Fluorophore-based spin qubit and associated methods

Abstract

A method includes applying an optical pulse to a fluorophore to drive the fluorophore from a ground singlet state to an excited singlet state. In response, the fluorophore undergoes an intersystem crossing from the excited singlet state to a metastable triplet state. A microwave pulse is then applied to the fluorophore to at least partially transfer the fluorophore from an initial spin-qubit state to an encoded spin-qubit state. A second optical pulse may be applied to the fluorophore to drive the fluorophore from the metastable triplet state to a higher-energy triplet state, wherein the fluorophore undergoes a reverse intersystem crossing to an excited singlet state. A photon emitted by the fluorophore, in response to the fluorophore decaying from the excited singlet state to the ground singlet state, is then detected.

Description

FLUOROPHORE-BASED SPIN QUBIT AND ASSOCIATED METHODSCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Patent Application No.63 / 712,179, filed October 25, 2024, and U.S. Provisional Patent Application No. 63 / 764,132, filed February 27, 2025. Each of these aforementioned applications is incorporated herein by reference in its entirety7.STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with government support under grant number 2121044 awarded by the National Science Foundation. The government has certain rights in the invention.BACKGROUND

[0003] Qubits are the fundamental building blocks of quantum technologies. Unlike classical bits, which may exist in only two states, qubits are two-level quantum systems that may exist in a superposition of both states and may be manipulated and measured with high precision [1]. In quantum-sensing applications, these qubits are used as nanoscale probes whose quantum state may be initialized, coherently controlled, and read out, allowing them to detect minute environmental changes with exceptional sensitivity [2-7], Optically addressable qubit sensors capable of measuring nanoscale magnetic fields [11-13], electric fields

[0014] and temperature [15-17] have had an impact on the physical sciences [3, 18-21],SUMMARY

[0004] The present embodiments include a new type of spin qubit that is encoded in the metastable triplet state of a fluorophore, such as a fluorescent protein or organic dye molecule. The qubit is initialized through optical pumping from the singlet ground state into the metastable triplet state through a spin-dependent intersystem crossing. In the triplet state, a microwave pulse is used to coherently manipulate the spin state. The spin state is then read out through a second optical pulse that excites the metastable triplet state to a higher laying spin state that more readily undergoes a reverse intersystem crossing back to the singlet manifold in a process known as optically activated delayed fluorescence (OADF). The spin state is thendetermined by detecting a fluorescent photon emitted from transitions in the singlet manifold. These protein-based qubits are genetically encodable and may be readily interfaced with living systems, thereby addressing an outstanding challenge in bio-quantum sensing. Furthermore, the qubits of the present embodiments are ten times smaller than nitrogen-vacancy (NV) centers while possessing similar spin coherence.

[0005] A leading spin qubit for biological sensing is the NV center in diamond because it has a ground-state spin that may be optically initialized and read out. remains coherent at room temperature, and may be hosted in diamond nanoparticles. However, nanodiamonds have complex surface chemistry, are approximately ten times larger than an average protein, and suffer from problems general to nanoparticle labeling, which has made their cellular delivery and specific targeting an outstanding challenge. Optically addressable molecular spin qubits, such as polycyclic aromatic hydrocarbons, metalorganic complexes, and diradical systems offer potential advantages over NV centers. However, it remains an open challenge to interface these systems with biological targets and achieve the signal strengths necessary’ for biosensing. In contrast, the spin qubits of the present embodiments may be used to make a qubit sensor with a water-soluble protein that may readily be genetically encoded in biological systems.BRIEF DESCRIPTION OF THE FIGURES

[0006] FIG. 1 illustrates a fusion protein that includes a fluorophore conjugated with a target protein.

[0007] FIG. 2 shows an energy -level diagram of a fluorophore.

[0008] FIG. 3 illustrates an experimental setup for optically addressing a sample of fluorophores, in embodiments.

[0009] FIG. 4 shows photoluminescence plots that demonstrate the effectiveness of using a fluorophore as a spin qubit, in embodiments.

[0010] FIG. 5 shows simulated optically detected magnetic resonance (ODMR) spectra of fluorophores as a function of external magnetic-field strength.

[0011] FIG. 6 shows simulated and experimental ODMR spectra that are in good agreement over a range of external magnetic-field strengths.

[0012] FIG. 7 demonstrates coherent control of a fluorophore-based spin qubit by applying a microwave drive resonant with one or more transitions between triplet sublevels of the fluorophore, in embodiments.

[0013] FIG. 8 show s a plot of a spin coherence time of a fluorophore-based spin qubit, in embodiments.

[0014] FIG. 9 shows a plot demonstrating that the coherence time may be extended through the use of dynamical decoupling sequences, in embodiments.

[0015] FIG. 10 shows a plot of spin-lattice relaxation times as a function of temperature, in embodiments.

[0016] FIG. 11 shows a plot of a measurable ODMR signal for fluorophore-based spin qubits in an aqueous environment.

[0017] FIG. 12 shows a plot revealing a magnetic origin of observed resonance shifts when fluorophore-based spin qubits are in the presence of an externally applied magnetic field.

[0018] FIG. 13 shows a plot of ODMR contrast varying linearly in response to small magnetic-field perturbations.

[0019] FIG. 14A, 14B, and 14C show experimental ODMR plots from fluorophore-based spin qubits within HEK cells and E. coli cells.

[0020] FIG. 15 shows plots of fluorophore-based spin qubits being used for spin-multiplexed optical detection, in embodiments.

[0021] FIG. 16 shows an experimental apparatus for initializing, coherently controlling, and reading out fluorophore-based spin qubits, in embodiments.

[0022] FIG. 17 shows a plot of sensitivity versus qubit-target molecule distance for a variety of quantum sensors.DETAILED DESCRIPTIONIntroduction

[0023] The adoption of optically addressable qubit sensors in the life sciences has been limited, with most applications remaining at the proof-of-concept stage. The present embodiments introduce a molecule-scale genetically encodable qubit sensor that may enable ultra-sensitive measurement techniques for fundamental research and medical diagnostics that are complementary to existing quantum sensing platforms [5, 6],

[0024] Current quantum-sensing platforms offer exceptional sensitivities but are often constrained by their size, complex surface chemistry, and incompatibility with genetic techniques — limiting their use in biological measurements. Nitrogen-vacancy (NV) centers in diamond nanocrystals stand out as sensors with a certain degree of cellular del i v ery [22, 23] and targeting capability' [24, 25], However, efficient delivery and targeting mechanisms with nanoparticles has remained a significant challenge. For example, quantum dots, arguably the most advanced nanoparticle-based imaging technology, struggle to efficiently labelintracellular structures and processes in vivo, despite over a decade of intensive research [26, 27], Optically addressable molecular spin qubits, such as polycyclic aromatic hydrocarbons [28-31], metal-organic complexes [32-34] and radical systems [35, 36], offer potential advantages over solid-state systems. However, the systems examined thus far each have their own shortcomings, including low spin contrast, poor photon-emission rates, lack of water solubility, and the requirement of a solid-state host, which preclude their use for most biosensing applications (a comparison of different sensing platforms is shown in FIG. 17).

[0025] The embodiments described herein introduce fluorophores (e.g., fluorescent proteins) as optically addressable spin qubits that may be readily genetically encoded in a wide range of target sy stems. Genetic encoding enables the deterministic tagging of a target protein with a fluorophore, thereby forming a fusion protein. As a result, the fluorophore precisely mirrors the expression level, nanoscopic location, and real-time concentration of the target protein. This one-to-one correspondence between the fluorescent probe and the biological target has profoundly advanced the life sciences, offering a degree of spatial and temporal correlation that synthetic fluorophores or nanoparticles cannot achieve. Decades of biochemical research have produced an extensive library of fusion proteins in which fluorophores are deterministically linked to thousands of target proteins. Interestingly, these fluorophores exhibit a metastable triplet state, enabling an optically addressable qubit.

[0026] FIG. 1 illustrates a fusion protein 100 that includes a fluorophore 102 conjugated with a target protein 106, in accordance with some of the present embodiments. The fluorophore 102 includes a light-emitting region 104 configured to emit fluorescence when optically excited. The fluorophore 102 may be a fluorescent protein that is genetically encodable such that when introduced into a biological system (e.g., a cell), the expressed protein product forms the fusion protein 100 through conjugation with the target protein 106.

[0027] When expressed within a living cell, the fusion protein 100 maintains the structural and functional characteristics of the target protein 1 6 while endowing it with the optical and spin properties of the fluorophore 102. The fluorophore 102 operates as a spin-based quantum sensor, allowing optical initialization, coherent control, and readout of a metastable spin state within the light-emitting region 104. The fusion protein 100 may thus be used as a genetically encoded quantum-sensing probe, enabling measurements of local magnetic fields, electric fields, temperature, or strain that reflect the molecular environment of the target protein 106 within the biological system.

[0028] In other embodiments, the fluorophore 102 is used as a spin qubit for quantum computation, quantum communication, a quantum memory, or any combination thereof. Thus,the fluorophore 102 of the present embodiments is not limited to use in biological systems, and may alternatively be used for other non-biological applications.

[0029] In certain embodiments, the fluorophore 102 includes a red fluorescent protein, an orange fluorescent protein, a cyan fluorescent protein, a green fluorescent protein, or a blue fluorescent protein. The fluorophore 102 may also be a yellow fluorescent protein, such as an enhanced yellow fluorescent protein (EYFP), Topaz, Venus, or YPet. In other embodiments, the fluorophore 102 is an organic dye molecule such as rhodamine or rhodamine 6G. In still other embodiments, the fluorophore 102 may be deuterated.Fluorophore-Based Qubit and Spin Readout

[0030] FIG. 2 shows an energy-level diagram200 of the fluorophore 102, in accordance with some of the present embodiments. The fluorophore exhibits an electronic-state structure having singlet and triplet manifolds. A ground singlet state (SO) represents the electronic ground configuration of the fluorophore 102. Upon absorption of a photon (e.g., a photon near 488 nm), the fluorophore 102 is excited to a first excited singlet state (SI). Radiative relaxation from SI to SO produces the characteristic fluorescence with a typical lifetime on the order of nanoseconds.

[0031] In addition to this radiative pathway, a small fraction of an excited-state population of SI undergoes intersystem crossing (ISC) into a metastable triplet state (Tl) (e.g., via spin-orbit coupling between the singlet and triplet manifolds). A population in Tl may be excited (e.g., upon absorption of a photon near 912 nm) to a higher-energy metastable triplet state T2 that rapidly decays radiatively to the singlet manifold via reverse intersystem crossing (RISC), generating a fluorescence intensity7based on the initial spin population. Alternatively, a population in Tl may decay non-radiatively to SO.

[0032] The triplet state T 1 contains three spin sublevels, commonly labeled Tx, Ty, and Tz. The transition rates of ISC from SI to Tl may be spin-dependent such that one spin state is preferentially populated, effectively polarizing the population. Other rates may depend on the spin state, such as RISC rates and non-radiative decay rates. Such spin dependence enables the fluorophore 102 to be used as a spin qubit. F or example, if the Tzsublevel couples more strongly to the singlet manifold than the Tx or Tysublevels, molecules initially in Tz will emit stronger fluorescence. The measured fluorescence intensity7therefore provides a direct, noninvasive probe of the spin state. By modulating microwave frequency or pulse timing and recording the corresponding fluorescence, optically detected magnetic resonance (ODMR) spectra are generated, from which spin-state energies and environmental perturbations may be deduced.

[0033] FIG. 3 illustrates an experimental setup 300 for optically addressing a sample of fluorophores 302, in accordance with some of the present embodiments. The experimental setup 300 includes a confocal microscope 304 used to illuminate a sample that includes the fluorophores 302. The sample is enclosed by a top window 306(1) and a bottom window 306(2). The confocal microscope 304 focuses an optical beam on the sample, thereby illuminating an optical excitation volume 308 (i.e., the volume of the sample that overlaps the optical beam). The experimental setup 300 may further be outfitted with a patterned microwave structure 310 used to drive the fluorophores 302, e.g., between sublevels of the metastable triplet state Tl. In certain embodiments, the patterned micro wave structure 310 is a lithographically patterned micro wave loop. In some embodiments, the experimental setup 300 includes an O-ring 312.

[0034] In some embodiments, a fluorophore includes an EYFP and a confocal microscope is used to optically address a metastable triplet spin state of the EYFP (see the energy-level diagram 200 of FIG. 2 and the experimental setup 300 of FIG. 3). The lightemitting region of the EYFP (e.g., the light-emitting region 104 of the fluorophore 102 in FIG. 1) is embedded within its -barrel structure, which exhibits a high absorption crosssection. high quantum yield, and short fluorescence lifetime. The EYFP spin state may be initialized by applying a 488-nm optical pulse that cycles the EYFP between the ground (SO) and first-excited (SI) singlet states, after which intersystem crossing (ISC) populates the metastable triplet state (Tl). The ISC process is strongly dependent on spin projection, resulting in a buildup of spin polarization within the Tl state. Time-dependent density functional theory (TDDFT) calculations indicate that the spin density of the metastable triplet state Tl is substantially delocalized within the light-emitting region of the EYFP. The presence of this metastable triplet state, however, introduces challenges for use in spin-qubit applications. For example, direct readout of the spin state via spontaneous decay from the Tl state is generally impractical because spin depolarization occurs at most temperatures on a timescale that is short relative to the millisecond-scale lifetime of the Tl state [10, 38], In addition, the extended lifetime of the Tl state may limit the repetition rate of measurement sequences, thereby constraining achievable sensitivity.

[0035] These challenges may be addressed by employing a photophysical technique to reduce the lifetime of the Tl state and enable on-demand spin readout. For example, an optical pulse having a wavelength of approximately 912 nm may be applied to drive the fluorophore from the Tl state to a higher-lying triplet state, such as a second triplet state (T2). TDDFT calculations suggest that the higher-lying triplet state corresponds to the T2 state. RISC from the T2 state to the singlet manifold may occur at an accelerated rate relative to the Tl state.Following RISC, the fluorophore emits a delay ed-fluorescence photon during a transition from the first-excited singlet state SI to the ground singlet state SO. The timing of the delay ed-fluorescence photon provides information indicative of the spin projection of the T1 state because the RISC rate is spin-dependent. Readout using this optically activated delayed-fluorescence (OADF)

[0039] technique may be approximately three orders of magnitude faster than readout via spontaneous decay of the T1 state. Furthermore, temporal separation of delayed fluorescence from prompt fluorescence may provide spin readout substantially free of autofluorescence background.

[0036] An OADF spectrum obtained from a fluorophore comprising an EYFP closely resembles a standard fluorescence spectrum measured at approximately 80 K. This similarity indicates that delay ed-fluorescence photons are emitted during a transition from a first excited singlet state (SI) to a ground singlet state (SO). Furthermore, the wavelength of the intensity maximum observed at cryogenic temperature and at room temperature is substantially consistent, suggesting that the fluorophore maintains structural integrity in the vicinity of the light-emitting region after being cooled to cryogenic temperatures.

[0037] The application of a microwave drive demonstrates that the spin sub-level populations may be coherently manipulated. For example, after initializing the spin qubit in the metastable triplet state Tl, a microwave IT -pulse may be applied to induce population transfer between magnetic sublevels of the Tl state (e.g., from Tzto Tx). Detection of OADF photons emitted in response to a subsequent optical pulse (e.g.. a 912-nm pulse) may provide a spinstate readout. In some implementations, the detected OADF signal exhibits a spin contrast of up to approximately 20% for a transition between a first magnetic sublevel (Tx) and a third magnetic sublevel (Tz), and up to approximately 10% for a transition between a second magnetic sublevel (Ty) and the third magnetic sublevel (Tz), when measured at a temperature of about 80 K, as shown in FIG. 4.Optically Detected Magnetic Resonance

[0038] Energy levels of metastable triplet spin states may be obtained via ODMR spectroscopy. In general, a spin-1 system has a Hamiltonian of the formH = hD ^ - ^ + hE^ - S^ +YelS - B,0)where h is Planck's constant divided by 2n. D and E are the zero-field splitting parameters, Yei= — 2TT) X 28.025 GHz-T1is the gyromagnetic ratio of an electron, S = (Sx, Sy, Sz) is thespin vector, and B is the magnetic field. For an ensemble of randomly oriented EYFP molecules, the zero-field splitting parameters D and E may be obtained by averaging the theoretical spectrum over all possible molecular orientations and fitting this averaged spectrum to an experimentally measured ODMR signal. The result is a powder spectrum and the fitting may be performed in regions of low magnetic field, where uncertainty in the field calibration is small.

[0039] The zero-field splitting parameters for EYFP are determined to be D = (2?r) X (2.356 ± 0.004) GHz and E = (2?r) X (0.458 ± 0.003) GHz. These experimentally obtained values correspond closely to results derived from ab initio calculations performed using a B3LYP-optimized geometry and the roB97X-D3 functional, which yield DDFT= (2rr) X 2.42 GHz and EDFT= (2rr) X 0.57 GHz. The fitted zero-field splitting parameters D and E may be used to simulate the ODMR spectrum of the sample under an applied magnetic field. In such simulations, the theoretical spectra are averaged over all possible molecular orientations (powder-averaged) and the corresponding transition frequencies are calculated as a function of magnetic-field strength. The simulated spectra reproduce the experimentally observed field-dependent broadening and asymmetric resonance profile (see FIG. 5). The model also extrapolates well to higher magnetic fields, as demonstrated at a magnetic-field strength of 34.1 mT (see FIG. 6).Qubit Coherence

[0040] Coherent control of the fluorophore spin sy stem may be achieved by applying a microwave drive that is resonant with one or more transitions between triplet sublevels of the fluorophore, as shown in FIG. 7. When the system is driven at a frequency corresponding to the Tx-Tz transition, coherent Rabi oscillations are observed between the spin sublevels. In one example, excitation of EYFP molecules at a resonant microwave frequency produces Rabi oscillations having a spin contrast of approximately 20%. The oscillations exhibit a damped envelope, with a decay rate that increases with the Rabi frequency. This damping behavior arises primarily from the random orientation of the molecular dipoles within the ensemble and from detuning effects associated with the spatial inhomogeneity of the applied microwave field.

[0041] FIG. 8 shows a spin coherence time (T2) of the fluorophore qubit measured using a Hahn-echo pulse sequence to refocus dephasing induced by quasi-static magnetic fields. In this example, the Hahn-echo coherence time (T2Hahn) is approximately 1.5 ± 0.2 ps. As the magnitude of an applied static magnetic field increases, the Hahn-echo coherence time decreases to approximately 140 ± 30 ns at 7 mT. This dependence on magnetic-field strengthreflects the field sensitivity of the Tx-Tzresonance, which behaves as a clock-like transition [42, 43] exhibiting a dephasing rate l / T2Hahnoc yeff=yBz / ((E / yei)2+ Bz2) proportional to the effective gyromagnetic ratio (yeff) °f the triplet manifold. Experimental results confirm that near this clock-transition regime, qubit dephasing remains primarily limited by magnetic-field fluctuations rather than by electric-field noise, as shown in the inset of FIG. 8.

[0042] FIG. 9 shows that the coherence time may be extended through the use of dynamical decoupling sequences, such as the Carr-Purcell-Meiboom-Gill (CPMG) protocol. Application of a CPMG sequence with 240 n-pulses enhances the measured coherence time (T2cpMG) to approximately 16 ± 2 ps under an applied field of 2.7 mT, representing an improvement of roughly fifteenfold relative to the Hahn-echo result. Performing CPMG measurements as a function of pulse number N yields a power-law scaling of T2CPMGoc y(o.4o±o.o3) (see tpe |nsel of pjQ 9), consistent with an environmental magnetic-noise spectrum exhibiting a powder spectral density S(co)~ci)-2 / 3, where higher-frequency fluctuations are progressively suppressed by the decoupling filter function [44, 45],

[0043] FIG. 10 shows one example of fitting for a spin-lattice relaxation time. The spinlattice relaxation time (7 ) of the fluorophore qubit may also be determined, as well as its dependence on temperature (T), by monitoring the decay of spin polarization between the Tzand Txsublevels as a function of time delay following initialization. At a temperature of approximately 80 K, the polarization decays exponentially with a characteristic lifetime of 141 ± 5 ps, corresponding to the Ti relaxation time. For integer-spin systems such as the EYFP triplet state, the depolarization rate is described by the empirical relation1 / ^ = A T + B T7, (2) where A and B are coefficients associated with direct and Raman relaxation processes, respectively

[0041] (see the inset of FIG. 10). The experimental data are well described by this model when A and B are treated as free parameters, although an unambiguous identification of the exact relaxation mechanisms requires a more thorough investigation.

[0044] Collectively, these measurements demonstrate that the fluorophore qubit exhibits coherent spin control, measurable Rabi dynamics, and microsecond-scale coherence and relaxation times under cryogenic conditions. The results confirm that optically addressable spin coherence may be achieved in a genetically encoded fluorophore, thereby enabling practical quantum sensing and information-processing applications within biological environments.Operation at Room Temperature

[0045] At room temperature, the characteristic depolarization time of the triplet spin state of the fluorophore is shorter than the duration of a typical measurement cycle. As a result, efficient spin initialization and readout are limited by rapid relaxation of the triplet sublevels. Nevertheless, finite spin-dependent optical contrast may be obtained at room temperature by simultaneously applying the optical readout pulse with the applied microwave drive. In certain embodiments, simultaneous application of the readout and microwave pulses produces a measurable ODMR signal in aqueous environments despite the short triplet relaxation time, as shown in FIG. 11.

[0046] The presence of this finite contrast may be understood as follows. In the absence of a resonant microwave field, the readout pulse preferentially depletes the Txand Tysublevels of the triplet manifold, which possess shorter effective lifetimes relative to the Tzsublevel. When a resonant microwave drive is applied to the Tx-Tzor Ty-Tztransitions, the microwave field mixes the spin populations among all three sublevels. This mixing accelerates the depletion of all triplet sublevels, resulting in an enhanced OADF signal whose time dependence reflects the combined decay lifetimes of the ensemble. The observed ODMR contrast thus arises from spin-dependent optical pumping within the triplet manifold.

[0047] FIG. 12 reveals that a magnetic origin of an observed resonance may be verified by repeating the measurement in the presence of an externally applied magnetic field. Under an applied field, the resonance frequency of the ODMR feature shifts in a manner consistent with Zeeman splitting of the triplet sublevels, confirming that the detected contrast originates from magnetic-field-dependent spin transitions.

[0048] In certain embodiments, inspired by an approach adapted from the atomic-clock community

[0046] , the fluorophore qubit functions as a room-temperature direct-current (DC) magnetic-field sensor. Detection of small static magnetic fields is achieved by monitoring differential fluorescence at two distinct microwave frequencies positioned above and below a target resonance (e.g., the two black circles on the right-hand-side of FIG. 12 positioned above and below the Tx-Tztransition). Variations in the external magnetic field produce corresponding frequency shifts in the resonance condition, resulting in a measurable change in the differential ODMR contrast. This ODMR contrast varies linearly in response to small magnetic-field perturbations (8B), as shown in FIG. 13.

[0049] From these differential ODMR measurements, a magnetic-field sensitivity on the order of 2.7 mT Hz1 2may be estimated for the ensemble of EYFP molecules under the specified optical and microwave drive conditions. This value represents the ensemble-averagedmagnetic-field sensitivity of the detected fluorophore population, normalized to the number of emitters contained within the optical excitation volume. Because of the clock-like transition near zero magnetic field, optimal sensitivity may be achieved under a small applied bias field.

[0050] These results demonstrate that the fluorophore qubit remains optically addressable under ambient conditions and may sen e as a magnetically sensitive probe even in aqueous or biologically relevant environments. The capability for room-temperature magnetic sensing with genetically encodable fluorophores establishes a pathway toward in-vivo quantum sensing and nanoscale biomagnetic field imaging.Qubit Sensor Expressed in Cells at Room Temperature

[0051] In certain embodiments, a fluorophore qubit is genetically encoded and expressed within living cells, enabling in situ spin readout and magneto-optical characterization in biological environments. Experiments were demonstrated using human embryonic kidney (HEK) 293T cells and BL21(DE3) Escherichia coli (E. coli) cells that express the fluorophore EYFP.

[0052] In one embodiment, (HEK) 293T cells were cultured on a sapphire substrate and imaged using confocal fluorescence microscopy. Fluorescence imaging confirmed that the expressed fluorophore remained localized within the cells and retained high emission intensity. After cooling the sample to approximately 175 K, confocal fluorescence scans were obtained and correlated with room-temperature wide-field fluorescence images, confirming that the fluorophore remained confined to the same cellular regions following cooling. Measurements conducted over multiple bright regions containing cells produced an ODMR signal (see FIG.14A) corresponding to the EYFP triplet spin transitions. The observed OADF signal spatially coincided with the fluorescent regions identified in both wide-field and confocal images.

[0053] Measurements obtained from regions outside of the cells exhibited only a weak background fluorescence and showed no discernible spin-resonance signature, indicating that the detected ODMR contrast originated from intracellular fluorophores rather than from extracellular EYFP molecules. In further embodiments, applying resonant microwave excitation to the same cellular regions generated Rabi oscillations between triplet sublevels (see FIG. 14B). The ODMR and Rabi signals obtained from the cellular samples were consistent with those measured in purified EYFP, demonstrating that the spin and optical interface remains functional when the fluorophore is expressed within a cellular environment.

[0054] Comparison of the OADF signal measured in HEK cells with that of a calibrated EYFP reference sample allows estimation of the intracellular EYFP concentration. In oneembodiment, the EYFP concentration within the transfected HEK 293T cells was 11 ± 7 pM, consistent with concentrations expected from transient transfection

[0047] ,

[0055] In another embodiment, the fluorophore qubit is expressed in living bacterial cells to demonstrate operation at room temperature. E. coll cells were collected and transferred directly onto the microscope sample stage for measurement. ODMR spectra, recorded in these bacterial cells at room temperature, both in the absence and presence of an externally applied magnetic field, exhibited high spin-dependent contrast (see FIG. 14C). The robust contrast was facilitated by the time-delayed nature of the OADF signal, which suppresses autofluorescence background signals originating from cellular environment.

[0056] FIG. 16 shows an experimental apparatus 1600 for initializing, coherently controlling, and reading out a sample of fluorophore-based spin qubits, in accordance with some of the present embodiments. The experimental apparatus 1600 employs two diode lasers, a 488-nm excitation laser and a 912-nm readout laser, each gated by an acousto-optic modulator (AOM). The modulated laser beams are coupled into single-mode optical fibers, which deliver light to a movable optical assembly configured to scan over the sample.

[0057] The two laser wavelengths are combined using dichroic mirrors such that both beams are spatially overlapped and focused onto a common spot within the sample by a microscope objective (for example, 60 x magnification, 0.7 numerical aperture). The optical powers at the back aperture of the objective are approximately 0.4 mW for the 488-nm beam and 65 mW for the 912-nm beam.

[0058] Fluorescence emitted from the sample passes back through the same optical path and is reflected by the dichroic mirrors into a collection channel. Optical filters remove residual excitation light, and the collected fluorescence is coupled into a single-mode fiber, which serves as a confocal pinhole to reject out-of-focus background. This configuration ensures that the detected signal originates primarily from fluorophores located within the focal region where laser intensity is highest. The output of the collection fiber is directed through a second AOM for gating and then detected either by a single-photon counting module or, in certain embodiments by a spectrometer for spectral analysis.

[0059] The sample is mounted within an imaging cell having an approximate internal volume of 5 pL. The cell encapsulates the fluorophore sample between two sapphire windows approximately 500 pm thick, sealed with an O-ring to maintain mechanical stability and prevent contamination. The sapphire substrate nearest to the cry ostat window is photolithographically patterned with microwave loop structures formed by a lift-off fabrication process.

[0060] The sample may include soluble fluorophores dissolved in a liquid solute, suchas water. The sample may include soluble fluorophores dissolved in a solid solute, such as ice. The sample may be at a cry ogenic or room temperature.

[0061] The imaging cell is installed within a vacuum cryostat evacuated to a pressure below approximately 1 Torr. The sample temperature is controlled using a programmable cooling profile. An external DC magnetic field is applied to the sample using a permanent magnet mounted on a motorized translation stage positioned outside the cryostat.

[0062] Microwave signals are generated by a radio-frequency system-on-chip (RFSoC) source and delivered to the microwave loop structures via a chain of power amplifiers. The total microwave power at the input to the cryostat is approximately 1 W. The microwave field generated by the loop structure provides the oscillating magnetic component required to drive spin transitions between magnetic sublevels of the metastable triplet manifold.

[0063] These results confirm that fluorophore qubits may be expressed, initialized, manipulated, and optically read out within living cells, maintaining their spin-dependent optical properties under physiological or cryogenic conditions. The compatibility of the fluorophore qubit with standard biological expression systems provides a platform for in-vivo quantum sensing and intracellular metrology.Spin-Multiplexing of Optical Probes

[0064] Fluorescence microscopy is a ubiquitous tool in the biological sciences. It allows for the detection of specific molecular targets with a signal-to-noise ratio much higher than absorption- or scattering-based measurements. However, one limitation of fluorescence microscopy is the number of molecular targets that can be imaged simultaneously.

[0065] Multiplexed imaging of optically-emissive fluorescent probes, or fluorophores, is limited by the probes' range of emission wavelengths and their optical linewidths (usually tens to hundreds of nanometers). Fluorescence microscopes are generally incapable of imaging more than approximately five different probes. There are many technologies that attempt to address this problem, but they all have significant drawbacks, such as requiring cell fixation, or not being robust to high densities of fluorescent labels.

[0066] In some embodiments, a method to increase the number of addressable imaging channels is to multiplex fluorescent probes in the microwave domain rather than the optical domain. Optically emissive probes with a spin degree of freedom may be multiplexed by their spin-resonance spectra rather than their optical emission. ODMR measurements may be conducted to image such a probe, provided its optical emission is coupled to its spin state. ODMR has been performed on many optically-emissive probes. In some embodiments, thefluorescent probe (i.e., the fluorophore) is a water-soluble molecule in a solution phase. The subsequent discussion concerns probes with optically-detected magnetic resonance.

[0067] Multiplexing based on a probe’s spin state may be achieved with lock-in detection by driving the spin state with a frequency-modulated microwave drive, and simultaneously detecting the modulated optical signal. Applying a micro wave frequency drive signal near the spin-resonance frequency of a probe may cause its emission to become brighter or dimmer. If the microwave signal is amplitude modulated, the optical emission of the probe will also be modulated. Using lock-in detection, the optical signal of the specific probe that is being addressed by the microwave signal may be extracted from other unmodulated optical signals. The microwave drive signal frequency may be set to the spin-resonance frequency of any arbitrary probe to uniquely image it.

[0068] The microwave signal modulation source may be a sine, square, or other waveform, depending on the particular detection method. For example, for optical detection using a photodiode, the microwave signal may be amplitude modulated using a sine wave, and subsequently detected from the electrical photodiode signal. With a widefield detector like a camera, square-wave modulation may be more suitable. If the microwave signal is modulated with a square wave, subtracting camera images with the microwave signal on versus off will produce an image that gives contrast to the unique probe resonant with the drive frequency.

[0069] To multiplex a set of probes, each probe must have a unique, differentiable spinresonance spectral fingerprint, and have ODMR. A non-exhaustive list of systems that may satisfy these criteria are: (i) a set of probes with unique spin zero-field splitting parameters, such as those shown in FIG. 15, and (ii) a hybrid system including an optically-active probe (e.g. anitrogen-vacancy center) fused with a magnetic dipole that creates a local magnetic field fixed to the probe, changing the spin-resonance spectra of the probe.

[0070] There are several advantages to multiplexing based on spin resonance as opposed to optical wavelength. First, spin-resonance linewidths may be on the order of megahertz, while having GHz-scale spin-resonance frequencies. For example, given a 1-GHz tuning range and a 10-MHz linewidth, approximately (1 GHz) / (10 MHz) = 100 unique probes may be differentiated. Second, tunable microwave sources are significantly cheaper than tunable lasers or optical filters, potentially allowing for more sophisticated spectral separation. By sweeping the microwave drive frequency in increments smaller than the probe linewidth and using hyperspectral unmixing methods, even probes with significantly overlapping spinresonance spectra may be resolved.

[0071] Using spin-based multiplexing, the number of available multiplexing channelscould be increased several-fold over current methods, with far fewer experimental hindrances than competing techniques. It also has a built-in rejection mechanism for background optical signals because the measurement is performed using lock-in detection, which may yield an increase in the signal-to-noise ratio. The optical components necessary for such an imaging apparatus may be even less demanding than a multispectral approach, since only a single set of excitation and collection optics are required. Meanwhile, the proliferation of high-performance microwave electronics and computing power means that the additional components required for the generation of microwave signals and signal-processing would be low-cost.Discussion and Outlook

[0072] The embodiments described herein establish fluorescent proteins as a new class of genetically encodable spin qubits. In certain implementations, an ensemble of EYFP molecules exhibits an upper-bounded alternating-current (AC) magnetic-field sensitivity of approximately 5.11 pT Hz'1 2at liquid-nitrogen temperatures and an upper-bounded DC sensitivity of approximately 2.7 mT Hz1 2at room temperature. These sensitivities are determined from ODMR measurements normalized to the number of fluorophores contained within the optical excitation volume.

[0073] For reference, a19F nuclear spin positioned approximately 5 nm from the EYFP qubit — a typical separation for an EYFP fusion protein

[0048] — would generate a magnetic field of about 18 nT at the qubit's location. For a nuclear polarization fraction p. this corresponds to a19F number sensitivity of (94 / p) pmol Hz'1. If an electron spin were instead detected, the corresponding electron-spin sensitivity would be (200 / p) amol Hz'1. Although these sensitivities are presently below those of state-of-the-art NV centers in bulk diamond sensors

[0049] , the ability to genetically encode and express the qubit within living cells provides substantial advantages for in-vitro and in-vivo quantum sensing without the need for exogenous nanofabrication.

[0074] In certain embodiments, the EYFP-based qubit sensor may enable microscale electron paramagnetic resonance (EPR) detection within biological systems. For instance, genetic fusion of the EYFP-based sensor to target proteins may facilitate probing the oxidation states of metalloproteins, enable double-electron-electron-resonance-style distance measurements, and permit investigation of drug-binding mechanisms.

[0075] The genetic encodability of the fluorophore qubit allows deterministic tagging of thousands of target proteins within a cell, tissue, or whole organism using existing expression libraries. At sufficiently high concentrations of target proteins, this approach may enableexperiments at the single-cell level. Furthermore, with substantial improvements in sensitivity, the detection of nuclear magnetic resonance (NMR) spectra may become feasible. This would offer insights into posttranslational modifications, such as phosphorylation events, conformational changes of15N-labeled proteins, and protein-ligand interactions involving opcontaining drugs. Realizing these long-term goals will require further improvements in photostability and sensitivity, as well as the development of new quantum sensing protocols.

[0076] The ability to optically detect and control the spin state of fluorophores (e.g., fluorescent proteins) also introduces possibilities for multiplexed optical imaging (see FIG. 15 and discussion above). For example, multiplexed detection of different fluorophores using more than just their emission spectra, has been demonstrated using additional degrees of freedom such as their fluorescence

[0050] or triplet lifetimes

[0051] , In one embodiment, the narrow roomtemperature ODMR resonances of a fluorophore qubit may serve as an additional dimension for multiplexed imaging. Assuming a 50-MHz ODMR linewidth and achievable shifts in the zero-field splitting parameters on the order of several hundred megahertz, such an approach may allow for up to 20 distinguishable “colors” (e.g., optical channels).

[0077] Combining this with the existing library of distinct fluorophores having distinct emission spectra may enable up to 100 orthogonal colors, with additional colors accessible through T1 lifetime-based multiplexing

[0051] , Engineering fluorescent proteins with tunable zero-field splittings and T1 lifetimes may be achieved through modifying the fluorophore’s primary structure in the vicinity of the light-emitting region

[0051] , Furthermore, taking advantage of the Zeeman shift in an external magnetic-field gradient enables parallelized superresolution imaging, similar to magnetic resonance imaging

[0052] , Realizing these novel imaging modalities will require advances in reducing photobleaching, improving spin readout efficiency, engineering fluorescent proteins with tunable zero-field splitting, and creating well-controlled magnetic-field gradients.

[0078] Enhancements in qubit sensitivity may be achieved by improving coherence or spin readout. At liquid-nitrogen temperatures, qubit coherence is limited by magnetic-field noise, which may drastically be reduced by substituting nearby proton spins with deuterium, resulting in expected coherence times approaching 100 ps [53. 54], Individual EYFP molecules are routinely detected in single-molecule microscopy

[0055] , This suggests that a readout signal may be improved by several orders of magnitude. The initialization of the qubit requires an efficient population transfer from the singlet ground to the metastable triplet state. This may be accomplished by optimizing the excitation conditions and reducing unwanted RISC caused by the initialization laser [38, 56], Furthermore, OADF readout yields at most one photon permolecule. This limitation may be addressed by exciting EYFP with 488-nm photons in the singlet state, enabling multiple fluorescent photons to be emitted per readout cycle. This fluorescent cycling may result in an up to 300-fold increase in photon count (the ultimate limit is set by a ratio of triplet yield [38, 39]). Optimizing the imaging optics may further improve per-molecule collection efficiency by a factor of 810.

[0079] Collectively, these improvements would yield at least a 500-fold improvement in AC and DC sensitivity. In addition to the above approaches for increasing the readout signal, integrating the present embodiments with existing single-molecule microscopy techniques may enable the detection of individual EYFP qubit sensors

[0057] , paving the way to single-molecule spin experiments. Finally, photobleaching poses the biggest limitation. However, over the years, different strategies have been developed to address photobleaching in fluorescence microscopy. Many of these strategies may be applied to the present embodiments. This includes purging oxygen from the cell media or the addition of an oxygen scavenger as well as replenishing bleached fluorophores, in an approach similar to Point Accumulation for Imaging in Nanoscale Topography (PAINT)

[0058] ,

[0080] The optically activated delayed fluorescence readout described herein is broadly applicable to other fluorescent molecules that have a singlet ground and excited state coupled to a metastable triplet state. In many organic dyes and fluorescent proteins, reverse intersystem crossing from triplet to singlet states has been observed [39, 40], suggesting that a wide variety of fluorophores may function as spin qubits under similar excitation conditions. Computational modeling methods disclosed herein may be used to predict optical transitions, zero-field-splitting parameters, and suitable candidate molecules.

[0081] The demonstration of optical initialization, coherent control, and readout of EYFP triplet spins with coherence times exceeding 15 ps establishes fluorophores (e.g., fluorescent proteins) as a new class of qubits. Fluorophore-based qubits open the door to applying both quantum information science and bioengineering strategies for further development. The quantum information science and bioengineering fields have developed a diverse array of approaches to engineering complex systems. For example, the creation of highly regular structures through molecular self-assembly

[0059] may allow for the engineering of one-, two-, and three-dimensional paramagnetic molecular arrays

[0060] , The many-body dynamics of these spin systems may be optically read out with a fluorophore-based qubit. Furthermore, traditional quantum engineering approaches to improving optical properties and spin coherence rely on gaining an understanding of qubit physics from first principles. Genetically-encodable qubits like EYFP may be engineered using directed evolution, a black-box optimization approach that uses high-throughput screening of protein variants. Directed evolution of fluorescent proteins has resulted in a vast array of different spectral properties and functions, which highlight their tunability and rich photo-physics

[0061] , Directed evolution on an EYFP qubit may be used to optimize its optical and spin properties and even reveal unexpected insights into qubit physics. Fluorophore-based qubits are positioned to take advantage of techniques from both quantum information sciences and bioengineering, with potentially transformative possibilities in both fields.Combinations of Features

[0082] Features described above as well as those claimed below may be combined in various ways without departing from the scope hereof. The following examples illustrate possible, non-limiting combinations of features and embodiments described above. It should be clear that other changes and modifications may be made to the present embodiments without departing from the spirit and scope of this invention:

[0083] (Al) A method includes applying an optical pulse to a fluorophore to drive the fluorophore from a ground singlet state to an excited singlet state. The fluorophore undergoes an intersystem crossing from the excited singlet state to a metastable triplet state. The method further includes using the fluorophore in the metastable triplet state as a spin qubit.

[0084] (A2) In the method denoted (Al), said using the fluorophore includes using the spin qubit for quantum sensing.

[0085] (A3) In the method denoted (A2), said using the spin qubit for quantum sensing includes using the spin qubit to sense a magnetic field, an electric field, a strain, or a temperature.

[0086] (A4) In any of the methods denoted (Al) to (A3), said using the fluorophore includes using the spin qubit for quantum computation, quantum communication, a quantum memory, or any combination thereof.

[0087] (A5) In any of the methods denoted (Al) to (A4), said using the fluorophore as a spin qubit includes optically reading out a state of the spin qubit.

[0088] (A6) In any of the methods denoted (Al) to (A5), the fluorophore undergoes the intersystem crossing from the excited singlet state to an initial spin-qubit state. The initial spinqubit state includes one of first, second, and third magnetic sublevels of the metastable triplet state. The method further includes applying a microwave pulse to the fluorophore to at least partially transfer the initial spin-qubit state to an encoded spin-qubit state. The encoded spinqubit state has a non-zero population in one or both of the second and third magnetic sublevels.

[0089] (A7) In the method denoted (A6), the first magnetic sublevel includes a Txstate, the second magnetic sublevel includes a Tystate, and the third magnetic sublevel includes a Tzstate.

[0090] (A8) In any of the methods denoted (Al) to (A7), the excited singlet state includes a first excited singlet state, and the metastable triplet state includes a first metastable triplet state.

[0091] (A9) In any of the methods denoted (Al) to (A8), the fluorophore is soluble in a liquid solute.

[0092] (A10) In the method denoted (A9), the liquid solute includes water.

[0093] (All) In the method denoted (A9), the fluorophore is dissolved in the liquid solute.

[0094] (A12) In the method denoted (Al 1), the liquid solute is at room temperature.

[0095] (Al 3) In the method denoted (All), the liquid solute is at a cryogenic temperature.

[0096] (A14) In any of the methods denoted (Al) to (A13), the fluorophore is soluble in a solid solute.

[0097] (Al 5) In the method denoted (A14), the solid solute includes ice.

[0098] (Al 6) In the method denoted (A14), the fluorophore is dissolved in the solid solute.

[0099] (Al 7) In the method denoted (Al 6), the solid solute is at room temperature.

[0100] (Al 8) In the method denoted (A16), the solid solute is at a cryogenic temperature.

[0101] (Al 9) In any of the methods denoted (Al) to (Al 8), the fluorophore is located within a cell.

[0102] (A20) In any of the methods denoted (Al) to (A19). the fluorophore includes a fluorescent protein.

[0103] (A21) In the method denoted (A20), the fluorescent protein includes a red fluorescent protein, an orange fluorescent protein, a cyan fluorescent protein, a green fluorescent protein, or a blue fluorescent protein.

[0104] (A22) In the method denoted (A20), the fluorescent protein includes a yellow fluorescent protein.

[0105] (A23) In the method denoted (A22), the yellow fluorescent protein includes enhanced yellow fluorescent protein (EYFP), Topaz, Venus, or YPet.

[0106] (A24) In any of the method denoted (Al) to (A23), the fluorophore includes anorganic dye molecule.

[0107] (A25) In the method denoted (A24), the organic dye molecule includes rhodamine.

[0108] (A26) In the method denoted (A25), the rhodamine includes rhodamine 6G.

[0109] (A27) In any of the methods denoted (Al) to (A26), the fluorophore is deuterated.

[0110] (A28) In any of the methods denoted (Al) to (A27), said applying the optical pulse includes applying the optical pulse to a plurality of fluorophores to drive each fluorophore, of the plurality of fluorophores, from the ground singlet state to the excited singlet state. The fluorophore undergoes the intersystem crossing from the excited singlet state to the metastable triplet state. Additionally, said using the fluorophore includes using the plurality of fluorophores in the metastable triplet state as an ensemble of spin qubits.

[0111] (Bl) A method for measuring a metastable triplet state of a fluorophore includes applying a microwave pulse to the fluorophore to coherently redistribute spin sub-level populations of the metastable triplet state, applying an optical pulse to the fluorophore to excite one or more of the spin sub-level populations to a higher-energy triplet state of the fluorophore. The fluorophore undergoes a reverse intersystem crossing from the higher-energy triplet state to an excited singlet state of the fluorophore. The fluorophore decays from the excited singlet state to a ground singlet state of the fluorophore. The method further includes detecting a photon emitted by the fluorophore when the fluorophore decays from the excited singlet state, and determining a spin state of the metastable triplet state based on at least a time at which the photon was detected.

[0112] (B2) In the method denoted (Bl), the fluorophore decays from the excited singlet state to an intermediate excited singlet state, and the fluorophore decays from the intermediate excited singlet state to the ground singlet state. Additionally, said detecting the photon includes detecting one or both of (i) a photon emitted by the fluorophore when the fluorophore decays from the excited singlet state and (ii) a photon emitted by the fluorophore when the fluorophore decays from the intermediate excited singlet state.

[0113] (B3) In the method denoted (B2). the metastable triplet state is a first triplet state of the fluorophore, the higher-energy triplet state is a second triplet state of the fluorophore, the excited singlet state is a second excited singlet state of the fluorophore, and the intermediate excited singlet state is a first excited singlet state of the fluorophore.

[0114] (B4) In any of the methods denoted (Bl) to (B3), the method further includes optically pumping the fluorophore between the ground singlet state and the excited singlet state.and said detecting the photon includes detecting several photons emitted by the fluorophore during said optically pumping.

[0115] (B5) In any of the methods denoted (Bl) to (B4), the fluorophore is soluble in a liquid solute.

[0116] (B6) In the method denoted (B5), the liquid solute includes water.

[0117] (B7) In the method denoted (B5), the fluorophore is dissolved in the liquid solute.

[0118] (B8) In the method denoted (B7), the liquid solute is at room temperature.

[0119] (B9) In the method denoted (B7), the liquid solute is at a cryogenic temperature.

[0120] (BIO) In any of the methods denoted (Bl) to (B9), the fluorophore is soluble in a solid solute.

[0121] (Bll) In the method denoted (BIO), the solid solute includes ice.

[0122] (B12) In the method denoted (BIO), the fluorophore is dissolved in the solid solute.

[0123] (B13) In the method denoted (B12), the solid solute is at room temperature.

[0124] (B14) In the method denoted (B12), the solid solute is at a cryogenic temperature.

[0125] (B15) In any of the methods denoted (Bl) to (B14), the fluorophore is located within a cell.

[0126] (B16) In any of the methods denoted (Bl) to (B15), the fluorophore includes a fluorescent protein.

[0127] (B17) In the method denoted (B16), the fluorescent protein includes a red fluorescent protein, an orange fluorescent protein, a cyan fluorescent protein, a green fluorescent protein, or a blue fluorescent protein.

[0128] (B18) In the method denoted (B16). the fluorescent protein includes a yellow fluorescent protein.

[0129] (B19) In the method denoted (B18), the yellow fluorescent protein includes enhanced yellow fluorescent protein (EYFP), Topaz, Venus, or YPet.

[0130] (B20) In any of the method denoted (Bl) to (Bl 9), the fluorophore includes an organic dye molecule.

[0131] (B21) In the method denoted (B20), the organic dye molecule includes rhodamine.

[0132] (B22) In the method denoted (B21), the rhodamine includes rhodamine 6G.

[0133] (B23) In any of the methods denoted (Bl) to (B22), the fluorophore isdeuterated.

[0134] (Cl) A method for using a fluorophore as a spin qubit includes applying an optical pulse to the fluorophore to initialize the spin qubit in a metastable triplet state of the fluorophore, the fluorophore includes a water-soluble molecule in solution phase. The method further includes applying an optical pulse to the fluorophore to read out a state of the spin qubit.

[0135] (DI) A method for spin-multiplexed optical detection includes simultaneously driving all of a plurality of fluorescent probes with a modulated microwave drive signal, and detecting fluorescence emitted by the plurality of fluorescent probes in response to said simultaneously driving. Each fluorescent probe of the plurality of fluorescent probes has a spinresonance spectrum that is unique to the fluorescent probe.

[0136] (D2) In the method denoted (DI), the method further includes demodulating, with a lock-in amplifier, the detected fluorescence at a modulation frequency of the modulated microwave drive signal.

[0137] (D3) In the method denoted (D2), the method further includes identifying, based on an output of the lock-in amplifier, which one of the plurality of fluorescent probes is driven by the modulated micro wave drive signal.

[0138] (D4) In the method denoted (D2), the method further includes modulating, with the lock-in amplifier, a microwave signal to generate the modulated microwave drive signal.

[0139] (D5) In the method denoted (D4), said modulating includes modulating an amplitude of the microwave signal.

[0140] (D6) In the method denoted (D4), said modulating includes modulating the microwave signal with a sinusoidal waveform or a square waveform.

[0141] (D7) In any of the methods denoted (DI) to (D6), a number of the plurality of fluorescent probes is between 2 and 100.

[0142] (D8) In any of the methods denoted (DI) to (D6). a number of the plurality of fluorescent probes is between 2 and 1000.

[0143] (D9) In any of the methods denoted (DI) to (D8), the spin-resonance spectrum of each fluorescent probe includes two spin resonances centered at two spin-resonant frequencies.

[0144] (DIO) In the method denoted (D9), the two spin-resonant frequencies are unique to the fluorescent probe.

[0145] (DI 1) In the method denoted (D9), each of the two spin-resonance frequencies is greater than 1 GHz.

[0146] (DI 2) In the method denoted (D9), the spin-resonance spectrum of eachfluorescent probe is based on a metastable triplet state of the fluorescent probe.

[0147] (D13) In the method denoted (D12), the metastable triplet state of the fluorescent probe has a pair of zero-field splitting parameters that is unique to the fluorescent probe.

[0148] (D14) In any of the methods denoted (DI) to (D13), the plurality of fluorescent probes includes a first fluorescent probe having a first spin-resonance spectrum with a first resonance, the plurality of fluorescent probes includes a second fluorescent probe having a second spin-resonance spectrum with a second resonance, and the first resonance and the second resonance are at least partially overlapped.

[0149] (DI 5) In the method denoted (DI 4), the method further includes spectrally unmixing the detected fluorescence to identify a quantity of fluorescence emitted by each fluorescent probe.

[0150] (DI 6) In any of the methods denoted (DI) to (DI 5), each fluorescent probe includes a hybrid system formed from an optically active probe joined with a magnetic dipole such that the spin-resonance spectrum of the fluorescent probe is based on a magnetic field generated by the magnetic dipole.

[0151] (D17) In any of the methods denoted (DI) to (D16), each fluorescent probe includes a fluorophore.

[0152] (DI 8) In any of the methods denoted (DI) to (DI 7), each fluorescent probe includes a spin-qubit fluorescent protein.

[0153] (D19) In any of the methods denoted (DI) to (D18), each fluorescent probe includes a point defect in a crystal.

[0154] (D20) In the method denoted (D19), the point defect in the crystal includes a nitrogen-vacancy center in diamond.

[0155] (D21) In any of the methods denoted (DI) to (D20), the method further includes driving the plurality of fluorescent probes with light to optically excite at least one of the plurality of fluorescent probes.

[0156] (D22) In the method denoted (D21), the light includes coherent light from a laser.

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Claims

CLAIMSWhat is claimed is:

1. A method, comprising:applying an optical pulse to a fluorophore to drive the fluorophore from a ground singlet state to an excited singlet state, wherein the fluorophore undergoes an intersystem crossing from the excited singlet state to a metastable triplet state; andusing the fluorophore in the metastable triplet state as a spin qubit.

2. The method of claim 1, wherein said using the fluorophore comprises using the spin qubit for quantum sensing.

3. The method of claim 2, wherein said using the spin qubit for quantum sensing comprises using the spin qubit to sense a magnetic field, an electric field, a strain, or a temperature.

4. The method of claim 1, wherein said using the fluorophore comprises using the spin qubit for quantum computation, quantum communication, a quantum memory, or any combination thereof.

5. The method of claim 1 , wherein said using the fluorophore as a spin qubit comprises optically reading out a state of the spin qubit.

6. The method of claim 1. wherein:the fluorophore undergoes the intersystem crossing from the excited singlet state to an initial spin-qubit state, the initial spin-qubit state comprising one of first, second, and third magnetic sublevels of the metastable triplet state; and the method further comprises applying a microwave pulse to the fluorophore to at least partially transfer the initial spin-qubit state to an encoded spin-qubit state, the encoded spin-qubit state having a non-zero population in one or both of the second and third magnetic sublevels.

7. The method of claim 6, wherein:the first magnetic sublevel comprises a Txstate;the second magnetic sublevel comprises a Tystate; andthe third magnetic sublevel comprises a Tzstate.

8. The method of claim 1. wherein:the excited singlet state comprises a first excited singlet state; andthe metastable triplet state comprises a first metastable triplet state.

9. The method of claim 1, the fluorophore being soluble in a liquid solute.

10. The method of claim 9, the liquid solute comprising water.

11. The method of claim 9, the fluorophore being dissolved in the liquid solute.

12. The method of claim 11, the liquid solute being at room temperature.

13. The method of claim 11, the liquid solute being at a cryogenic temperature.

14. The method of claim 1. the fluorophore being soluble in a solid solute.

15. The method of claim 14, the solid solute comprising ice.

16. The method of claim 14, the fluorophore being dissolved in the solid solute.

17. The method of claim 16, the solid solute being at room temperature.

18. The method of claim 16, the solid solute being at a cryogenic temperature.

19. The method of claim 1, the fluorophore being located within a cell.

20. The method of claim 1. the fluorophore comprising a fluorescent protein.

21. The method of claim 20, the fluorescent protein comprising a red fluorescent protein, an orange fluorescent protein, a cyan fluorescent protein, a green fluorescent protein, or a blue fluorescent protein.

22. The method of claim 20, the fluorescent protein comprising a yellow fluorescent protein.

23. The method of claim 22, the yellow fluorescent protein comprising enhanced yellow fluorescent protein (EYFP), Topaz, Venus, or YPet.

24. The method of claim 1, the fluorophore comprising an organic dye molecule.

25. The method of claim 24, the organic dye molecule comprising rhodamine.

26. The method of claim 25, the rhodamine comprising rhodamine 6G.

27. The method of claim 1, the fluorophore being deuterated.

28. The method of claim 1, wherein:said applying the optical pulse comprises applying the optical pulse to a plurality of fluorophores to drive each fluorophore, of the plurality of fluorophores, from the ground singlet state to the excited singlet state, wherein said each fluorophore undergoes the intersystem crossing from the excited singlet state to the metastable triplet state; andsaid using the fluorophore comprises using the plurality of fluorophores in the metastable triplet state as an ensemble of spin qubits.

29. A method for measuring a metastable triplet state of a fluorophore, comprising:applying a microwave pulse to the fluorophore to coherently redistribute spin sublevel populations of the metastable triplet state;applying an optical pulse to the fluorophore to excite one or more of the spin sub-level populations to a higher-energy triplet state of the fluorophore, wherein: the fluorophore undergoes a reverse intersystem crossing from the higher- energy' triplet state to an excited singlet state of the fluorophore; and the fluorophore decays from the excited singlet state to a ground singlet state of the fluorophore;detecting a photon emitted by the fluorophore when the fluorophore decays from the excited singlet state; anddetermining a spin state of the metastable triplet state based on at least a time at which the photon was detected.

30. The method of claim 29, wherein:the fluorophore decays from the excited singlet state to an intermediate excited singlet state;the fluorophore decays from the intermediate excited singlet state to the ground singlet state; andsaid detecting the photon comprises detecting one or both of (i) a photon emitted by the fluorophore when the fluorophore decays from the excited singlet state to the intermediate spin state and (ii) a photon emitted by the fluorophore when the fluorophore decays from the intermediate excited singlet state.

31. The method of claim 30, wherein:the metastable triplet state is a first triplet state of the fluorophore;the higher-energy triplet state is a second triplet state of the fluorophore;the excited singlet state is a second excited singlet state of the fluorophore; and the intermediate excited singlet state is a first excited singlet state of the fluorophore.

32. The method of claim 29, wherein:the method further comprises optically pumping the fluorophore between the ground singlet state and the excited singlet state; andsaid detecting the photon comprises detecting several photons emitted by the fluorophore during said optically pumping.

33. The method of claim 29, the fluorophore being soluble in a liquid solute.

34. The method of claim 33, the liquid solute comprising water.

35. The method of claim 33, the fluorophore being dissolved in the liquid solute.

36. The method of claim 35, the liquid solute being at room temperature.

37. The method of claim 35, the liquid solute being at a cryogenic temperature.

38. The method of claim 29, the fluorophore being soluble in a solid solute.

39. The method of claim 38, the solid solute comprising ice.

40. The method of claim 38, the fluorophore being dissolved in the solid solute.

41. The method of claim 40, the solid solute being at room temperature.

42. The method of claim 40, the solid solute being at a cry ogenic temperature.

43. The method of claim 29, the fluorophore being located within a cell.

44. The method of claim 29, the fluorophore comprising a fluorescent protein.

45. The method of claim 44, the fluorescent protein comprising a red fluorescent protein, an orange fluorescent protein, a cyan fluorescent protein, a green fluorescent protein, or a blue fluorescent protein.

46. The method of claim 44, the fluorescent protein comprising a yellow fluorescent protein.

47. The method of claim 46, the yellow fluorescent protein comprising enhanced yellow fluorescent protein (EYFP), Topaz, Venus, or YPet.

48. The method of claim 29, the fluorophore comprising an organic dye molecule.

49. The method of claim 48, the organic dye molecule comprising rhodamine.

50. The method of claim 49, the rhodamine comprising rhodamine 6G.

51. The method of claim 29, the fluorophore being deuterated.

52. A method for using a fluorophore as a spin qubit, comprising:applying an optical pulse to the fluorophore to initialize the spin qubit in a metastable triplet state of the fluorophore, the fluorophore comprising a water-soluble molecule in solution phase; andapplying an optical pulse to the fluorophore to read out a spin state of the spin qubit.

53. A method for spin-multiplexed optical detection, comprising:simultaneously driving all of a plurality of fluorescent probes with a modulated microwave drive signal; anddetecting fluorescence emitted by the plurality of fluorescent probes in response to said simultaneously driving;wherein each fluorescent probe of the plurality' of fluorescent probes has a spinresonance spectrum that is unique to the fluorescent probe.

54. The method of claim 53, further comprising demodulating, with a lock-in amplifier, the detected fluorescence at a modulation frequency of the modulated microwave drive signal.

55. The method of claim 54, further comprising identifying, based on an output of the lock-in amplifier, which one of the plurality of fluorescent probes is driven by the modulated microwave drive signal.

56. The method of claim 54, further comprising modulating, with the lock-in amplifier, a microwave signal to generate the modulated microwave drive signal.

57. The method of claim 56, wfierein said modulating comprises modulating an amplitude of the microwave signal.

58. The method of claim 56, wherein said modulating comprises modulating the microwave signal with a sinusoidal waveform or a square waveform.

59. The method of claim 53, wherein a number of the plurality of fluorescent probes is between 2 and 100.

60. The method of claim 53, wfierein a number of the plurality of fluorescent probes is between 2 and 1000.

61. The method of claim 53, wfierein the spin-resonance spectrum of each fluorescent probe comprises two spin resonances centered at two spin-resonant frequencies.

62. The method of claim 61, wherein the two spin-resonant frequencies are unique to the fluorescent probe.

63. The method of claim 61, wherein each of the two spin-resonance frequencies is greater than 1 GHz.

64. The method of claim 61, wfierein the spin-resonance spectrum of each fluorescent probe is based on a metastable triplet state of the fluorescent probe.

65. The method of claim 64, wfierein the metastable triplet state of the fluorescent probe has a pair of zero-field splitting parameters that is unique to the fluorescent probe.

66. The method of claim 53, wherein:the plurality of fluorescent probes includes a first fluorescent probe having a first spinresonance spectrum with a first resonance;the plurality of fluorescent probes includes a second fluorescent probe having a second spin-resonance spectrum with a second resonance; andthe first resonance and the second resonance are at least partially overlapped.

67. The method of claim 66, further comprising spectrally unmixing the detected fluorescence to identity7a quantity7of fluorescence emitted by each fluorescent probe.

68. The method of claim 53, wherein each fluorescent probe comprises a hybrid system formed from an optically active probe joined with a magnetic dipole such that the spin-resonance spectrum of the fluorescent probe is based on a magnetic field generated by the magnetic dipole.

69. The method of claim 53, wherein each fluorescent probe comprises a fluorophore.

70. The method of claim 53, wherein each fluorescent probe comprises a spin-qubit fluorescent protein.

71. The method of claim 53, wherein each fluorescent probe comprises a point defect in a crystal.

72. The method of claim 71 , the point defect in the crystal comprising a nitrogen-vacancy center in diamond.

73. The method of claim 53, further comprising driving the plurality of fluorescent probes with light to optically excite at least one of the plurality of fluorescent probes.

74. The method of claim 73, the light comprising coherent light from a laser.

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