yield the product (0.21g, 67%). The following physical, chemical, and spectroscopic parameters were obtained. Rf(SiO2, CH2Cl2 / hexane) = 0.16; Mp.151.2 – 151.5 °C;1H NMR (600 MHz, CDCl3): δ 8.09 (s, residual C-H), 8.09 (s, residual C-H, 0.011 H), 8.08 (s, residual C-H, 0.011 H), 8.00 (s, residual C-H, , 0.011 H), 7.95 (s, residual C-H, 0.011 H), 7.93 (s, residual C-H, 0.012 H), 7.86 (s, residual C-H, 0.011 H), 7.85 (s, residual C-H, 0.011 H), 7.67 (s, residual C-H, 0.011 H), 7.64 (s, residual C-H, 0.011 H), 7.61 (s, residual C-H, 0.012 H), 7.59 (s, residual C-H, 0.011 H), 7.47 (s, residual C-H, 0.011 H), 7.46 (s, residual C-H, 0.012 H), 7.42 (s, residual C-H, 0.011 H), 5.60 (s, 2H) ppm.13C UDEFT NMR (151 MHz, CDCl3): δ 149.2 (s), 136.1 (s), 133.5 (s), 133.4 (s), 133.3 (s), 133.1 (s), 130.3 (s),129.4 (s, residual C-H), 129.1 (t, J1C-D= 24.5 Hz), 128.6 – 127.0 (m), 127.0 – 125.3 (m), 123.7 (s), 123.4 (t, J1C-D= 24.0 Hz) ppm; IR (ATR): ^^�^^ 3324 (m), 3185 (w), 2259 (w), 1621 (w), 1578 (m), 1438 (w), 1402 (w), 1375 (w), 1341 (w), 1306 (w), 1254 (m), 1145 (m), 1090 (m), 1062 (m), 991 (m), 931 (m), 868 (m), 846 (m), 832 (m), 809 (m), 799 (m), 777 (m), 758 (m), 732 (s), 704 (w), 665 (w), 647 (m), 583 (m) cm-1. e) Formation of 2,2’-(diazomethylene)dinaphthalene-d1414584.0034-00304

[0253] 2,2’-(diazomethylene)dinaphthalene-d14 was prepared by modifying the procedure described in M. I. Javed and M. Brewer, Org. Synth.2008, 85, 189. Handling and isolation of the product was done under exclusion of daylight. To a solution of dimethylsulfoxide (47.8 μL, 53.0 g, 0.67 mmol, 1.10 equiv.) and tetrahydrofuran (anhydrous, 2.5 mL, 0.26 M) was added oxalyl chloride (55.1 μL, 82.0 mg, 0.64 mmol, 1.05 equiv.) in tetrahydrofuran (2.5 mL) at –55 °C over 5 min. The solution was maintained between –55 °C and –50 °C for 30 min while stirring and then cooled to –78 °C. A mixture of (di(naphthalen-2-yl)methylene)hydrazine-d14(190 mg, 0.61 mmol, 1.00 equiv.) and triethylamine (0.18 mL, 0.13 g, 1.29 mmol, 2.10 equiv.) in tetrahydrofuran (2 mL) was added to the reaction solution over 5 min to provide a deep-red solution containing a copious white precipitate. The reaction mixture was maintained at –78 °C for 30 min, and then filtered while cold through a medium porosity sintered-glass funnel into round-bottom flask and the solid was rinsed with tetrahydrofuran (2 × 3 mL). The filtrate was concentrated at room temperature by rotary evaporation. The red residue was redissolved in n- hexane (20 mL) and rapidly filtered through a plug of activated basic alumina supported in a medium porosity sintered glass funnel and the solids are rinsed with n-hexane (~30 mL) until the filtrate was colorless. The filtrate was concentrated at room temperature by rotary evaporation (to ca.20 mL) and stored at 7 °C overnight. The formed precipitate was filtered off and dried under vacuum to give the product as purple crystalline solid (53.0 mg, 28%). The following physical, chemical, and spectroscopic parameters were obtained. Rf (Al2O3 basic, hexane) = 0.51; Mp.134.0 – 134.2°C;1H NMR (600 MHz, CDCl3): δ 7.90 (s, residual C-H), 7.84 (s, residual C-H), 7.81(s, residual C-H) 7.77 (s, residual C-H) 7.49, (s, residual C-H), 7.4714584.0034-00304 (s, residual C-H), 7.46 (s, residual C-H) ppm;13C UDEFT NMR (151 MHz, CDCl3): δ 133.9 (s), 131.7 (s), 128.9 (s), 128.6 (t, J1C-D= 24.5 Hz), 127.7 (s), 127.4 (t, J1C-D= 24.5 Hz)z, 126.98 (t, J1C-D = 24.5 Hz), 126.95 (s), 126.6 (s), 126.3 (t, J1C-D = 24.0 Hz), 125.3 (t, J1C-D = 24.5 Hz), 123.4 (t, J1C-D = 24.0 Hz), 123.1 (t, J1C-D = 24.0 Hz) ppm; IR (ATR): ^^�^^ 2267 (w), 2013 (s), 1600 (m), 1557 (m), 1442 (m), 1395 (m), 1323, (w), 1218 (m), 1029 (w), 872 (w), 853 (m), 831 (m), 727 (s), 644 (m), 616 (m), 602 (s), 579 (m) cm-1. f) Formation of dilute molecular crystals of 2,2’-(diazomethylene)dinaphthalene-d14in di(naphthalen-2-yl)methanone-d14

[0254] Di(naphthalen-2-yl)methanone-d14(0.80 grams) was dissolved in hot ethyl acetate (HPLC grade, 90 mL, 0.030 M) and the solution was allowed to cool to RT. In the dark, to this solution, 2,2’-(diazomethylene)dinaphthalene-d14(4.5 milligrams, 5400 ppm) was added. Aliquots (5 milliliters, mL) of this resulting parent solution were added into 10 mL vials using a syringe equipped with a 0.45 µm pore size syringe filter and the vials were placed in a screw top jar filled with ethanol (HPLC grade). Dilute molecular crystals (parallelepiped ca.3 × 3 × 4 mm) formed within storage in the dark at RT for 7 days. The crystals were isolated in the dark, washed with ethanol (HPLC grade) and dried in vacuum. The dilute molecular crystals could be stored in the freezer (T = -22 °C) in the dark for several months without detectable degradation.

[0255] To generate the di(napthalen-2-yl)carbene-d14 dopant molecules in the di(naphthalen-2- yl)methanone-d14 host material, the dilute molecular crystals of 2,2’- (diazomethylene)dinaphthalene-d14in di(napthalen-2-yl)methanone-d14need only be exposed to light of the correct wavelength, as described herein. Example 6: Synthesis of the compounds required to embed di(phenyl)carbene-d10in di(phenyl)methanone-d10

[0256] The synthetic route for formation of di(phenyl)carbene-d10 dopant molecules in a di(phenyl)methanone-d10host material is shown below.14584.0034-00304a) Formation of di(phenyl)methanone-d10

[0257] Di(phenyl)methanone-d10was prepared as follows. A solution of bromobenzene-d5(7.86 g, 48.5 mmol, 2.0 equiv., 99.5%D ) in diethyl ether (anhydrous, 97 mL, 0.5 M) was cooled to 0 °C and n-butyllithium (2.5 M in hexanes, 20.3 mL, 2.1 equiv.) was added via dropping funnel within 5 min. The solution was stirred for 1 h at RT. To the resulting yellowish dispersion, a solution of N-carboethoxypiperidine (3.81 g, 24.3 mol, 1.00 equiv.) in diethyl ether (anhydrous, 20 mL) was added at 0 °C within 10 min. After the addition was complete the cooling bath was removed, and the reaction mixture was allowed to warm to RT within 30 min and stirred at RT for another 2 h. The reaction was quenched by addition of 10% aqueous HCl (150 mL). The organic phase was separated, and the aqueous phase extracted with diethyl ether (2 × 70 mL). The combined organic phases were washed with saturated sodium bicarbonate solution (50 mL), water (100 mL), and brine (80 mL), and then dried over MgSO4.The solvent was removed under reduced pressure to give the crude product as an off-white14584.0034-00304 solid. The product was obtained by twofold recrystallization from hot n-hexane (2 × 40 mL) as colorless crystals (3.36 g, 72%, 99.5 %D determined by internal standard1H NMR with mesitylene). The following physical, chemical, and spectroscopic parameters were obtained. Rf (SiO2, 40% CH2Cl2 / hexane) = 0.30; Mp.49.8 – 50.3 °C;1H NMR (400 MHz, CDCl3): δ 7.82 (s, residual H), 7.60 (s, residual H), 7.49 (s, residual H) ppm;13C UDEFT NMR (151 MHz, CDCl3): δ 196.8 (s), 137.6 (s), 132.2 (t, J1C-D = 24.3 Hz), 129.8 (t, J1C-D = 24.7 Hz), 127.9 (t, J1C-D = 24.7 Hz) ppm; IR (ATR): ^^�^^ 2291 (w), 2265 (w), 1646 (s), 1558 (m), 1385 (s), 1332 (m), 1216 (s), 954 (m), 912 (s), 821 (m), cm-1. b) Formation of (di(phenyl)methylene)hydrazine-d10

[0258] (Di(phenyl)methylene)hydrazine-d10 was prepared by modifying the procedure described in E. Schmitt, G. Landelle, J.-P. Vors, N. Lui, S. Pazenok, F. R. Leroux, Eur. J. Org. Chem.2015, 2015, 6052.

[0259] A mixture of di(phenyl)methanone-d10 (0.50 g, 2.60 mmol), hydrazine hydrate (0.18 mL, 3.64 mmol, 1.40 equiv.), and EtOH (0.9 mL, 4.0 M) was heated to reflux for 12 h. The mixture was left to cool to RT over 1 h and stored at 7 °C for another 3 h. The colorless needles formed were recrystallized from EtOH (anhydrous, 1.0 mL), filtered, and dried in vacuo, to yield the product (0.43 g, 80%, 99.5 %D determined by internal standard1H NMR with mesitylene). The following physical, chemical, and spectroscopic parameters were obtained. Rf (SiO2, CH2Cl2) = 0.31; Mp.98.5 – 100.4 °C;1H NMR (400 MHz, CDCl3): δ 7.53 (m, residual H), 7.47 (m, residual H), 7.29 (m, residual H) ppm;13C UDEFT NMR (151 MHz, CDCl3): δ 149.3 (s), 138.4 (s), 132.9 (s), 129.0 (t, J1C-D= 24.4 Hz), 128.5 (t, J1C-D= 24.4 Hz), 127.74 (t, J1C-D = 24.4 Hz), 127,72 (t, J1C-D = 24.4 Hz), 126.2 (t, J1C-D = 24.4 Hz) ppm (one set of triplets14584.0034-00304 overlapping at 129.0 ppm); IR (ATR): ^^�^^ 3419 (m), 3266 (w), 2273 (w), 1609 (m), 1578 (m), 1554 (m), 1320 (m), 1290 (m), 1144 (m), 1059 (m), 1024 (w), 930 (m), 818 (m) cm-1. c) Formation of (diazomethylene)dibenzene-d10

[0260] (Diazomethylene)dibenzene-d10was prepared by modifying the procedure described in M. I. Javed and M. Brewer, Org. Synth. 2008, 85, 189. Handling and isolation of the product was done under exclusion of daylight. To a solution of dimethylsulfoxide (0.15 mL, 0.17 g, 2.13 mmol, 1.10 equiv.) and tetrahydrofuran (anhydrous, 17 mL, 0.13 M) was added oxalyl chloride (0.17 mL, 0.26 g, 2.04 mmol, 1.05 equiv.) in tetrahydrofuran (4 mL) at –55 °C over 5 min. The solution was maintained between –55 °C and –50 °C for 30 min while stirring and then cooled to –78 °C. A mixture of di(phenyl)methylene)hydrazine-d10 (0.40 g, 1.94 mmol, 1.00 equiv.) and triethylamine (0.56 mL, 0.41 g, 4.07 mmol, 2.10 equiv.) in tetrahydrofuran (10 mL) was added to the reaction solution over 5 min to provide a deep-red solution containing a copious white precipitate. The reaction mixture was maintained at –78 °C for 30 min, and then filtered while cold through a medium porosity sintered-glass funnel into round-bottom flask and the solid was rinsed with tetrahydrofuran (2 × 50 mL). The filtrate was concentrated at RT by rotary evaporation. The red residue was redissolved in n-pentane (20 mL) and rapidly filtered through a plug of activated basic alumina supported in a medium porosity sintered glass funnel and the solids were rinsed with n-pentane (~50 mL) until the filtrate is colorless. The filtrate was concentrated at RT by rotary evaporation to provide 1,1'-(diazomethylene)dibenzene-d10(0.25 g, 63%) as an analytically pure violet liquid which solidified upon storage at 7 °C to a crystalline solid. The following physical, chemical, and spectroscopic parameters were14584.0034-00304 obtained. Rf (Al2O3 basic, hexane) = 0.93; Mp.30.3 – 30.8 °C; UVvis (CH2Cl2): λmax (ε, M-1cm-1) 290 (20800) nm;1H NMR (400 MHz, CDCl3): 7.42 (s, residual H), 7.34 (s, residual H), 7.22 (m, residual H) ppm;13C UDEFT NMR (151 MHz, CDCl3): δ 129.5 (s), 128.8 (t, J1C-D = 24.5 Hz), 125.2 (t, J1C-D = 24.6 Hz), 124.9 (t, J1C-D = 24.2 Hz) ppm (one set of triplets overlapping at 129.0 ppm); IR (ATR): ^^�^^ 2269 (w), 2028 (s), 1556 (m), 1404 (m), 1376 (m), 1238 (m), 1068 (w), 916 (w), 823 (m), 755 (m), cm-1. d) Formation of dilute molecular crystals of (diazomethylene)dibenzene-d10in di(phenyl)methanone-d10

[0261] Di(phenyl)methanone-d10(0.30 grams, purified by sublimation) was dissolved in hot n- pentane (HPLC grade, 7.8 milliliter, 0.20 M) and the solution was allowed to cool to RT. In the dark, to this solution (diazomethylene)dibenzene-d10(0.08 mg, 247 ppm) was added. Aliquots (1.0 milliliters, mL) of this resulting parent solution were added into 3.0 mL vials and sealed with a punctuated screw cap. Dilute molecular crystals (ca.3× 5 × 4 mm) formed upon storage in the dark at 7 °C for 12 days. The crystals were isolated in the dark, washed with cold n- pentane (HPLC grade) and dried in vacuum. The dilute molecular crystals could be stored in the freezer (T = -22 °C) in the dark for several months without detectable degradation.

[0262] To generate the di(phenyl)carbene-d10 dopant molecules in the di(phenyl)methanone- d10host material, the dilute molecular crystals of 1,1’-(diazomethylene)dinbenzene-d10in di(phenyl)methanone-d10 need only be exposed to light of the correct wavelength, as described herein. Example 7: Synthesis of the compounds required to embed di(naphthalen-2-yl)carbene-13C-d14in di(naphthalen-2-yl)methanone-13C-d14

[0263] The synthetic route for formation of di(napthalen-2-yl)carbene-13C-d14dopant molecules in a di(naphthalene-2-yl)methanone-13C-d14 host material is shown below.14584.0034-00304a) Formation of 2-bromonapthalene-d7

[0264] 2-bromonaphthalene-d7 was prepared by modifying the procedure described in X. Liang, S. Duttwyler, Asian J. Org. Chem.2017, 6, 1063. A flame dried 350 mL high pressure reaction vessel was charged with 2-bromonaphthalene (5.0 g, 24.1 mmol), C6D6 (99.5%D, 80.5 mL, 0.3 M), and perfluorobutanesulfonic acid (0.40 mL, 2.41 mmol, 10mol%) and a stir bar. The mixture was cooled to 0 °C and sparged with argon for 5 min. The vial was sealed with a PTFE-lined screw cap and the reaction mixture was stirred at 130 °C for 2 days. The reaction was allowed to cool to RT and quenched with D2O (4 mL). Saturated aqueous NaHCO3solution (50 mL) was added, and the mixture was transferred to a separation funnel. The organic layer was separated, and the aqueous layer was extracted with Et2O (3×30 mL). The combined organic layers were dried over Na2SO4, and the solvent was removed under reduced pressure. The as obtained crude product (4.85 g, 94% yield, 95.0%D determined by internal standard mesitylene) was resubjected to a second deuteration cycle using the same reaction conditions14584.0034-00304 as described above. The crude product resulting from the second cycle was purified by sublimation (2.6 x 10-2mbar, 60 °C) to give a colorless microcrystalline solid (4.71 g, 91% yield, 98.8%D determined by internal standard mesitylene). The following physical, chemical, and spectroscopic parameters were obtained. Rf (SiO2, hexane) = 0.68; Mp.56.9 – 57.0 °C;1H NMR (400 MHz, CDCl3): δ 8.02 (s, residual H), 7.82 (s, residual H), 7.76 (s, residual H), 7.72 (s, residual H), 7.55 (s, residual H), 7.51 (s, residual H), 7.50 (s, residual H) ppm;13C UDEFT NMR (151 MHz, CDCl3): δ 134.5 (s), 131.9 (s), 130.0 (s, residual CH), 129.7 (t, J1C-D= 24.8 Hz), 129.6 (s, residual CH), 129.28 (s, residual CH), 129.26 (t, J1C-D = 24.5 Hz), 129.0 (t, J1C-D = 25.5 Hz), 127.9 (s, residual CH), 127.5 (t, J1C-D = 24.4 Hz), 127.0 (s, residual CH), 126.7 (t, J1C-D= 24.3 Hz), 126.5 (t, J1C-D= 24.2 Hz), 126.2 (s, residual CH), 125.9 (t, J1C-D= 24.5 Hz), 119.7 (s) ppm. IR (ATR): ^^�^^ 2272 (w), 1626 (m), 1553 (m), 1448 (m), 1380 (w), 1247 (m), 1098 (w), 1004 (s), 886 (s), 784 (s), 710 (s), 653 (m), 591 (s) cm-1. b) Formation of 2-naphthoic acid-13C-d7

[0265] 2-naphthoic acid-13C-d7 was formed according to the following procedure. A solution of 2-lithium naphthalene-d7was prepared by slowly adding n-butyllithium (2.5 M in hexanes, 5.42 mL, 13.5 mmol, 1.00 equiv.) to a solution of 2-bromonaphthalene-d7 (2.9 g, 13.5 mmol, 1.00 equiv.) in THF (54.1 mL, 0.25 M) at -78 °C. The solution was stirred for 30 h at -78 °C. Gaseous13CO2(99.0%13C, exc.) was slowly introduced via a gas inlet tube under Ar atmosphere at -78 °C until no blue color formation was observed any more. The solution was allowed to warm to RT for 2 h and subsequently quenched by addition of 1 M aqueous NaOH (20 mL) at RT. The aqueous layer was extracted with Et2O (2 x 40 mL). To the aqueous layer was added 3 M HCl aqueous until pH < 3, and the aqueous layer was extracted with Et2O (2 x14584.0034-00304 40 mL). The combined organic phase was dried over Na2SO4 and concentrated. Trituration with hexane produced a white solid which was filtered off, washed with hexanes (30 mL), and dried under vacuum for 4 h to yield 2-naphthoic acid-13C-d7 (1.90 g, 10.5 mmol, yield 78%). The following physical, chemical, and spectroscopic parameters were obtained. Rf (SiO2, 10% MeOH / CH2Cl2) = 0.75; Mp.184.6 – 184.7 °C;1H NMR (600 MHz, DMSO-d6): δ 13.05 (s, br, 1H), 8.61 (d, JC-H = 4.7 Hz, residual H), 8.12 (s, residual H), 8.01 (s, residual H), 8.00 (s, residual H), 7.98 (d, JC-H= 3.4 Hz, residual H), 7.65 (s, residual H), 7.60 (s, residual H) ppm;13C UDEFT NMR (151 MHz, DMSO-d6): δ 167.4, 134.7, 132.0 (d, JC-C = 4.9 Hz), 130.1 (t, J1C-D = 24.7 Hz), 128.8 (t, J1C-D = 24.5 Hz), 127.79 (t, J1C-D = 23.8 Hz), 127.78 (d, JC-C = 71.3 Hz), 127.5 (s, residual CH), 127.1 (t, J1C-D= 24.3 Hz), 126.5 (s, residual CH), 126.3 (t, J1C-D= 24.0 Hz), 125.0 (s, residual CH), 124.7 (t, J1C-D = 24.7 Hz) ppm; IR (ATR): ^^�^^ 2893 (br), 2557 (w), 1642 (s), 1552 (m), 1415 (m), 1327 (m), 1262 (s), 1247 (m), 1122 (m), 932 (s), 867 (m), 840 (m), 741 (s), 690 (s) 650 (m), 576 (s), 533 (s) cm-1. c) Formation of N-methoxy-N-methyl-2-naphthamide-13C-d7

[0266] N-methoxy-N-methyl-2-naphthamide-13C-d7was formed according to the following procedure.2-Naphthoic acid-13C-d7 (1.85 g, 10.3 mmol, 1.00 equiv.) was dissolved in CH2Cl2 (anhydrous, 37.6 mL, 0.3 M) and one drop of DMF was added under Ar atmosphere. Then oxalyl chloride (0.97 mL, 1.10 equiv.) was added quickly and after 2 h of stirring, the solvent was evaporated under reduced pressure to yield the crude acyl chloride as an off-white solid. N,O-Dimethylhydroxylamine (1.16 g, 1.00 equiv.) was dissolved in CH2Cl2(anhydrous, 37.6 mL, 0.3 M) under Ar atmosphere and cooled to 0 °C. Triethylamine (3.31 mL, 2.0 equiv.) was added dropwise and stirred for 5 min at 0 °C. The acyl chloride was redissolved CH2Cl214584.0034-00304 (anhydrous, ca.10.0 mL) and added dropwise to the amine solution. The solution was warmed to RT and stirred for 2 h. Then the reaction was quenched with HCl aq. (10 mL, 1.0 M) and transferred into a separatory funnel. The organic layer was separated and the aqueous phase extracted with CH2Cl2 (20 mL). The combined organic phases were washed with saturated aqueous NaHCO3(30 mL), water (20 mL), and brine (20 mL). After drying the organic phase over Na2SO4, all volatiles were removed under reduced pressure. The residue was purified by flash column chromatography (SiO2, 20-50% ethyl acetate / hexanes) to give the product as a yellowish oil (2.01 g, 88%). The following physical, chemical, and spectroscopic parameters were obtained. Rf (SiO2, 50% EtOAc / hexane) = 0.56;1H NMR (600 MHz, CDCl3): δ 8.23 (d, JC-H= 4.4 Hz, residual H), 7.91 (s, residual H), 7.86 (s, residual H), 7.76 (d, JC-H= 3.3 Hz, residual H), 7.55 (s, residual H), 7.52 (s, residual H), 3.57 (s, 3H), 3.42 (d, JC-H = 2.1 Hz, 3H) ppm;13C UDEFT NMR (151 MHz, CDCl3): δ 170.1 (s), 134.2 (s, residual CH), 132.5 (d, J = 4.6 Hz), 131.4 (d, J = 67.5 Hz), 128.8 (s, residual CH), 128.5 (t, J1C-D = 24.9 Hz), 127.8 – 126.7 (m, multiple CD and residual CH), 126.4 (s, residual CH), 126.1 (t, J1C-D= 24.4 Hz), 125.1 (s, residual CH), 124.8 (t, J1C-D= 25.1 Hz), 61.3 (s), 34.0 (s) ppm; IR (ATR): ^^�^^ 2968 (w), 2993 (w), 2275 (w), 1593 (s), (w), 1410 (m), 1376 (m), 1352 (m), 1438 (m), 1182 (m), 1074 (m), 988 (m), 940 (m), 855 (m), 792 (m), 683 (m), 649 (m), 604 (m), 556 (m), 516 (m) cm-1. d) Formation of di(naphthalen-2-yl)methanone-13C-d14

[0267] Di(naphthalen-2-l)methanone-13C-d14was prepared according to the following procedure. A solution of 2-bromonaphthalene-d7 (1.73 g, 8.08 mmol, 1.00 equiv.) in THF (anhydrous, 32.3 mL, 0.25 M) was cooled to −78 °C. Then, n-butyllithium (2.5 M in hexanes, 3.56 mL, 1.10 equiv.) was added dropwise within 5 min so that the temperature did not exceed14584.0034-00304 −70 °C and the solution was stirred for another 20 min at −78 °C. The corresponding Weinreb amide N-methoxy-N-methyl-2-naphthamide-13C-d7(1.80 g, 8.08 mmol, 1.00 equiv,) was dissolved in THF (anhydrous, 10 mL) and added slowly to the lithiate solution. The mixture was stirred for 10 min at −78 °C before it was allowed to warm to RT within 2 h. The reaction was quenched by the addition of HCl aq. (10 mL, 1.0 M). The crude product was extracted with Et2O (4 × 20 mL), and the combined organic layers were washed with saturated NaHCO3 (30 mL), water (20 mL), and brine (20 mL). The solution was dried (MgSO4), filtered, and the volatiles removed under reduced pressure. The crude product was dissolved in minimum amount of CH2Cl2 and triturated with methanol. The formed solid was filtered off and washed with methanol (30 mL) to obtain the product as a colorless microcrystalline solid (2.24 g, 93%). Analytically pure product was obtained by sublimation (165 °C, 1.8 · 10-1mbar) as colorless crystals within 6 h. The following physical, chemical, and spectroscopic parameters were obtained. Rf (SiO2, CH2Cl2) = 0.81; Mp.167.6 - 167.9 °C;1H NMR (400 MHz, CDCl3): δ 8.35 (d, JC-H= 4.4 Hz, residual H), 8.02 (d, JC-H= 3.2 Hz, residual H), 7.99 (s, residual H), 7.94 (d, JC-H= 7.4 Hz, residual H), 7.63 (s, residual H), 7.57 (s, residual H) ppm;13C UDEFT NMR (151 MHz, CDCl3): δ 135.3, 135.2 (d, J1C-C = 55.2 Hz), 132.3 (d, JC-C = 4.4 Hz), 131.9 (s, residual C-H), 131.6 (t, J1C-D= 24.3 Hz), 129.4 (s, residual C-H), 129.1 (t, J1C-D= 24.4 Hz), 128.3 (d, JC-C = 3.9 Hz), 128.2 (t, J1C-D = 24.4 Hz), 128.0 (td, J1C-D = 24.4, JC-C = 3.1 Hz), 128.0 (t, J1C-D= 24.2 Hz), 127.5 (t, J1C-D= 24.4 Hz), 126.8 (s, residual C-H), 126.5 (t, J1C-D= 24.5 Hz), 125.9 (s, residual C-H), 125.6 (t, J1C-D= 24.6 Hz) ppm; IR (ATR): ^^�^^ 2271 (w), 1619 (s), 1591 (s), 1540 (m), 1388 (m), 1315 (m), 1243 (w), 792 (s), 733 (m), 679 (m), 637 (m), 584 (s) cm-1. e) Formation of (di(naphthalen-2-yl)methylene-13C)hydrazine-d1414584.0034-00304

[0268] (Di(naphthalen-2-yl)methylene-13C)hydrazine-d14was prepared by modifying the procedure described in E. Schmitt, G. Landelle, J.-P. Vors, N. Lui, S. Pazenok, F. R. Leroux, Eur. J. Org. Chem.2015, 2015, 6052. A mixture of di(naphthalen-2-yl)methanone-13C-d14(1.00 g, 3.36 mmol), hydrazine hydrate (0.23 mL, 4.71 mmol, 1.40 equiv.), and EtOH (anhydrous, 4.71 mL, 1.0 M) was heated to 160 °C for 12 h in a high pressure vessel that was sealed with a PTFE-lined screw cap. The mixture was left to cool to RT over 1 h and stored at 7 °C for another 2 h. The colorless needles formed were filtered off and washed with cold EtOH to yield the product (0.21g, 67%). The following physical, chemical, and spectroscopic parameters were obtained. Rf (SiO2, CH2Cl2 / hexane) = 0.15; Mp.151.4 – 151.7 °C;1H NMR (600 MHz, CDCl3): δ 8.06 (s, residual H), 8.05 (d, JC-H = 3.2 Hz, residual H), 7.97 (s, residual H), 7.92 (s, residual H), 7.89 (d, JC-H= 3.8 Hz, residual H), 7.82 (s, residual H), 7.81 (s, residual H), 7.64 (s, residual H), 7.61 (s, residual H), 7.58 (s, residual H), 7.55 (d, JC-H = 5.3 Hz, residual H), 7.44 (d, JC-H = 2.9 Hz, residual H), 7.43 (s, residual H), 7.39 (s, residual H), 5.57 (d, JC-H= 6.9 Hz, 2H) ppm;13C UDEFT NMR (151 MHz, CDCl3): δ 149.3 (s), 136.1(d, JC-C = 66.0 Hz), 133.6 (d, JC-C = 4.0 Hz), 133.4 (s), 133.3 (s), 133.2 (d, JC-C = 5.3 Hz), 130.3 (d, JC-C = 52.5 Hz), 129.5 (s, residual CH), 129.1 (t, JC-D= 24.4 Hz), 128.5 – 125.4 (m, multiple CD and residual CH signals), 123.7 (s, residual CH), 123.46 (t, JC-D= 24.7 Hz) ppm; IR (ATR): ^^�^^ 3324 (m), 3182 (w), 2258 (w), 1620 (w), 1550 (m), 1438 (w), 1392 (w), 1335 (w), 1304 (w), 1252 (m), 1144 (m), 1088 (m), 1058 (m), 997 (m), 930 (m), 862 (m), 847 (m), 832 (m), 809 (m), 799 (m), 777 (m), 758 (m), 731 (s), 704 (w), 672 (w), 646 (m), 583 (m) cm-1. f) Formation of 2,2’-(diazomethylene-13C)dinaphthalene-d1414584.0034-00304

[0269] 2,2’-(Diazomethylene-13C)dinaphthalene-d14 was prepared by modifying the procedure described in M. I. Javed and M. Brewer, Org. Synth.2008, 85, 189. Handling and isolation of the product was done under exclusion of daylight. To a solution of dimethylsulfoxide (0.10 mL, 0.11 g, 1.41 mmol, 1.10 equiv.) and tetrahydrofuran (anhydrous, 11.3 mL, 0.13 M) was added oxalyl chloride (0.12 mL, 0.17 g, 1.35 mmol, 1.05 equiv.) in tetrahydrofuran (5.0 mL) at –55 °C over 5 min. The solution was maintained between –55 °C and –50 °C for 30 min while stirring and then cooled to –78 °C. A mixture of (di(naphthalen-2-yl)methylene-13C)hydrazine- d14(0.40 g, 1.28 mmol, 1.00 equiv.) and triethylamine (0.37 mL, 2.70 mmol, 2.10 equiv.) in tetrahydrofuran (3.0 mL) was added to the reaction solution over 5 min to provide a deep-red solution containing a copious white precipitate. The reaction mixture was maintained at –78 °C for 30 min, and then filtered while cold through a medium porosity sintered-glass funnel into round-bottom flask and the solid was rinsed with tetrahydrofuran (2 × 5 mL). The filtrate was concentrated at RT by rotary evaporation. The red residue was redissolved in n-hexane (20 mL) and rapidly filtered through a plug of activated basic alumina supported in a medium porosity sintered glass funnel and the solids were rinsed with n-hexane (~50 mL) until the filtrate was colorless. The filtrate was concentrated at RT by rotary evaporation (to ca.20 mL) and stored at 7 °C overnight. The formed precipitate was filtered off and dried under vacuum to give the product as purple crystalline solid (53.0 mg, 28%). The following physical, chemical, and spectroscopic parameters were obtained. Rf (Al2O3 basic, hexane) = 0.49; Mp. 134.3 °C;1H NMR (600 MHz, C6D6): δ 7.66 (d, JC-H= 5.4 Hz, residual H), 7.60 (s, residual H), 7.58 (s, residual H), 7.46 (s, residual H), 7.28 (d, JC-H = 4.3 Hz, residual H) 7.23 (s, residual H), 7.22 (s,14584.0034-00304 residual H) ppm;13C UDEFT NMR (151 MHz, C6D6): δ 134.4 (d, J = 5.2 Hz), 132.2 (s), 129.2 (d, JC-C= 4.8 Hz), 128.9 (t, J1C-D= 24.2 Hz), 127.7 (t, J1C-D= 24.2 Hz), 127.3 (t, J1C-D= 24.4 Hz), 127.2 (d, JC-C = 68.1 Hz), 126.6, 126.3 (t, J1C-D = 24.3 Hz), 125.6, 125.4 (t, J1C-D = 24.5 Hz), 123.8, 123.6 (t, J1C-D = 24.2 Hz), 123.5 (t, J1C-D = 24.2 Hz), 63.5 (s) ppm; IR (ATR): ^^�^^ 2267 (w), 2012 (s), 1600 (m), 1557 (m), 1439 (m), 1393 (m), 1322, (w), 1201 (m), 912 (w), 872 (w), 852 (m), 795 (m), 782 (m), 726 (s), 645 (m), 616 (m), 601 (s), 579 (m) cm-1. g) Formation of dilute molecular crystals of (diazomethylene)dinaphthalene-13C-d14in di(naphthalen-2-yl)methanone-13C-d14

[0270] Di(naphthalen-2-yl)methanone-13C-d14(0.80 grams) was dissolved in hot ethyl acetate (HPLC grade, 90 mL, 0.030 M) and the solution was allowed to cool to RT. In the dark, to this solution, 2,2’-(diazomethylene)dinaphthalene-13C-d14(4.5 milligrams, 5400 ppm) was added. Aliquots (5 milliliters, mL) of this resulting parent solution were added into 10 mL vials using a syringe equipped with a 0.45 µm pore size syringe filter and the vials were placed in a screw top jar filled with ethanol (HPLC grade). Dilute molecular crystals (parallelepiped ca.3 × 3 × 4 mm) formed within storage in the dark at RT for 7 days. The crystals were isolated in the dark, washed with ethanol (HPLC grade) and dried in vacuum. The dilute molecular crystals could be stored in the freezer (T = -22 °C) in the dark for several months without detectable degradation.

[0271] To generate the di(napthalen-2-yl)carbene-13C-d14 dopant molecules in the di(naphthalen-2-yl)methanone-13C-d14 host material, the dilute molecular crystals of (diazomethylene)dinaphthalene13C-d14in di(napthalen-2-yl)methanone-13C-d14need only be exposed to light of the correct wavelength, as described herein. Example 8: Synthesis of the compounds required to embed (4-(N-carbazoyl)phenyl)- (phenyl)carbene in (4-(N-carbazoyl)phenyl)(phenyl)methanone

[0272] The synthetic route for formation of (4-(N-carbazoyl)phenyl)-(phenyl)carbene dopant molecules in a (4-(N-carbazoyl)phenyl)(phenyl)methanone host material is shown below.14584.0034-00304a) Formation of (4-(N-carbazoyl)phenyl)(phenyl)methanone

[0273] Bis(dibenzylidenaceton)palladium(0) (0.10 equiv., 0.35 mmol, 0.20 g), sodium tert- butoxide (3.00 equiv., 10.4 mmol, 1.00 g), and toluene (11.6 mL, 0.3 M) were added to a round- bottom flask under Argon atmosphere and the solution was sparged with Ar for 5 min. The aryl bromide (1.00 equiv., 3.47 mmol, 0.90 g) and carbazole (1.00 equiv., 3.47 mmol, 0.58 g) dissolved in degassed toluene were added by syringe and the reaction was allowed to stir for ON at 80 °C in a PTFE screw cap sealed high pressure vessel. The reaction mixture was then adsorbed on Celite and purified by flash chromatography (SiO2, 30-60% CH2Cl2 / cHex) to give the product as fine yellow needles (0.69 g, 58%). Rf(SiO2, 50% CH2Cl2 / nHex) = 0.29;1H NMR (400 MHz, CDCl3) δ 8.16 (d, J = 7.8 Hz, 2H), 8.08 (d, J = 8.2 Hz, 2H), 7.92 (d, J = 6.7 Hz, 2H), 7.74 (d, J = 8.7 Hz, 2H), 7.65 (t, J = 7.4 Hz, 1H), 7.60 – 7.50 (m, 4H), 7.45 (t, J = 8.3 Hz, 2H), 7.34 (t, J = 7.5 Hz, 2H).;13C NMR (101 MHz, CDCl3) δ 195.8, 141.9, 140.5, 137.7, 136.2, 132.8, 132.06, 130.2, 128.6, 126.5, 126.4, 124.0, 120.8, 120.7, 110.0 ppm. b) Formation of (4-(N-carbazoyl)phenyl)(phenyl)methylene hydrazine14584.0034-00304

[0274] A mixture of (4-(N-carbazoyl)phenyl)(phenyl)methanone (0.800 g, 2.30 mmol), hydrazine hydrate (0.16 mL, 3.22 mmol, 1.40 equiv.), and EtOH (anhydrous, 3.22 mL, 1.00 M) was heated to 160 °C for 12 h in a high pressure vessel that was sealed with a PTFE-lined screw cap. The mixture was left to cool to RT over 1 h and stored at 7 °C for another 2 h. The colorless powder formed were filtered off and washed with cold EtOH to yield the product (0.76 g, 91%). Rf (SiO2, CH2Cl2) = 0.46;1H NMR (400 MHz, CDCl3) δ 8.19 (d, J = 7.8 Hz, 2H), 8.15 (d, J = 7.7 Hz, 2H), 7.79 (d, J = 6.9 Hz, 2H), 7.72 (d, J = 8.6 Hz, 2H), 7.65 – 7.16 (m, 26H), 5.60 (s, 2H), 5.55 (s, 2H), the product mixture contains two isomers in a ca.1:1 ratio;13C NMR (101 MHz, CDCl3) δ 148.5, 140.7, 138.6, 138.5, 132.0, 130.8, 128.53, 128.48, 127.9, 126.7, 126.3, 123.8, 120.6, 120.5, 109.9 ppm. c) Formation of (4-(diazo(phenyl)methyl)phenyl)-N-carbazole

[0275] (4-(diazo(phenyl)methyl)phenyl)-N-carbazole was prepared by modifying the procedure described in M. I. Javed and M. Brewer, Org. Synth. 2008, 85, 189. Handling and isolation of the product was done under exclusion of daylight. To a solution of dimethylsulfoxide (64.8 µL, 0.91 mmol, 1.10 equiv.) and tetrahydrofuran (anhydrous, 7.3 mL, 0.13 M) was added oxalyl chloride (74.7 µL, 0.87 mmol, 1.05 equiv.) in tetrahydrofuran (3.0 mL) at –55 °C over 5 min. The solution was maintained between –55 °C and –50 °C for 30 min while stirring and then cooled to –78 °C. A mixture of (4-(N-carbazoyl)phenyl)-14584.0034-00304 (phenyl)methylene hydrazine (0.30 g, 0.083 mmol, 1.00 equiv.) and triethylamine (0.24 mL, 1.74 mmol, 2.10 equiv.) in tetrahydrofuran (2.0 mL) was added to the reaction solution over 5 min to provide a dark purple solution containing a copious white precipitate. The reaction mixture was maintained at –78 °C for 30 min, and then filtered while cold through a medium porosity sintered-glass funnel into round-bottom flask and the solid was rinsed with tetrahydrofuran (2 × 5 mL). The filtrate was concentrated at RT by rotary evaporation to ca.2 mL and triturated with n-hexane to give a purple crystalline solid (210 mg, 70%). The following physical, chemical, and spectroscopic parameters were obtained: Rf (Al2O3 basic, n-hexane) = 0.63;1H NMR: (400 MHz, CD2Cl2) δ 8.17 (d, J = 7.7 Hz, 2H), 7.61 (d, J = 8.0 Hz, 2H), 7.53 (d, J = 7.6 Hz, 2H), 7.50 – 7.38 (m, 6H), 7.35 – 7.20 (m, 3H) ppm;13C NMR (101 MHz, CD2Cl2) δ 140.7, 134.6, 129.0, 128.9, 128.8, 127.5, 125.9, 125.79, 125.75, 125.2, 123.1, 120.0, 119.7, 109.5, 62.3 ppm. Example 9: X-ray crystal structure of (diazomethylene)dinaphthalene embedded in di(naphthalen-2-yl)methanone

[0276] A dilute single crystal of 2,2'-(diazomethylene)dinaphthalene embedded in di(naphthalen-2-yl)methanone was grown by slow vapor diffusion of ethanol into a solution of a diluted solution of 2,2'-(diazomethylene)dinaphthalene (340 ppm) and di(naphthalen-2- yl)methanone (0.035 M) ethyl acetate at RT under exclusion of light within seven days. A suitable crystal was selected and mounted on a SuperNova, Dual, Cu using Cu-Kαradiation, λ = 1.54178 Å, Atlas diffractometer. The crystal was kept at 150.00(14) Kelvin during data collection. Using Olex2, the structure was solved with the XT structure solution program using Intrinsic Phasing and refined with the XL refinement package using least squares minimization. All non-H atoms were refined with anisotropic thermal parameters. H atoms in all structures were refined in calculated positions in a rigid group model. Table 1 shows the resulting crystal data. Due to the nature of the diffraction measurement only periodically assembled molecules (i.e., the host material) appear in the crystal structure, and the carbene precursor is not observed.14584.0034-00304 Table 1: Crystal data and structure refinement for a dilute molecular crystal of 340 ppm 2,2’(diazomethylene)dinaphthalene in di(naphthalen-2-yl)methanone Empirical formula C21H14O Formula weight 282.32 Temperature / K 150.00(14) Crystal system Triclinic Space group P-1 a / Å 7.3689(4) b / Å 12.2023(6)Z 4 ρcalcg / cm31.338 μ / mm-10.628 F(000) 592.0 Crystal size / mm30.316 × 0.286 × 0.181 Radiation Cu Kα (λ = 1.54184) 2Θ range for data collection / ° 7.382 to 145.982 Index ranges -8 ≤ h ≤ 9, -15 ≤ k ≤ 13, -19 ≤ l ≤ 19 Reflections collected 9762 Independent reflections 5418 [Rint= 0.0245, Rsigma= 0.0306] Data / restraints / parameters 5418 / 0 / 398 Goodness-of-fit (GooF) on F2 (a)1.057 Final R indexes [I>=2σ (I)](b)R1= 0.0542, wR2= 0.1768 Final R indexes [all data] R1 = 0.0852, wR2 = 0.2075 Largest diff. peak / hole / e Å-30.24 / -0.17where n is the number of reflections and p is the total number of parameters refined. (b) R1 =∑||F0| − |Fc| / ∑|F0|; wR2 = [∑[w(F20 − F2c )2] / ∑[w(F20)2]]1 / 2Example 10: Generic synthetic route for the formation of nitrene dopant molecules

[0277] The general synthetic route for formation of nitrene dopant molecules in organic host materials is shown below.14584.0034-00304

[0278] The nitrene materials are prepared following similar principles as those outlined for the preparation of carbenes above. That is, a photoactive nitrene precursor is embedded in an inert matrix (i.e., host material) by substitutional doping and the activated nitrene 10 is obtained after photolysis using an appropriate light source. The nitrene may be directly linked to an aryl group or via a sulfonyl group (–SO2–) linker. Substituents at the nitrene aryl unit can be used to fine tune the thermodynamic / kinetic stability and the electronic properties. Here, again, one or more substituents R can be attached, such as one or more nitrile groups, carbonyl groups, carboxylic acid groups, ester groups, alkyl groups, aryl groups, heteroaryl groups, imine groups, amine groups, nitro groups, phosphine groups, alcohol groups, ether groups, thiol groups, thioether groups, or halogen groups. As in the case of carbenes, such groups may be selected (e.g., using computational molecular modeling, high-throughput synthesis and screening, or the like) to fine tune the electronic properties such as the ZFS, zero-phonon lines, spectral stability, and / or thermodynamic / kinetic stability.

[0279] The precursors to nitrenes (10) are aryl azides (–N3, 11), aryl isocyanates (–NCO, 12), or iminoiodinanes (13). Each of these groups can be photolyzed with UV / vis light (λ = 200 to 500 nm) to obtain a nitrene and a molecule of dinitrogen N2, carbon monoxide CO, or14584.0034-00304 aryliodide, respectively. i. embedding into molecular matrix ii. photoactivationi. embedding into molecular matrix ii. photoactivationi. embedding into molecular matrix ii. photoactivation

[0280] An exemplary route for embedding an aryl azide precursor (15) into a structurally related matrix (16) is shown below.Example 11: Formation of dilute molecular crystals of 4-azidobenzoic acid in 4- iodobenzoic acid

[0281] 4-Iodobenzoic acid (1.00 grams) was dissolved in methanol (HPLC grade, 50 mL, 0.080 M) and the solution was allowed to cool to RT. In the dark, to this solution, 4-azidobenzoic acid (0.2 M in tert-butyl methyl ether, ≥ 95.0%, 130 µL, 6600 ppm) was added. Aliquots (8 milliliters, mL) of this resulting parent solution were added into 10 mL vials using a syringe equipped with a 0.20 µm pore size syringe filter and the vials were stored in the dark at room temperature for 4 days. Dilute molecular crystals (thin rectangular plates ca.5 × 10 × 0.01 mm)14584.0034-00304 were isolated in the dark, washed with small amounts of cold methanol (HPLC grade) and dried in vacuum.

[0282] To generate the 4-nitrenebenzoic acid dopant molecules in the 4-iodobenzoic acid host material, the dilute molecular crystals of 4-azidobenzoic acid in 4-iodobenzoic acid need only be exposed to light of the correct wavelength, as described herein. Example 12: Optical crystal alignment for characterization of dopant molecules in host materials

[0283] The chemical system created by embedding a dopant molecule (or a precursor thereto) in a host material may also be referred to herein as a “dilute molecular crystal.” The dilute molecular crystals exhibit intrinsic birefringence, i.e., are optically anisotropic. This property can be used to identify a set of axes of the material (i.e., the orthogonal axial system of the optical index ellipsoid axes n1, n2, and n3) for later alignment in experimental setups. A microscope in transmission mode with two crossed linear polarizers (denoted as polarizer and analyzer) can be used to identify such axes.

[0284] Here, an example is given of a typical configuration when the crystal is rotated in the field of view. Whenever the crossed polarizer axes are parallel with the vectors n1 and n2 (or more generally to their projections in the plane normal to the viewing direction), the crystal appears dark while in cases where the crystal is positioned at all other orientations some light will pass through the analyzer and the crystal displays variable degree of brightness. The maximum brightness for the birefringent material is observed when the polarizer and analyzer axes are at a 45° angle with respect to n1 and n2. This method can also be used to examine the crystal for microscopic imperfections, such as strain-induced extended effects (e.g., edge or screw dislocations). Example 13: Preparation, photoactivation, and annealing of carbenes in host materials

[0285] After the crystal index ellipsoid has been determined macroscopically via the optical alignment method described above, a suitably sized crystal is prepared via micro-mechanic14584.0034-00304 methods (e.g., doctor blade cleaving, diamond wire saw, etc.) from a raw crystal and, if needed, the surface is cleaved or polished with suitable organic solvents (e.g., hexane, pentane, ethanol, methanol). The prepared crystal is transferred to a suitable sample holder (e.g., electron paramagnetic resonance (EPR) tube, glass sample holder, etc.) and put into the device of interest (e.g., EPR, optical instrument) with an integrated cryostat. The specimen is cooled to temperatures at which the generated carbenes or nitrenes are stable (depends on the carbene or nitrene itself and the hos). Using an integrated optical access such as an optical fiber or window the sample is irradiated with light (e.g., UV LED in a wavelength range between 300 and 400 nm) for a certain amount of time (depending on the light source output power, seconds to hours) in a macroscopic fashion to activate the complete sample. This process includes the conversion of the carbene or nitrene precursor molecules that have been embedded into a suitable matrix to their corresponding carbenes and one dinitrogen molecule (for nitrenes, carbon monoxide and aryl iodides are also possible). Alternatively, a focused laser beam which can be adjusted in lateral dimensions (x and y axis) can be used to activate regions of carbenes or nitrenes with dimensions > 200 nm.

[0286] FIG.6A shows exemplary continuous wave (cw) EPR signals associated with stepwise photoactivation of di(naphthalen-2-yl)carbene (500 ppm) in di(naphthalen-2-yl)methanone at a temperature of 25 K using a green laser (λ = 532 nm). The emergence of ground state triplet carbenes can be seen. FIG.6B shows the double integral of the cw EPR signals from FIG.6A as a function of the applied light energy and depicts the activation process for obtaining activated carbenes in a dilute molecular crystal. Such a plot can be used as a calibration curve for activating dopant molecules (e.g., carbene dopant molecules) in the dilute molecular crystals. By using such calibration curves (i.e., amount of carbenes activated per time of irradiation), a well-defined density of carbenes can be generated within a doped molecular crystal. Lithographic methods can be used to write patterns of qubits into the specimen (e.g., gradients, connected regions, lattices).14584.0034-00304

[0287] For very low temperatures (in some cases < 140 K, for other samples below 260 K) carbenes and dinitrogen molecules are kinetically trapped within the matrix, such that the molecular geometries that are typical for carbenes cannot be adopted. An annealing procedure which includes warming the sample controllably to a specimen-dependent temperature (here 140 K, for other samples > 50 K) over a sufficient amount of time (minutes to hours), triggers the reorientation of the activated carbenes and their direct molecular environment within dilute molecular crystals. The process can be monitored by cw EPR.

[0288] FIG. 7A shows exemplary cw EPR signals associated with the conversion of freshly photoactivated di(naphthalen-2-yl)carbene (340 ppm) in di(naphthalen-2-yl)methanone to an annealed form at a temperature of 140 K. The annealing process is observed as a disappearance of the cw EPR signals at 6925 G and the emergence of new signals at 7065 G. FIG.7B shows the double integral of the cw EPR signals from FIG. 7A as a function of the annealing time. The process is typically accompanied by line sharpening and can, thus, be used to further control the inhomogeneous broadening within the specimen, required for efficient single molecule manipulation via optical control. FIG.7B illustrates the emergence and disappearance of annealed and non-annealed signals, respectively, at specific times.

[0289] FIG. 7C shows exemplary cw EPR signals after photoactivation of (4-(N- carbazoyl)phenyl)(phenyl)carbene (350 ppm) in (4-(N-carbazoyl)phenyl)-(phenyl)methanone at a temperature of 25 K using a green laser (λ = 532 nm). The existence of ground state triplet carbenes can be seen. Example 14: Spin-lattice (T1) and spin-spin relaxation times for di(naphthalen-2-yl)carbene-d14in di(napthalen-2-yl)methanone-d14

[0290] Spin-lattice (T1) relaxation times were measured for a sample of di(naphthalen-2- yl)carbene-d14(5400 ppm) in di(naphthalen-2-yl)methanone-d14at 466.6 mT where the magnetic field is approximately parallel to one principal axis of the zero-field splitting tensor ^^^^0||^^^^^^^^. For the T1 measurements, an inversion recovery sequence with Hahn echo-based14584.0034-00304 detection (π —T — π / 2 — τ — π — τ — echo) was used. The measurements used rectangular 10 ns π / 2 pulses and 20 ns π pulses and 16-step phase cycling. The data were fit using a stretched exponential function to extract an average and a maximum value of T1. Deviations from monoexponential behavior of the recorded T1 curves can be associated to the inhomogeneity of the microscopic spin environments in the sample, e.g., by the non-uniform distribution of thecarbene spins. Briefly, a stretched exponential curvecan be rewritten as acontinuous distribution of monoexponential functions of which an average (T1,av) and a most likely value (T1,max) can be evaluated, dependent on T1,charand the exponent beta. FIG.8A shows an exemplary decay curve together with the stretched exponential fit curve used to extract the average and maximum T1times at a temperature of 3.5 K. FIG.8B shows an exemplary plot of the temperature dependence of the average and most likely T1times in the temperature range of 3.5 K to 25 K.

[0291] Spin-spin (T2) relaxation times were measured using the Hahn echo pulse sequence (π / 2 — τ — π — τ — echo) and fit to a stretched exponential decay, analogous to the procedure described above. The measurements used rectangular 10 ns π / 2 pulses and 20 ns π pulses and four-step phase cycle. FIG. 9 shows decay curves for protonated and deuterated dilute molecular crystals and highlights the drastic increase in T2 upon perdeuteration of the dilute molecular crystal. As an example, a most likely T2,maxof 4.78 µs and an average T2,av.of 2.67 µs was observed for a protonated sample ((di(naphthalen-2-yl)carbene (5400 ppm) in di(naphthalen-2-yl)methanone), whereas a perdeuterated sample of di(naphthalen-2- yl)carbene-d14(5400 ppm) in di(naphthalen-2-yl)methanone-d14gave a most likely T2,maxof 53.6 µs and an average T2,av. of 16.0 µs. We note that distortions to the lineshapes of these spectra may occur due to inhomogeneous broadening and electron spin echo envelope modulation (ESEEM) effects arising from the coupling of the electronic spin to nearby hydrogen and deuterium nuclei, respectively.14584.0034-00304 Example 15: Intermolecular coupling strengths for di(naphthalen-2-yl)carbene-d14in di(napthalen-2-yl)methanone-d14

[0292] Double electron-electron resonance (DEER) experiments were conducted to probe the intermolecular coupling between the randomly distributed carbenes in the dilute molecular crystal. Echo-detected field swept spectra were collected using a Hahn echo pulse sequence with a fixed τ value while sweeping the magnetic field. A large coupling of 214.6 MHz observed for the crystal orientation ^^^^0||^^^^^^^^was used due to hyperfine coupling (HFC) with the13C carbene carbon to selectively address probe and pump pulses in the DEER experiments. A π pump pulse, optimized by an adiabatic inversion chirped pulse,flips the coupling partner and thus the probe spins experience an additional decoherence due to the static dipolar coupling to the pump spins throughout the whole evolution time of the sequence. As an example, FIG.10 shows the decay of curves for experiments with pump pulse off and on together with the time elapsed for each decay where the initial signal had dropped to 1 / e. The two sets refer to different photoactivation steps (partial and full activation) which additionally highlights the tunability of the intermolecular coupling. Example 16: Preparation, photoactivation, and annealing nitrenes in host materials

[0293] FIG.11A shows exemplary continuous wave (cw) EPR signals associated with stepwise photoactivation of 4-nitrenebenzoic acid in 4-iodobenzoic acid at a temperature of 25 K using light with a wavelength of λ = 370 nm. The emergence of ground state triplet nitrenes can be seen. FIG.11B shows the double integral of the cw EPR signals from FIG.11A as a function of the activation time and depicts the activation process for obtaining activated nitrenes in a dilute molecular crystal. Such a plot can be used as a calibration curve for activating dopant molecules (e.g., nitrene dopant molecules) in the dilute molecular crystals. By using such calibration curves (i.e., amount of nitrenes activated per time of irradiation), a well-defined density of nitrenes can be generated within a doped molecular crystal. Lithographic methods can be used to write patterns of qubits into the specimen (e.g., gradients, connected regions,14584.0034-00304 lattices).

[0294] FIG. 12 shows an exemplary cw EPR signal associated with the conversion of freshly photoactivated 4-nitrenebenzoic acid in 4-iodobenzoic acid to an annealed form at RT. Example 17: Preparation of single-crystalline thin films of di(naphthalen-2-yl)methanone and integration into micro-cavities

[0295] In order to incorporate the host materials and dopant molecules described herein into the micro-cavities described herein, high-quality single-crystalline thin films must be produced. Thus, single-crystalline thin films of di(naphthalen-2-yl)methanone were prepared. Di(naphthalen-2-yl)methanone was prepared according to the procedures described herein with respect to Example 3(a). The di(naphthalen-2-yl)methanone was dissolved in 1,3,5- trimethylbenzene (mesitylene) until a saturated mixture was obtained. A droplet with a volume of a few tens of nanoliters (nL) was pipetted onto a dielectric mirror (dimensions 8 mm x 8 mm) and pressed onto the mirror with a microscope cover slip. The mesitylene was allowed to evaporate for approximately one hour, producing thin single-crystalline platelets of di(naphthalen-2-yl)methanone crystals having lateral dimensions of approximately 100 µm on a side and a thickness of approximately 300 nm. FIG.13A shows an exemplary 5x magnified microscope image of a thin film di(naphthalen-2-yl)methanone crystal on a dielectric mirror. FIG. 13B shows an exemplary 100x magnified microscope image of the same crystal on the same dielectric mirror.

[0296] Surface properties of the thin film were investigated using atomic force microscopy (AFM). The AFM results showed very homogeneous surfaces, with a roughness of approximately 1 nm on a lateral length scale of 5 µm and a roughness of approximately 5 nm on a lateral length scale of 20 µm. FIG. 14 shows an exemplary AFM image of a thin film di(napthalen-2-yl)methanone crystal on a dielectric mirror.

[0297] The di(naphthalen-2-yl)methanone thin film was placed on the dielectric mirror of an open Fabri-Perot micro-cavity. The micro-cavity showed no substantial loss in performance14584.0034-00304 when loaded with the thin film. In fact, the finesse of the micro-cavity actually increased from approximately 3,000 when unloaded to approximately 4,000 when loaded with the thin film. FIG.15 shows an exemplary image depicting the finesse of the micro-cavity in the presence of the thin film. The image was obtained by scanning the micro-cavity curved mirror over the thin film and recording the finesse of the micro-cavity.

[0298] This demonstrates that the host materials described herein can be integrated into micro- cavities without degrading the performance of such micro-cavities. Such behavior stands in stark contrast to, e.g., quantum dots, which tend to drastically degrade micro-cavity performance.

[0299] Taken together, the results of Examples 1-17 demonstrate that the host material-dopant molecule complexes described herein may be combined with micro-cavities without degrading the performance of the micro-cavities. Example 18: Manipulation of ground state triplet (GST) spin states using microwaves

[0300] The most direct method for manipulating the electronic spin states of the dopant molecules described herein is to direct an oscillating magnetic field that is resonant with the energy splittings of the electronic spin states. Such methods are commonly used in fields such as EPR. For the dopants molecules described herein, such energy splittings are generally resonant with electromagnetic radiation in the microwave range of the electromagnetic spectrum. Thus, the electronic spin states of the dopant molecules described herein may generally be manipulated by directing microwaves to the dopant molecules. In order to create entangled photons, the source of the photons (e.g., the dopant molecule described herein) should initially be put in a superposition state. Using EPR, evidence of such superposition states manifest as a free induction decay (FID) after one resonant microwave pulse and as a Hahn echo after two resonant microwave pulses. The signal and hence the superposition state are maximized when the first and second pulses are a pi / 2 and pi pulses, respectively. FIG. 16 shows an exemplary 2D Rabi plot associated with 2,2’-dinaphthylcarbene dopant molecules in14584.0034-00304 a 2,2’-dinaphtylketone host material. The Rabi plot shows how the strength of the Hahn echo varies as the length of the first and second pulses is varied. As shown in FIG.16, the Hahn echo is first maximized for a first pulse length of approximately 8 nanoseconds (ns) and a second pulse length of approximately 17 ns. Thus, the pi / 2 pulse length is approximately 8 ns and the pi pulse length is approximately 17 ns. Example 18 shows that the electronic spin states of the dopant molecules described herein can be effectively manipulated to generate superposition states. Taken together, Examples 1-18 thus demonstrate that micro-cavities loaded with host material-dopant molecule complexes similar to those described herein are likely to form nearly pure optical emitters whose electronic spin states can be manipulated at will and to thereby serve as sources of entangled photons having any desired optical state described herein.

[0301] The foregoing description has been presented for purposes of illustration. It is not exhaustive and is not limited to precise forms or embodiments disclosed. Modifications and adaptations of the embodiments will be apparent from consideration of the specification and practice of the disclosed embodiments. For example, the described implementations include hardware, but systems and methods consistent with the present disclosure can be implemented with hardware and software. In addition, while certain components have been described as being coupled to one another, such components may be integrated with one another or distributed in any suitable fashion.

[0302] Moreover, while illustrative embodiments have been described herein, the scope includes any and all embodiments having equivalent elements, modifications, omissions, combinations (e.g., of aspects across various embodiments), adaptations or alterations based on the present disclosure. The elements in the claims are to be interpreted broadly based on the language employed in the claims and not limited to examples described in the present specification or during the prosecution of the application, which examples are to be construed as nonexclusive. Further, the steps of the disclosed methods can be modified in any manner, including reordering steps or inserting or deleting steps.14584.0034-00304

[0303] The features and advantages of the disclosure are apparent from the detailed specification, and thus, it is intended that the appended claims cover all systems and methods falling within the true spirit and scope of the disclosure. Further, since numerous modifications and variations will readily occur from studying the present disclosure, it is not desired to limit the disclosure to the exact construction and operation illustrated and described, and accordingly, all suitable modifications and equivalents may be resorted to, falling within the scope of the disclosure.

[0304] Other embodiments will be apparent from consideration of the specification and practice of the embodiments disclosed herein. It is intended that the specification and examples be considered as an example only, with a true scope and spirit of the disclosed embodiments being indicated by the following claims.

Claims

14584.0034-00304 CLAIMS A system for generating entangled photons, the system comprising: at least one micro-cavity configured to support a material therein; at least one host material supported within the at least one micro-cavity, the host material comprising at least one organic molecule; and at least one dopant molecule contained in the host material, wherein: the at least one dopant molecule is associated with an electronic energy level structure that includes a ground state triplet (GST) electronic manifold and at least one excited state triplet (EST) electronic manifold.

2. The system of claim 1, wherein the at least one micro-cavity comprises a mode volume of at least 0.1 cubic micrometers (µm3). The system of claim 1 or 2, wherein the at least one micro-cavity comprises a mode volume of at most 10 µm3.

4. The system of any one of claims 1-3, wherein the at least one micro-cavity is characterized by a quality (Q) factor of at least 100,000.

5. The system of any one of claims 1-4, wherein the at least one micro-cavity is characterized by a Q factor of at most 10,000,000.

6. The system of any one of claims 1-5, wherein the at least one micro-cavity is characterized by a finesse of at least 10,000.

7. The system of any one of claims 1-6, wherein the at least one micro-cavity is characterized by a finesse of at most 100,000. The system of any one of claims 1-7, wherein the at least one micro-cavity is configured to enhance radiative decay via a zero-phonon line (ZPL) electronic transition following excitation of an electronic state of the at least one dopant molecule from the GST electronic manifold to the at least one EST electronic manifold.14584.0034-00304 9. The system of claim 8, wherein the enhanced radiative decay via the ZPL electronic transition is increased by a Purcell factor of at least 100 in comparison to a radiative decay via the ZPL electronic transition in the absence of the at least one micro-cavity.

10. The system of claim 8 or 9, wherein the enhanced radiative decay via the ZPL electronic transition is increased by a Purcell factor of at most 10,000 in comparison to a radiative decay via the ZPL electronic transition in the absence of the at least one micro-cavity.

11. The system of any one of claims 8-10, wherein the at least one dopant molecule is configured to emit at least one photon following the enhanced radioactive decay via the ZPL electronic transition.

12. The system of claim 11, wherein an optical state of the at least one photon is entangled with an electronic spin state of the at least one dopant molecule.

13. The system of claim 12, wherein the optical state comprises a polarization state of the at least one photon.

14. The system of claim 12 or 13, wherein the optical state is entangled with the electronic state by time-domain entanglement, time-domain-to-polarization entanglement, multi- photon time-domain entanglement, or multi-photon time-domain-to-polarization entanglement.

15. The system of any one of claims 1-14, wherein the host material comprises a crystalline host material, a single crystalline host material, a polycrystalline host material, a liquid crystalline host material, a powder host material, an amorphous host material, or a frozen solution host material.

16. The system of any one of claims 1-15, wherein the host material comprises a C4-C20 linear or branched alkane; an aromatic hydrocarbon; a polyaromatic hydrocarbon optionally substituted with a methylene, nitrile, carbonyl, carboxylate, alkyl, deuterated alkyl, aryl, deuterated aryl, heteroaryl, deuterated heteroaryl, borane, imine, amine, nitro, phosphine, thioether, ether, fluoro, chloro, bromo, iodo, or thiocarbonyl group; a14584.0034-00304 diarylketone; naphthalene; anthracene; benzoic acid; fluorene; biphenyl; benzene; biphenylene; ortho-terphenyl; meta-terphenyl; para-terphenyl; di(phenyl)methanone; phenanthrene; di(naphthalen-2-yl)methanone; or any partially or fully isotopically labeled derivative thereof.

17. The system of any one of claims 1-16, wherein the host material and the at least one dopant molecule comprise a thin film having a thickness of at most 100 nanometers (nm).

18. The system of any one of claims 1-17, wherein the host material and the at least one dopant molecule are deposited on the at least one micro-cavity using spin coating or chemical vapor deposition.

19. The system of any one of claims 1-18, wherein the at least one micro-cavity is formed from a substrate selected from the group consisting of silicon, mono-crystalline silicon, polysilicon, silicon on insulator, silicon carbide, and silicon nitride.

20. The system of any one of claims 1-19, wherein the at least one dopant molecule comprises an organic molecule.

21. The system of any one of claims 1-20, wherein the at least one dopant molecule comprises a carbene molecule; a nitrene molecule; a radical molecule; a biradical molecule; a diradical molecule; a diaryl diazomethane molecule; a di(napthalen-2- yl)carbene molecule; a di(phenyl)carbene molecule; or any partially or fully isotopically labeled derivative thereof.

22. The system of any one of claims 1-21, wherein the at least one dopant molecule is contained in the at least one host material at a concentration of at most 106dopant molecules per cubic micrometer (µm3).

23. The system of any one of claims 1-22, further comprising at least one optical unit configured to direct light to the at least one dopant molecule to thereby excite an14584.0034-00304 electronic state of the at least one dopant molecule from the GST electronic manifold to the at least one EST electronic manifold.

24. The system of claim 23, wherein the light comprises laser light.

25. The system of claim 24, wherein the laser light comprises a central wavelength of at least 500 nm.

26. The system of claim 24 or 25, wherein the laser light comprises a central wavelength of at most 2,000 nm.

27. The system of any one of claims 1-26, further comprising at least one electromagnetic (EM) unit configured to direct EM radiation to the at least one dopant molecule to thereby alter an electronic spin state of the at least one dopant molecule.

28. The system of claim 27, wherein the EM radiation comprises microwave (MW) radiation or radio-frequency (RF) radiation.

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