Technologies for long optical coherence times in a rare-earth-doped antiferromagnet

Abstract

A rare-earth-doped antiferromagnetic crystal is disclosed, designed to achieve long optical coherence times and enable coherent coupling between optical and magnon modes. The crystal includes a host lattice, such as gadolinium vanadate, gadolinium oxide, or gadolinium silicate, which is antiferromagnetic below a Néel temperature and is doped with a second rare-earth ion, such as erbium. By operating at cryogenic temperatures, electron spins in the host are magnetically ordered, providing a quiet magnetic environment that minimizes decoherence for the dopant ions. The system achieves long optical coherence times for the rare-earth dopant ions, supporting robust quantum memory and communication. Additionally, coherent coupling between the optical transitions of the dopant and magnon modes of the host enables efficient microwave-to-optical quantum transduction. Isotopic purification of the host and / or dopant ions can further reduce nuclear spin noise, enhancing coherence times.

Description

Docket no. 10872-0005-PCTTECHNOLOGIES FOR LONG OPTICAL COHERENCE TIMES IN A RARE- EARTH-DOPED ANTIFERROMAGNETCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of United States Provisional Patent Application No. 63 / 695,640, entitled “Long optical coherence times and coherent rare earthmagnon coupling in a rare earth doped anti-ferromagnet,” filed on September 17, 2024, the entirety of which is incorporated herein by reference.BACKGROUND

[0002] Rare-earth ions doped into solid-state crystals have long been recognized for their exceptionally narrow optical and spin transition linewidths, which enable long coherence times. These properties arise from the shielding of the 4 / electrons by outer closed shells, making rare-earth ions relatively insensitive to environmental magnetic fluctuations, a primary source of decoherence in solid-state systems. As a result, rare-earth-doped crystals have become important platforms for applications in quantum memory, quantum communication, and precision sensing.

[0003] A key challenge in maximizing coherence times is the selection of host materials with minimal electronic and nuclear spin backgrounds. Hosts such as yttrium orthosilicate (Y2SiOs) are commonly used because the substitution of rare-earth ions for similar ions in the crystal lattice minimizes strain and inhomogeneous broadening. Despite extensive efforts to identify ideal host materials, it has not been possible to achieve a crystal in which all constituent ions possess both zero nuclear spin and zero electron spin and where the rare earths can be substituted with low strain. This limitation arises because no trivalent rare-earth ion has isotopes that are simultaneously free of both nuclear and electronic spins, resulting in an unavoidable background of magnetic noise in even the best available host crystals.BRIEF DESCRIPTION OF THE DRAWINGS

[0004] The concepts described herein are illustrated by way of example and not by way of limitation in the accompanying figures. For simplicity and clarity of illustration, elements illustrated in the figures are not necessarily drawn to scale. Where considered appropriate, reference labels have been repeated among the figures to indicate corresponding or analogous elements.

[0005] FIG. 1 is a simplified block diagram of one embodiment of a system for long optical coherence times in a rare-earth-doped antiferromagnetic crystal.Docket no. 10872-0005-PCT

[0006] FIG. 2 is a simplified illustration showing the energy states of a rare earth ion in a host crystal in accordance with embodiments disclosed herein.

[0007] FIGS. 3 is a simplified block diagram of one embodiment of a system for a microwave-optical transduction in a rare-earth-doped antiferromagnet.

[0008] FIGS. 4 A and 4B are simplified diagrams of a microwave cavity of the system of FIG. 3.

[0009] FIG. 5 is a plot showing transmission through one embodiment of the crystal in FIG. 1 as a function of applied magnetic field.DETAILED DESCRIPTION OF THE DRAWINGS

[0010] Rare-earth ions can be incorporated into host crystals to exploit their shielded 4 / electronic transitions, which are naturally resistant to environmental magnetic fluctuations. However, a persistent challenge in these systems is the unavoidable presence of either nuclear spin, electron spin, or both, in the constituent rare earth ions of the host lattice that the dopant ions substitute for. This results in a background of magnetic noise that limits the achievable coherence times for both spin and optical transitions.

[0011] To address these limitations, the approach described here utilizes host crystals that are antiferromagnetic below a characteristic Neel temperature. At sufficiently low temperatures, the electron spins in the host lattice become magnetically ordered, effectively freezing out the primary source of magnetic fluctuations. This ordered state creates a quiet magnetic environment for the rare-earth dopant ions, allowing their optical transitions to exhibit exceptionally narrow linewidths and coherence times that rival or exceed those found in non-magnetic hosts. For example, erbium-doped gadolinium vanadate crystals have demonstrated optical coherence times on the order of hundreds of microseconds, a regime that is highly favorable for quantum information applications.

[0012] The ability to achieve such long optical coherence times in a solid-state platform opens the door to a range of quantum technologies. Quantum memory devices can leverage these materials to store and retrieve quantum states of light with high fidelity over extended durations. Quantum communication systems benefit from the robust coherence, enabling secure transmission of quantum information over long distances. Precision quantum sensors can exploit the narrow optical transitions for enhanced sensitivity and stability in measurement protocols.

[0013] A further distinguishing feature of these antiferromagnetic host crystals is their support for collective spin excitations known as magnons. The rare-earth dopant ions can beDocket no. 10872-0005-PCT coherently coupled to these magnon modes, as evidenced by avoided crossings in the optical spectra and strong coupling phenomena observed experimentally. This coherent interaction between optical transitions and magnons enables efficient quantum transduction between microwave and optical domains. Such transduction is essential for interfacing superconducting qubits, which operate at microwave frequencies, with optical quantum networks, facilitating the development of hybrid quantum systems and scalable quantum architectures.

[0014] The optical-magnon coupling also provides new avenues for quantum memory protocols, including persistent spectral hole burning and atomic frequency comb techniques, as well as the potential for entanglement generation between microwave and optical photons. By tuning the system to operate at zero or near-zero applied magnetic field, or at specific points where transitions are insensitive to magnetic field fluctuations (ZEFOZ points), further enhancements in coherence and transduction efficiency can be realized.

[0015] Optional features, such as isotopic purification of the host lattice or the rare- earth dopant ions, can be employed to further suppress nuclear spin noise, pushing coherence times even longer. The choice of host material, dopant species, and doping concentration can be tailored to optimize performance for specific quantum applications. This flexible and powerful platform thus provides a foundation for next-generation quantum memory, communication, and sensing technologies, as well as for the realization of efficient quantum transducers linking disparate quantum systems.

[0016] In the following description, specific details are set forth, but embodiments of the technologies described herein may be practiced without these specific details. Well-known circuits, structures, and techniques have not been shown in detail to avoid obscuring an understanding of this description. Phrases such as “an embodiment,” “various embodiments,” “some embodiments,” and the like may include features, structures, or characteristics, but not every embodiment necessarily includes the particular features, structures, or characteristics.

[0017] Some embodiments may have some, all, or none of the features described for other embodiments. “First,” “second,” “third,” and the like describe a common object and indicate different instances of like objects being referred to. Such adjectives do not imply objects so described must be in a given sequence, either temporally or spatially, in ranking, or any other manner.

[0018] Connected” may indicate elements are in direct physical or electrical contact with each other and “coupled” may indicate elements cooperate or interact with each other, but they may or may not be in direct physical or electrical contact. Furthermore, the termsDocket no. 10872-0005-PCT“comprising,” “including,” “having,” and the like, as used with respect to embodiments of the present disclosure, are synonymous.

[0019] As used herein, the phrase “located on” in the context of a first layer or component located on a second layer or component refers to the first layer or component being directly physically attached to the second part or component (no layers or components between the first and second layers or components) or physically attached to the second layer or component with one or more intervening layers or components. As used herein, the term “adjacent” refers to layers or components that are in physical contact with each other. That is, there is no layer or component between the stated adjacent layers or components. For example, a layer X that is adjacent to a layer Y refers to a layer that is in physical contact with layer Y. As used herein, the phrase “electrically coupled” refers to the presence of one or more electrically conductive paths between components that are recited as being electrically coupled.

[0020] Certain terminology may also be used herein for the purpose of reference only, and thus are not intended to be limiting. For example, terms such as “upper,” “lower,” “above,” “below,” “bottom,” and “top” refer to directions in the Figures to which reference is made. Terms such as “front,” “back,” “rear,” and “side” describe the orientation and / or location of layers, components, portions of components, etc., within a consistent but arbitrary frame of reference, which is made clear by reference to the text and the associated Figures describing the layers, component, portions of components, etc. under discussion. Such terminology may include the words specifically mentioned above, derivatives thereof, and words of similar import.

[0021] Reference is now made to the drawings, which are not necessarily drawn to scale, wherein similar or the same numbers may be used to designate the same or similar parts in different figures. The use of similar or the same numbers in different figures does not mean all figures including similar or the same numbers constitute a single or same embodiment. Like numerals having different letter suffixes may represent different instances of similar components. The drawings illustrate generally, by way of example, but not by way of limitation, various embodiments discussed in the present document.

[0022] In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding thereof. It may be evident, however, that the novel embodiments can be practiced without these specific details. In other instances, well-known structures and devices are shown in block diagram form in order to facilitate a description thereof. The intention is to cover all modifications, equivalents, and alternatives within the scope of the claims.Docket no. 10872-0005-PCT

[0023] As used in this application and the claims, a list of items joined by the term “and / or” can mean any combination of the listed items. For example, the phrase “A, B, and / or C” can mean A; B; C; A and B; A and C; B and C; or A, B and C. As used in this application and the claims, a list of items joined by the term “at least one of’ can mean any combination of the listed terms. For example, the phrase “at least one of A, B, or C” can mean A; B; C; A and B; A and C; B and C; or A, B, and C. Moreover, as used in this application and the claims, a list of items joined by the term “one or more of’ can mean any combination of the listed terms. For example, the phrase “one or more of A, B, and C” can mean A; B; C; A and B; A and C; B and C; or A, B, and C.

[0024] As used in this application and the claims, the phrase “individual of’ or “respective of’ followed by a list of items recited or stated as having a trait, feature, etc., means that all of the items in the list possess the stated or recited trait, feature, etc. For example, the phrase “individual of A, B, or C, comprise a sidewall” or “respective of A, B, or C, comprise a sidewall” means that A comprises a sidewall, B comprises a sidewall, and C comprises a sidewall.

[0025] The disclosed methods, apparatuses, and systems are not to be construed as limiting in any way. Instead, the present disclosure is directed toward all novel and nonobvious features and aspects of the various disclosed embodiments, alone and in various combinations and subcombinations with one another. The disclosed methods, apparatuses, and systems are not limited to any specific aspect or feature or combination thereof, nor do the disclosed embodiments require that any one or more specific advantages be present or problems be solved.

[0026] Theories of operation, scientific principles, or other theoretical descriptions presented herein in reference to the apparatuses or methods of this disclosure have been provided for the purposes of better understanding and are not intended to be limiting in scope. The apparatuses and methods in the appended claims are not limited to those apparatuses and methods that function in the manner described by such theories of operation.

[0027] Although the operations of some of the disclosed methods are described in a particular, sequential order for convenient presentation, it is to be understood that this manner of description encompasses rearrangement, unless a particular ordering is required by specific language set forth herein. For example, operations described sequentially may in some cases be rearranged or performed concurrently. Moreover, for the sake of simplicity, the attached figures may not show the various ways in which the disclosed methods can be used in conjunction with other methods.Docket no. 10872-0005-PCT

[0028] Referring now to FIG. 1, in one embodiment, a system 100 includes a crystal 102, a refrigerator 104, a laser 106 or other optical source, an acousto-optic modulator 108, a fiber-to-free-space coupler 110, mirrors 112, a waveplate 114, a polarizer 116, a beam-splitter 118, lenses 120, detectors 122, lock-in amplifiers 124, and a data acquisition device 126. In use, the system 100 is designed to exploit long optical coherence times in a rare-earth-doped antiferromagnetic crystal 102. To achieve the necessary low temperatures for optimal coherence and antiferromagnetic ordering, the crystal 102 is housed within a refrigerator 104, which maintains the environment well below the Neel temperature of the host material. This cryogenic cooling suppresses thermal fluctuations and ensures that the electron spins in the host lattice are magnetically ordered, thereby minimizing decoherence sources that would otherwise broaden and decohere the optical transitions of the rare-earth ions.

[0029] Optical interrogation of the crystal 102 is performed using a laser 106 or other suitable optical source. The laser 106 is configured to emit light at wavelengths resonant with one or more optical transitions of the rare-earth dopant ions. The output from the laser 106 may be modulated or otherwise controlled or modified using various components such as an acousto-optic modulator 108, a waveplate 114, a polarizer 116, a beam-splitter 118, etc., allowing precise control over the timing and intensity of the optical pulses delivered to the crystal 102. The modulated light is then directed through a fiber-to-free-space coupler 110, which transitions the optical signal from fiber optics to free-space propagation, facilitating alignment and delivery to the crystal 102.

[0030] To ensure optimal polarization and intensity of the incident light, the system incorporates a series of optical components, including mirrors 112, a waveplate 114, a polarizer 116, and a beam-splitter 118. These elements collectively condition the laser beam, allowing for selection of the desired polarization state and precise control of the optical path. Lenses 120 are used to focus the light onto the crystal 102, maximizing the interaction between the optical field and the rare-earth ions within the host lattice.

[0031] Detection of the laser pulses and optical response from the crystal 102 is accomplished using detectors 122, which are positioned to collect transmitted or emitted light following interaction with the crystal. In one embodiment, the output signals from detectors 122 may be processed by lock-in amplifiers 124. This approach may be used to perform sensitive characterization of the ErGdVCL crystal’s absorption features at very low optical powers, minimizing sample heating, to identify and analyze transition frequencies and line shapes, rather than to measure optical coherence times. Finally, the processed data is acquiredDocket no. 10872-0005-PCT and analyzed using a data acquisition device 126, enabling precise measurement of optical coherence times and other relevant parameters.

[0032] During operation, the system 100 uses the laser 106 to excite specific optical transitions in the rare-earth-doped antiferromagnetic crystal 102. In FIG. 2, an energy level diagram 200 for erbium ions in a GdVCh crystal is shown. The diagram 200 shows various energy levels for the4 / is 2(Z|) — >4 / 13 / 2OT, I2) transition. Energy levels 202 correspond to the Zi states, energy levels 204 correspond to the Ki states, and energy levels 206 correspond to the Y2 states. Energy levels 208 correspond to the energy levels in zero magnetic field, energy levels 210 correspond to the energy levels for erbium ions oriented opposite to the applied magnetic field, and energy levels 212 correspond to the energy levels for the erbium ions aligned with the applied magnetic field.

[0033] When the laser 106 is tuned to the appropriate wavelength, photons are absorbed by the erbium ions in crystal 102, promoting them from the Zl ground state (energy levels 202) to one of the excited states (energy levels 204 or 206). The system 100 is designed to precisely control and measure these transitions. By modulating the laser 106 with the acousto-optic modulator 108 to produce optical pulses and analyzing the resulting photon echoes detected by detector 122, the system can determine the coherence properties of the optical transitions. The narrow linewidths and long coherence times observed are direct consequences of the quiet magnetic environment provided by the antiferromagnetic ordering in crystal 102, as well as the careful selection and control of the energy levels involved. This enables high-fidelity quantum memory and sensing applications, as the rare-earth ions maintain their quantum states for extended periods, with minimal decoherence from environmental magnetic fluctuations.

[0034] The crystal 102 serves as the host lattice for rare-earth ion doping. In a representative embodiment, the host crystal is an antiferromagnetic material with a rare earth ion, such as gadolinium vanadate (GdVO4), which is doped with a second rare-earth ion, such as erbium (Er3+). The antiferromagnetic ordering of the host lattice at temperatures below its Neel temperature (for GdVCh, approximately 2.5 K) suppresses electronic spin fluctuations, thereby minimizing magnetic noise and enabling the rare-earth dopant ions to maintain quantum coherence for extended durations.

[0035] Within the crystal, dopant ions can occupy different lattice sites and exhibit distinct orientations relative to the applied magnetic field. For example, in GdVCh, erbium ions substitute for gadolinium ions and are distributed among two sublattices. Depending on the orientation of the external magnetic field with respect to the crystal’s c-axis, the local environment of each dopant ion varies: some erbium ions are aligned parallel to the field, whileDocket no. 10872-0005-PCT others are anti -parallel. This leads to different energy level shifts and transition frequencies for each orientation, which can be exploited for selective optical addressing and for identifying transitions that are less sensitive to magnetic field fluctuations (such as ZEFOZ points).

[0036] The host crystal may be fabricated in a variety of geometries to accommodate different experimental configurations or device architectures, including cylindrical rods, rectangular prisms, thin films (e.g., epitaxially grown thin films), or thin slabs. Beyond gadolinium vanadate, alternative host materials include gadolinium oxide (Gd2Os), gadolinium silicate (Gd2SiOs), gadolinium gallium garnet (GdsGasO ), double tungstates of gadolinium and alkali metals (e.g., GdK(WO4)2), and rare-earth fluorides such as gadolinium fluoride (GdFs), lithium gadolinium fluoride (LiGdF4), or erbium lithium fluoride (ErLiF4). The choice of host material affects the magnetic ordering temperature, the nuclear spin background, and the compatibility with different rare-earth dopants.

[0037] The host crystal may be fabricated in a variety of geometries to accommodate different experimental configurations or device architectures, including cylindrical rods, rectangular prisms, or thin slabs. Beyond gadolinium vanadate, alternative host materials include gadolinium oxide (Gd2Os), gadolinium silicate (Gd2SiOs), gadolinium gallium garnet (GdsGasO ), double tungstates of gadolinium and alkali metals (e.g., GdK / WChk), and rare- earth fluorides such as gadolinium fluoride (GdFs), lithium gadolinium fluoride (LiGdF4), or erbium lithium fluoride (ErLiEt). The choice of host material affects the magnetic ordering temperature, the nuclear spin background, and the compatibility with different rare-earth dopants.In addition to gadolinium-based hosts, other rare-earth ions may be used as the primary constituent of the host lattice. Possible host ions and / or dopants include Yttrium (Y), Neodymium (Nd), Ytterbium (Yb), Dysprosium (Dy), Cerium (Ce), Samarium (Sm), Europium (Eu), Praseodymium (Pr), Terbium (Tb), Holmium (Ho), Thulium (Tm), Erbium (Er), Lanthanum (La), Lutetium (Lu), and Scandium (Sc). The selection of host and dopant ions can be tailored to optimize specific quantum properties, such as transition wavelengths, magnetic ordering, and nuclear spin backgrounds. For example, hosts with low nuclear spin isotopes and dopants with zero nuclear spin (e.g., erbium-166, erbium-168, ytterbium- 174) may be preferred for maximizing coherence times. In other embodiments, such as quantum memory protocols, it may be advantageous to use a dopant ion with nonzero nuclear spin, as this enables persistent spectral hole burning and facilitates advanced storage techniques. This flexibility allows for the design of crystals suited to a wide range of quantum memory, communication, and sensing applications.Docket no. 10872-0005-PCT

[0038] Doping concentrations of the rare-earth ions can be precisely controlled, typically ranging from as low as 1 part per million (ppm) up to several percent. Lower concentrations (e.g., 10-1000 ppm) are preferred for maximizing coherence times, as higher concentrations can introduce additional magnetic noise and inhomogeneous broadening, while higher concentrations may be desirable for applications requiring stronger optical or microwave signals.

[0039] To further suppress decoherence, isotopic purification of the host lattice and / or the dopant ions can be employed. For gadolinium-based hosts, the nuclear spin background is primarily due to the isotopes gadolinium-155 and gadolinium- 157, both of which have nuclear spin I = 3 / 2. By isotopically enriching the host crystal to reduce the combined concentration of Gd-155 and Gd-157 to less than 5% of the total gadolinium content, the nuclear spin noise can be significantly diminished. For the rare-earth dopant ions, isotopic purification can be used to select isotopes with zero nuclear spin, such as erbium-166 ( / = 0), erbium-168 ( / = 0), or ytterbium- 174 ( / = 0), achieving purities of at least 95% of the desired isotope. This level of purification is feasible with current enrichment technologies and can push coherence times even longer.

[0040] In some embodiments, the crystal may be further engineered with functional layers or coatings to enhance optical coupling, improve thermal management, or provide mechanical stability. Such integration supports the deployment of the crystal in advanced quantum devices, including quantum memories, transducers, and sensors.

[0041] The refrigerator 104 is configured to maintain the crystal 102 at temperatures well below the Neel temperature of the host material, typically in the milli-Kelvin to a few Kelvin range. This cryogenic cooling achieves antiferromagnetic ordering of the electron spins in the host lattice, thereby suppressing thermal fluctuations and magnetic noise that would otherwise degrade the coherence of the rare-earth dopant ions. The refrigerator may be a dilution refrigerator, a helium-3 cryostat, or another suitable cryogenic system, and may include features such as vibration isolation, thermal shielding, and optical access ports. In some embodiments, the refrigerator may be equipped with temperature sensors, heaters, or feedback control systems to precisely regulate the sample environment. The refrigerator may also be designed to accommodate additional components, such as microwave cavities for hybrid quantum experiments, as discussed below in more detail in regard to FIG. 3.

[0042] In an illustrative embodiment, the refrigerator 102 includes a superconducting magnet, which may be positioned to apply a static magnetic field along a desired axis of theDocket no. 10872-0005-PCT crystal, such as the c axis in GdVCk The superconducting magnet may be capable of generating fields up to several Tesla, with precise control over field strength, orientation, and stability. The magnet may be integrated with the refrigerator 102 using cryogenic-compatible wiring, thermal shielding, and vibration isolation to prevent disturbance of the sample environment. The presence of the superconducting magnet enables tuning of magnon and spin transition frequencies, exploration of phase transitions (e.g., antiferromagnetic to spin-flop or paramagnetic phases), and investigation of field-dependent phenomena such as avoided crossings and ZEFOZ points. In alternative embodiments, the refrigerator may be equipped with multiple magnets, vector magnets, or active feedback systems to enable complex field profiles or dynamic field modulation.

[0043] The laser 106 or other optical source is used to interrogate the crystal 102 by exciting specific optical transitions of the rare-earth dopant ions. The optical source may be a tunable external cavity diode laser, a fiber laser, non-classical source (e.g., single photon, entangled photon, etc.), or another source capable of emitting light at wavelengths resonant with the desired transitions, such as the 4IIS / 2(ZI) —> 4Ii3 / 2(Yi, Y2) transition in erbium. The laser may be operated in continuous-wave or pulsed mode, and may include features such as frequency stabilization, amplitude modulation, or polarization control. In some embodiments, multiple lasers or broadband sources may be used to address different transitions or perform multi-photon experiments. The laser output may be modulated using an acousto-optic modulator 108, which allows precise control over the timing, intensity, and frequency of the optical pulses delivered to the crystal. The acousto-optic modulator may be driven by a radiofrequency generator and may be configured for amplitude, frequency, or phase modulation as required by the experimental protocol.

[0044] The fiber-to-free-space coupler 110 transitions the optical signal from fiber optics to free-space propagation, facilitating alignment and delivery of the laser beam to the crystal 102. The coupler may include collimating lenses, alignment stages, and mechanical mounts to ensure stable and efficient coupling. In some embodiments, the coupler may be integrated with polarization-maintaining fibers, mode-matching optics, or beam-shaping elements to optimize the spatial profile and polarization state of the incident light. The coupler may also provide optical isolation or filtering to suppress unwanted reflections or stray light. Mirrors 112 are used to direct and steer the laser beam along the desired optical path, enabling precise alignment of the beam onto the crystal 102. The mirrors may be dielectric or metallic, and may be mounted on adjustable stages for fine-tuning of the beam trajectory. In some embodiments, the mirrors may be coated for specific wavelength ranges, or may be integratedDocket no. 10872-0005-PCT with beam-splitters or other optical elements to facilitate multi-path experiments or simultaneous interrogation of multiple samples. The arrangement of mirrors may be varied to accommodate different laboratory layouts or device architectures. Additionally or alternatively, in some embodiments, the optical path may include optical fibers or integrated optical waveguides, which can be placed on or fabricated within the host crystal to guide light efficiently. These configurations enable flexible coupling and routing of optical signals for both laboratory experiments and device integration.

[0045] The waveplate 114 is used to control the polarization state of the laser beam, allowing selection of the desired polarization for optimal interaction with the rare-earth ions in the crystal 102. The waveplate may be a half-wave or quarter-wave plate, and may be rotatable to adjust the polarization angle. In some embodiments, multiple waveplates or polarization controllers may be used to achieve complex polarization states or to compensate for birefringence in the optical path. The waveplate may be positioned before or after other polarization-sensitive components, such as polarizers or beam-splitters, depending on the experimental requirements.

[0046] The polarizer 116 and beam-splitter 118 are used to further refine the polarization state of the laser beam and to separate different polarization components for analysis or detection. The polarizer may be a Gian-Taylor prism, a wire-grid polarizer, or another suitable device. The beam-splitter 118 may be configured to transmit any suitable fraction of the light while reflecting any suitable fraction to the detector 122, which transmits a signal to a lock-in amplifier 124.. In some embodiments, the polarizer and beam-splitter may be integrated with feedback systems for active polarization control or stabilization.

[0047] Lenses 120 are used to focus the laser beam into and out of the crystal 102, maximizing the interaction between the optical field and the rare-earth ions. The lenses may be selected for their focal length, numerical aperture, and aberration characteristics to achieve the desired spot size and intensity profile. In some embodiments, compound lens systems or microscope objectives may be used to achieve high-resolution focusing or to image the transmitted or emitted light from the crystal. The lenses may be mounted on translation stages for precise positioning and alignment.

[0048] Detectors 122 are positioned to collect transmitted or emitted light following interaction with the crystal 102. The detectors may be silicon photodiodes, avalanche photodiodes, superconducting nanowire detectors, or other devices suitable for the wavelength and intensity of the optical signal. The detectors may be operated in single-photon counting mode, analog mode, or time-resolved mode, depending on the measurement protocol. In someDocket no. 10872-0005-PCT embodiments, multiple detectors may be used to monitor different spatial, spectral, or polarization channels, or to perform coincidence measurements for quantum optics experiments. The detectors may be integrated with preamplifiers, filters, or cooling systems to enhance sensitivity and reduce noise.

[0049] Lock-in amplifiers 124 are used to process the output signals from the detectors 122, enhancing the signal-to-noise ratio by synchronizing detection with the modulation frequency of the laser 106. The lock-in amplifiers may be configured for amplitude, phase, or frequency demodulation, and may include features such as digital filtering, auto-ranging, or multi-channel operation. In some embodiments, the lock-in amplifiers may be integrated with data acquisition systems or computer interfaces for automated measurement and analysis. The use of lock-in detection enables precise measurement of weak optical signals, such as photon echoes or spectral holes, even in the presence of background noise or drift. In some embodiments, photon echoes and other weak optical signals are measured using optical heterodyne detection, where the output light is mixed with a local oscillator to generate a beat signal that can be analyzed with high sensitivity and temporal resolution. This technique allows for precise characterization of coherence properties and spectral features, especially at high switching speeds. Additionally or alternatively, in some embodiments, the output light may be detected using single-photon counters, such as avalanche photodiodes or superconducting nanowire detectors, to enable photon counting and time-resolved measurements. The detected light can also be routed for use in subsequent quantum information operations, such as entanglement generation, quantum state transfer, or interfacing with other quantum systems.

[0050] The data acquisition device 126 collects and analyzes the processed signals from the lock-in amplifiers 124, enabling precise measurement of optical coherence times, spectral features, and other relevant parameters. The data acquisition device may be a computer-based system with analog-to-digital converters, timing modules, and software for data visualization, storage, and analysis. In some embodiments, the data acquisition system may be integrated with feedback control loops, automated experiment routines, or remote monitoring capabilities. The device may support real-time data processing, statistical analysis, and export of results for further interpretation or publication.Beyond measuring optical coherence times, system 100 may serve as a platform for advanced quantum technologies, including quantum memory, quantum communication, and entanglement generation. For example, in a quantum memory application, the rare-earth-doped antiferromagnetic crystal 102 acts as a storage medium for quantum states of light. The laser 106 may be used to deliver precisely timed optical pulses, which are resonant with the Zi toDocket no. 10872-0005-PCTY\!Yi transitions (energy levels 202 to 204 / 206 in FIG. 2). A single photon or a sequence of photons, encoded with quantum information, can be directed into the crystal 102 via the optical path defined by mirrors 112, waveplate 114, polarizer 116, polarizing beam-splitter 118, and focused by lenses 120. In addition to Raman processes and spontaneous parametric downconversion, entanglement generation in rare-earth-doped crystals can also be achieved using rephased amplified spontaneous emission (RASE). In the RASE protocol, the ensemble of rare- earth ions is first inverted to produce amplified spontaneous emission (ASE), which creates entanglement between the emitted light and the collective atomic state. A subsequent rephasing pulse sequence, such as a photon echo technique, is then applied to the ensemble, causing the atomic coherence to rephase and emit a second optical field that is entangled with the original ASE. This approach enables the generation of temporally separated, multimode entangled photon pairs, and can be integrated with spin-wave storage to allow on-demand retrieval of entanglement. The long coherence times and tailored absorption profiles of rare-earth-doped crystals make them an ideal platform for implementing RASE, supporting scalable quantum memory and quantum networking applications.

[0051] To store quantum information, the system 100 may employ protocols such as an atomic frequency comb (AFC) or persistent spectral hole burning. For AFC, the laser 106 is used to tailor the absorption profile of the erbium ions in crystal 102, creating a comb-like structure in the frequency domain. When a single photon enters the system, it is absorbed by the ions, and the quantum state is mapped onto the collective excitation of the ensemble. After a controlled delay, the stored quantum state is re-emitted as an echo, which is detected by detectors 122. The long optical coherence times enabled by the antiferromagnetic ordering ensure that the quantum state can be stored and retrieved with high fidelity.

[0052] For entanglement generation, system 100 can be configured to interact with single photons or entangled photon pairs. By using laser 106 to excite specific transitions (such as the Z1 to Y1 or Y2 states), one can induce Raman processes or spontaneous parametric down-conversion within crystal 102. For example, a pump pulse from laser 106 can excite an erbium ion from the Z1 ground state (energy level 202) to an excited state (energy level 204 or 206), followed by emission of a photon as the ion relaxes back to the ground state. If the process is engineered such that two photons are emitted in a correlated fashion (e.g., one optical and one microwave photon via magnon coupling), the system can generate entangled photon pairs. These photons can be routed through the optical path and detected by detectors 122, with their quantum correlations analyzed by the downstream electronics.Docket no. 10872-0005-PCT

[0053] In quantum communication scenarios, system 100 can be used to interface with optical fibers or free-space links via the fiber-to-free-space coupler 110. Single photons carrying quantum information can be injected into the crystal 102, stored using the quantum memory protocol, and later retrieved for transmission to another node in a quantum network. The ability to operate at telecom wavelengths (as enabled by erbium ions) makes the system compatible with existing fiber-optic infrastructure, while the long coherence times and robust storage capabilities support secure and efficient quantum information transfer.

[0054] Referring now to FIG. 3, in one embodiment, a system 300 for microwave- optical transduction is shown. The system 300 includes several of the same components of the system 100, a description of which will not be repeated in the interest of clarity, as well as a microwave cavity 302, a vector network analyzer 304 (VNA), a microwave cable 306 connected from the VNA 304 to the microwave cavity 302, and a microwave cable 308 connected from the microwave cavity 302 to the VNA 304. In the system 300, the rare-earth- doped antiferromagnetic crystal 102 is integrated with a set of microwave components designed to enable coherent interaction between microwave fields and magnon modes within the host lattice. The microwave cavity 302 is positioned to surround or closely couple to the crystal 102. The microwave cavity 302 serves as a resonant structure that supports electromagnetic modes at microwave frequencies, enabling efficient coupling of microwave energy into the crystal. The microwave cavity 302 is described in more detail below in regard to FIGS. 4A and 4B. The VNA 304 is used to generate and analyze microwave signals, allowing precise control over the frequency and amplitude of the microwaves delivered to the cavity 302.

[0055] During operation, the vector network analyzer 304 injects a microwave signal through cable 306 into the microwave cavity 302. The microwave cavity 302 is tuned to a resonance frequency that matches or closely approaches the magnon mode frequency of the host lattice in crystal 102. When the microwave field inside cavity 302 is resonant with the magnon mode, collective spin excitations (magnons) are coherently excited within the host lattice. The high quality factor and concentrated field of the cavity 302 enhance the interaction between the microwave field and the magnon mode, maximizing the efficiency of magnon excitation.

[0056] The system response is monitored by the VNA 304, which receives the transmitted or reflected microwave signal via cable 308. By sweeping the frequency and analyzing the transmission and reflection spectra, the system can identify magnon resonances, including features such as avoided crossings or shifts in the cavity response that indicate strongDocket no. 10872-0005-PCT coupling between the microwave field and the magnon mode. These measurements also reveal the interaction between the magnons and the rare-earth dopant ions in crystal 102, as the rare- earth ions can be coherently coupled to the magnon modes.

[0057] The rare-earth dopant ions in crystal 102 possess well-defined optical transitions that are highly sensitive to their local magnetic environment. The antiferromagnetic crystal 102 supports magnon modes, or collective spin excitations. These magnons modulate the local magnetic field experienced by the rare-earth ions, which in turn perturbs the energy levels associated with their optical transitions. As a result of this coupling, the optical absorption spectrum of the rare-earth ions exhibits features such as avoided crossings and line splittings when the magnon mode is excited by the microwave cavity 302. These spectral signatures indicate that the rare-earth ions and the magnons are coherently interacting, allowing energy and quantum information to be exchanged between the optical and microwave domains. For example, when a laser 106 is used to excite an optical transition in the rare-earth ion, the presence of an excited magnon mode can facilitate processes such as Raman heterodyne conversion, where an optical photon is upconverted or downconverted to a microwave photon via the intermediary magnon excitation.

[0058] This physical mechanism enables system 300 to serve as a platform for quantum transduction, quantum memory, and entanglement generation. By carefully tuning the microwave cavity 302 and the optical excitation parameters, the system can maximize the coherent coupling between the rare-earth ion’s optical transitions and the magnon modes. This allows for efficient transfer of quantum states between microwave and optical photons, supporting advanced hybrid quantum technologies that leverage both the long coherence times of rare-earth ions and the collective excitations of the antiferromagnetic host.

[0059] The microwave cavity 302 may be configured as a resonant structure designed to support electromagnetic modes at microwave frequencies, enabling efficient coupling of microwave energy into the rare-earth-doped antiferromagnetic crystal 102. The cavity may be constructed from high-conductivity materials such as oxygen-free copper to minimize losses and maximize the quality factor (Q) of the resonator. In some embodiments, the cavity may be a loop-gap resonator, a rectangular or cylindrical cavity, a two-dimensional cavity (which may be made, e.g., using photolithography) or another suitable geometry optimized for uniform field distribution and strong coupling to both the magnon modes of the host lattice and the rare- earth dopant ions. The cavity may include features such as tuning plungers, adjustable coupling ports, and optical access windows to facilitate integration with optical measurement systems. The cavity may be designed to accommodate crystals of various shapes and sizes, and may beDocket no. 10872-0005-PCT thermally anchored to the cold finger of a dilution refrigerator 104 to ensure stable cryogenic operation. In some embodiments, the cavity may be tunable over a range of frequencies, for example, by mechanical adjustment or by incorporating variable capacitive or inductive elements, allowing the resonance to be matched to specific magnon or spin transition frequencies in the host crystal. The microwave cavity 302 may also be configured to support multiple modes or to selectively couple to particular magnon branches, depending on the experimental requirements.

[0060] The vector network analyzer 304 (VNA) may be used to generate, deliver, and analyze microwave signals within the system. The VNA may be configured to sweep microwave frequencies, measure transmission (S21) and reflection (Si l) parameters, and provide precise control over the amplitude and phase of the microwave signals delivered to the cavity 302. In some embodiments, the VNA may be a benchtop instrument with high frequency resolution, low phase noise, and multi-channel capability, or it may be integrated into a computer-controlled measurement system for automated data acquisition and analysis. The VNA may be used to characterize the resonance properties of the microwave cavity 302, identify magnon resonances, and monitor the system response during experiments involving coherent coupling between microwave fields, magnons, and rare-earth ions. The VNA may also be used to perform advanced measurements such as vector signal analysis, time-domain reflectometry, or pulsed microwave experiments, depending on the needs of the application. In alternative embodiments, other microwave sources and analyzers, such as signal generators, spectrum analyzers, or homodyne / heterodyne receivers, may be used in place of or in addition to the VNA 304.

[0061] Microwave cable 306 may provide a low-loss, impedance-matched connection between the output port of the VNA 304 and the input port of the microwave cavity 302. The cable may be constructed from coaxial or semi-rigid materials, with appropriate connectors and thermal anchoring to ensure reliable operation at cryogenic temperatures. In some embodiments, the cable may include attenuators, filters, or isolators to suppress unwanted reflections, noise, or spurious signals. The length and routing of the cable may be optimized to minimize insertion loss and maintain signal integrity, especially when operating at high frequencies or in environments with significant electromagnetic interference. The cable may be thermally anchored at various stages within the dilution refrigerator 104 to prevent heat leakage and maintain the low temperature required for antiferromagnetic ordering in the host crystal. In alternative embodiments, waveguides, superconducting transmission lines, orDocket no. 10872-0005-PCT optical fiber-based microwave links may be used to deliver microwave signals to the cavity 302, depending on the system architecture and performance requirements.

[0062] Microwave cable 308 may provide a return path for the transmitted or reflected microwave signals from the microwave cavity 302 back to the VNA 304 for analysis. This cable may be constructed and routed similarly to cable 306, with attention to impedance matching, thermal anchoring, and noise suppression. In some embodiments, cable 308 may include amplifiers, cryogenic low-noise amplifiers, or filters to boost the signal and reduce background noise before it reaches the VNA 304. The cable may be configured to support bidirectional signal flow, enabling simultaneous measurement of transmission and reflection spectra, or it may be dedicated to a single measurement channel. The interaction between cables 306 and 308, the cavity 302, and the VNA 304 enables precise characterization of the microwave response of the system, including identification of magnon resonances, avoided crossings, and strong coupling phenomena between the microwave field, magnons, and rare- earth ions. In alternative embodiments, additional microwave components such as circulators, switches, or multiplexers may be included to support more complex measurement protocols or multi-sample experiments.

[0063] Referring now to FIGS. 4A and 4B, in one embodiment, a microwave cavity 302 incorporating a loop-gap resonator 402 is shown. The loop-gap resonator 402 is designed to provide a strong, spatially uniform microwave magnetic field within the cavity. The cavity body is typically constructed from high-conductivity materials such as oxygen-free copper to minimize resistive losses and maximize the quality factor (Q) of the resonator, often achieving Q values in the range of 500 to 2000, depending on geometry and surface finish.

[0064] FIG. 4 A presents an external perspective of the microwave cavity 302, highlighting its robust mechanical structure and the integration of mounting features. The cavity 302 includes a precision-machined slot 404, which is specifically dimensioned to securely hold the crystal sample in the region of highest microwave field intensity. This slot ensures optimal alignment of the crystal relative to the microwave field and the external static magnetic field, which may be applied along a desired axis (such as the c-axis of the crystal).

[0065] FIG. 4B provides a closer view of the loop-gap resonator 402, illustrating the internal configuration and the placement of the crystal within the slot 404 resonator 302. The loop-gap design consists of a central loop, which acts as an inductor, and a narrow gap, which acts as a capacitive element. The geometry of the loop and gap can be adjusted to achieve resonance frequencies typically in the 6-12 GHz range, suitable for coupling to magnon modes in antiferromagnetic host crystals.Docket no. 10872-0005-PCT

[0066] To facilitate simultaneous optical and microwave measurements, the microwave cavity 302 is equipped with optical access holes 406. These holes are positioned to allow laser beams or other optical signals to pass through the cavity 302 and interact with the crystal 102 in the slot 404, enabling optical excitation and detection without compromising the microwave performance. The optical access holes 406 are aligned with the crystal mounting slot to ensure that the optical path intersects the active region of the sample.

[0067] Additional features may include adjustable coupling ports for microwave input and output, tuning plungers or screws for fine frequency adjustment, and thermal anchoring points to ensure stable cryogenic operation when integrated into a dilution refrigerator or other low-temperature apparatus. The cavity may also be designed to accommodate crystals of various shapes and sizes, and may include vibration isolation or shielding to minimize environmental noise.Overall, the microwave cavity 302 with loop-gap resonator 402 provides a highly controlled environment for studying coherent interactions between microwave fields, magnons, and rare- earth dopant ions, supporting advanced quantum transduction and hybrid quantum system experiments.

[0068] Referring now to FIG. 5, a plot 500 shows transmission through one embodiment of a crystal 102 of ErGdVC . The vertical axis of this plot represents the optical frequency detuning relative to a central transition frequency, while the horizontal axis indicates the applied magnetic field strength. The intensity in the plot corresponds to the measured transmission through the crystal, with regions of lower transmission indicating stronger optical absorption by the erbium ions.

[0069] This plot is an experimental measurement of the optical absorption spectrum for the 4IIS / 2(ZI) —> 4Ii3 / 2(Yi, Y2) transitions of erbium ions doped into an antiferromagnetic gadolinium vanadate host. The frequency-tunable laser source has the polarization set at 45° between 71 (electric field parallel to the c-axis) and c (electric field perpendicular to the c-axis) polarizations.

[0070] At zero magnetic field, the plot reveals four distinct absorption lines, each corresponding to transitions from the lowest level of the Zi Kramers’ doublet to the various Yi and Y2 excited states. The erbium ions occupy two distinct sublattices within the antiferromagnetic host, with each sublattice experiencing a different local magnetic environment due to the orientation of the gadolinium spins. As the external magnetic field is increased along the c-axis, each of these four absorption lines splits into two, with one branch tuning to a higher frequency and the other to a lower frequency. This splitting reflects the factDocket no. 10872-0005-PCT that erbium ions in the two sublattices respond oppositely to the applied field: in one sublattice, the erbium spin is parallel to the field, while in the other it is anti-parallel. The resulting energy level shifts are a direct consequence of the antiferromagnetic ordering and the exchange and dipole-dipole interactions between erbium and gadolinium ions.

[0071] The plot 500 shows avoided crossings, where two absorption lines approach each other as a function of magnetic field but do not cross; instead, they exhibit a characteristic gap. The rich structure observed in the plot 500, including the mixing of the Yi and Y2 doublets and the field-dependent splitting, is further complicated by the internal fields produced by the ordered gadolinium spins. Numerical simulations using crystal field models, extended to include both static exchange fields and magnon coupling, are able to reproduce the main features of the experimental spectra. These models confirm that the observed transitions and their field dependence are governed by the interplay of crystal field effects, exchange interactions, and coherent magnon coupling. The magnitude of the gap at the avoided crossing provides a direct measure of the coupling strength, which in this system is on the order of several gigahertz, indicating robust interaction between the rare-earth dopant and the host’s collective spin dynamics.

[0072] Beyond the absorption spectra, additional experimental data for the ErGdVCh crystal demonstrate its exceptional quantum properties. Two-pulse photon echo measurements reveal long optical coherence times for the erbium transitions, with the longest measured coherence time T2reaching approximately 236 microseconds on the Zi — Yi transition at a magnetic field of 0.24 T. This field corresponds to a quasi-ZEFOZ (zero first-order Zeeman) point, where the transition frequency is relatively insensitive to magnetic field fluctuations, further suppressing decoherence. The temperature dependence of the homogeneous linewidths shows that at low temperatures, the linewidths are nearly constant, but they broaden rapidly above approximately 100 mK, consistent with thermal excitation of magnon modes in the host. The residual linewidth at the lowest temperatures is attributed to nuclear spin fluctuations, which can be further suppressed by isotopic purification of the host and dopant ions.

[0073] Persistent spectral hole burning has also been observed in the crystal, indicating the ability to tailor the absorption profile and implement quantum memory protocols such as atomic frequency comb storage. The combination of long coherence times, strong magnon coupling, and the ability to operate at or near zero applied magnetic field positions this material as a highly promising platform for quantum memory, quantum communication, and microwave-to-optical quantum transduction.Docket no. 10872-0005-PCT

[0074] It should be appreciated that the embodiments described above are merely some of the possible embodiments envisioned, and other embodiments are possible as well. For example, in some embodiments, the host crystal may be a ferromagnetic material rather than an antiferromagnetic material. Utilizing ferromagnetic hosts may be advantageous in scenarios where strong net magnetization is desired, such as for enhanced coupling to external magnetic fields, or for applications requiring tunable magnon spectra and collective spin dynamics distinct from those found in antiferromagnets. Possible ferromagnetic host materials include rare-earth orthoferrites (e.g., gadolinium orthoferrite, GdFeCh), rare-earth garnets (such as yttrium iron garnet, YsFesO , doped with other rare-earth ions), or rare-earth chalcogenides. The choice of ferromagnetic host can be tailored to optimize properties such as magnetic ordering temperature, magnon bandwidth, and compatibility with specific dopant ions.

[0075] Additionally, other variations may include the use of ferrimagnetic or multiferroic host crystals, which can offer unique combinations of magnetic and electric ordering, potentially enabling new functionalities in quantum transduction or sensing. The host lattice may be engineered with composite structures, thin films, or heterostructures to further control strain, interface effects, or coupling to external fields. Doping concentrations may be varied outside the specified range to suit particular device requirements, and the system may incorporate additional functional layers, coatings, or integrated photonic and microwave components for improved performance or device integration. Isotopic purification strategies may be extended to other constituent ions in the host lattice, and the rare-earth dopant may be selected from a broader set of elements to access different transition wavelengths, spin properties, or quantum protocols. These and other modifications are within the scope of the disclosure, and the disclosed concepts may be adapted to a wide variety of materials systems and quantum technology applications.

[0076] It is appreciated that various features of the invention which are, for clarity, described in the contexts of separate embodiments may also be provided in combination in a single embodiment. Conversely, various features of the invention which are, for brevity, described in the context of a single embodiment may also be provided separately or in any suitable subcombination.EXAMPLES

[0077] Illustrative examples of the technologies disclosed herein are provided below. An embodiment of the technologies may include any one or more, and any combination of, the examples described below.Docket no. 10872-0005-PCT

[0078] Example 1 includes a rare-earth-doped crystal for long optical coherence, the crystal comprising a host lattice, wherein a unit cell of the host lattice has a first rare earth ion, the host lattice being antiferromagnetic below a Neel temperature or ferromagnetic below a Curie temperature, wherein the host lattice is doped with a second rare-earth ion, the second rare-earth ion present at a concentration between 10 and 1000 parts per million.

[0079] Example 2 includes the subject matter of Example 1, and wherein the crystal exhibits optical coherence times for the rare-earth ion greater than 200 microseconds.

[0080] Example 3 includes the subject matter of any of Examples 1 and 2, and wherein the host lattice is gadolinium vanadate (GdVCN).

[0081] Example 4 includes the subject matter of any of Examples 1-3, and wherein the host lattice is gadolinium oxide (Gd2Os).

[0082] Example 5 includes the subject matter of any of Examples 1-4, and wherein the host lattice is gadolinium silicate (Gd2SiOs).

[0083] Example 6 includes the subject matter of any of Examples 1-5, and wherein the host lattice is gadolinium gallium garnet (GdsGasO ).

[0084] Example 7 includes the subject matter of any of Examples 1-6, and wherein the host lattice is a double tungstate of gadolinium and an alkali metal.

[0085] Example 8 includes the subject matter of any of Examples 1-7, and wherein the host lattice comprises a rare-earth fluoride, selected from the group consisting of gadolinium fluoride, lithium gadolinium fluoride, and erbium lithium fluoride.

[0086] Example 9 includes the subject matter of any of Examples 1-8, and wherein the first rare earth ion in the host lattice is selected from the group consisting of gadolinium, yttrium, neodymium, ytterbium, and dysprosium.

[0087] Example 10 includes the subject matter of any of Examples 1-9, and wherein the second rare-earth ion is erbium.

[0088] Example 11 includes the subject matter of any of Examples 1-10, and wherein the second rare-earth ion is selected from the group consisting of neodymium, ytterbium, cerium, samarium, gadolinium, dysprosium, and europium(II).

[0089] Example 12 includes the subject matter of any of Examples 1-11, and wherein the second rare-earth ion is selected from the group consisting of europium, praseodymium, thulium, terbium, holmium.

[0090] Example 13 includes the subject matter of any of Examples 1-12, and wherein an optical mode and a magnon mode of the host lattice are coherently coupled via the second rare-earth ion.Docket no. 10872-0005-PCT

[0091] Example 14 includes the subject matter of any of Examples 1-13, and wherein the host lattice is isotopically purified to reduce a nuclear spin background.

[0092] Example 15 includes the subject matter of any of Examples 1-14, and wherein the host lattice is gadolinium silicate, wherein the host lattice is isotopically purified such that a combined concentration of gadolinium-155 and gadolinium- 157 isotopes is reduced to less than 5% of a total gadolinium content..

[0093] Example 16 includes the subject matter of any of Examples 1-15, and wherein the second rare-earth ion is isotopically purified to at least 95% of a single isotope with zero nuclear spin.

[0094] Example 17 includes the subject matter of any of Examples 1-16, and wherein the host lattice is antiferromagnetic below a Neel temperature of less than 20 Kelvin.

[0095] Example 18 includes the subject matter of any of Examples 1-17, and wherein the host lattice is ferromagnetic below a Curie temperature.

[0096] Example 19 includes the subject matter of any of Examples 1-18, and wherein the host lattice is a multiferroic material.

[0097] Example 20 includes the subject matter of any of Examples 1-19, and wherein the crystal is configured for use in quantum communication, quantum sensing, or entanglement generation.

[0098] Example 21 includes a system for achieving long optical coherence times, comprising a rare-earth-doped crystal, the crystal including a host lattice comprising first rare earth ions, wherein the host lattice is antiferromagnetic below a Neel temperature or ferromagnetic below a Curie temperature, wherein the host lattice is doped with a second rare- earth ion; a cryogenic cooling apparatus configured to maintain the crystal at a temperature below the Neel temperature such that electron spins in the host lattice are magnetically ordered; and an optical source configured to excite optical transitions of the second rare-earth ion, wherein, in use, the system is configured to provide optical coherence times for the second rare-earth ion greater than 200 microseconds.

[0099] Example 22 includes the subject matter of Example 21, and wherein the optical source is configured to selectively excite transitions between ground and excited states of the second rare-earth ion to enable quantum memory operations.

[0100] Example 23 includes the subject matter of any of Examples 21 and 22, and wherein the system is configured for use in quantum communication, quantum sensing, or entanglement generation.Docket no. 10872-0005-PCT

[0101] Example 24 includes the subject matter of any of Examples 21-23, and wherein the host lattice is isotopically purified to reduce a nuclear spin background and further enhance an optical coherence time.

[0102] Example 25 includes the subject matter of any of Examples 21-24, and wherein the second rare-earth ion is erbium.

[0103] Example 26 includes the subject matter of any of Examples 21-25, and wherein the host lattice is gadolinium vanadate (GdVO4), gadolinium oxide (Gd2Os), gadolinium silicate (Gd2SiOs), or gadolinium gallium garnet (GdsGasO ).

[0104] Example 27 includes the subject matter of any of Examples 21-26, and wherein the system is configured to perform persistent spectral hole burning for quantum memory protocols.

[0105] Example 28 includes the subject matter of any of Examples 21-27, and further including a superconducting magnet configured to apply a magnetic field to the rare-earth- doped crystal.

[0106] Example 29 includes the subject matter of any of Examples 21-28, and further including a microwave cavity resonator positioned to couple electromagnetic energy to magnon modes of the host lattice.

[0107] Example 30 includes the subject matter of any of Examples 21-29, and wherein the microwave cavity resonator is tunable to match a resonance frequency of a magnon mode in the host lattice.

[0108] Example 31 includes the subject matter of any of Examples 21-30, and wherein the system is configured to enable coherent coupling between an optical transition of the second rare-earth ion and a magnon mode of the host lattice.

[0109] Example 32 includes the subject matter of any of Examples 21-31, and wherein the system is configured to transduce quantum information between microwave and optical domains via a coherent coupling between the second rare-earth ion and a magnon mode.

[0110] Example 33 includes the subject matter of any of Examples 21-32, and wherein the system is operable at zero or near-zero applied magnetic field to achieve magnon-enhanced optical coherence or quantum transduction.

[0111] Example 34 includes the subject matter of any of Examples 21-33, and wherein the system is configured to operate at a zero first-order Zeeman (ZEFOZ) point to further enhance optical coherence time or transduction efficiency.

[0112] Example 35 includes the subject matter of any of Examples 21-34, and wherein the system is configured to generate entanglement using a rephased amplified spontaneousDocket no. 10872-0005-PCT emission (RASE) protocol, comprising inverting a population of a rare-earth ion ensemble to produce amplified spontaneous emission, and applying a rephasing pulse sequence to emit a second optical field entangled with an original emission.

[0113] Example 36 includes a method for achieving long optical coherence times in a rare-earth-doped crystal, the method comprising cooling a host crystal to a temperature below a magnetic transition temperature of the host crystal such that electron spins in the host crystal are antiferromagnetically or ferromagnetically ordered; and providing an optical source to couple to an optical transition of rare-earth ion dopants in the host crystal.

[0114] Example 37 includes the subject matter of Example 36, and wherein the host crystal is doped with a rare-earth ion selected from the group consisting of erbium, neodymium, ytterbium, cerium, samarium, gadolinium, dysprosium, and europium(II).

[0115] Example 38 includes the subject matter of any of Examples 36 and 37, and wherein the host crystal is selected from the group consisting of gadolinium vanadate (GdVO4), gadolinium oxide (Gd2Os), gadolinium silicate (Gd2SiOs), gadolinium gallium garnet (GdsGasO ), and a double tungstate of gadolinium and an alkali metal.

[0116] Example 39 includes the subject matter of any of Examples 36-38, and wherein a concentration of the rare-earth ion dopant is between 10 and 1000 parts per million.

[0117] Example 40 includes the subject matter of any of Examples 36-39, and wherein the host crystal is formed using host lattice materials that have been isotopically enriched to reduce a nuclear spin background.

[0118] Example 41 includes the subject matter of any of Examples 36-40, and wherein the host crystal is gadolinium silicate and a combined concentration of gadolinium-155 and gadolinium- 157 isotopes is reduced to less than 5% of a total gadolinium content.

[0119] Example 42 includes the subject matter of any of Examples 36-41, and further including isotopically purifying the rare-earth ion dopant to at least 95% of a single isotope with zero nuclear spin.

[0120] Example 43 includes the subject matter of any of Examples 36-42, and wherein the host crystal is cooled to a temperature below a Neel temperature of less than 20 Kelvin.

[0121] Example 44 includes the subject matter of any of Examples 36-43, and wherein the crystal exhibits optical coherence times for the rare-earth ion greater than 200 microseconds.

[0122] Example 45 includes the subject matter of any of Examples 36-44, and further including measuring the optical coherence time using a two-pulse photon echo technique.Docket no. 10872-0005-PCT

[0123] Example 46 includes the subject matter of any of Examples 36-45, and further including performing persistent spectral hole burning for quantum memory protocols.

[0124] Example 47 includes the subject matter of any of Examples 36-46, and wherein the method is used for quantum communication, quantum sensing, or entanglement generation.

[0125] Example 48 includes the subject matter of any of Examples 36-47, and further including assembling a system including the rare-earth-doped antiferromagnetic crystal, a cryogenic cooling apparatus configured to maintain the crystal at a temperature below a Neel temperature, and an optical source configured to excite optical transitions of the rare-earth ion dopant.

[0126] Example 49 includes the subject matter of any of Examples 36-48, and further including configuring a superconducting magnet to apply a magnetic field to the rare-earth- doped antiferromagnetic crystal.

[0127] Example 50 includes the subject matter of any of Examples 36-49, and further including configured a microwave cavity resonator positioned to couple electromagnetic energy to magnon modes of the host crystal.

[0128] Example 51 includes the subject matter of any of Examples 36-50, and wherein an optical mode and a magnon mode of a host lattice are coherently coupled via the rare-earth ion dopant.

[0129] Example 52 includes the subject matter of any of Examples 36-51, and further including performing transduction of quantum information between microwave and optical domains via the coherent coupling between the rare-earth ion and the magnon mode.

Claims

Docket no. 10872-0005-PCTCLAIMS:

1. A rare-earth-doped crystal for long optical coherence, the crystal comprising: a host lattice, wherein a unit cell of the host lattice has a first rare earth ion, the host lattice being antiferromagnetic below a Neel temperature or ferromagnetic below a Curie temperature, wherein the host lattice is doped with a second rare-earth ion, the second rare-earth ion present at a concentration between 10 and 1000 parts per million.

2. The rare-earth-doped crystal of claim 1, wherein the crystal exhibits optical coherence times for the rare-earth ion greater than 200 microseconds.

3. The rare-earth-doped crystal of claim 1, wherein the host lattice is gadolinium vanadate (GdVCh).

4. The rare-earth-doped crystal of claim 1, wherein the second rare-earth ion is erbium.

5. The rare-earth-doped crystal of claim 1, wherein the second rare-earth ion is selected from the group consisting of neodymium, ytterbium, cerium, samarium, gadolinium, dysprosium, and europium(II).

6. The rare-earth-doped crystal of claim 1, wherein the second rare-earth ion is selected from the group consisting of europium, praseodymium, thulium, terbium, holmium.

7. The rare-earth-doped crystal of claim 1, wherein an optical mode and a magnon mode of the host lattice are coherently coupled via the second rare-earth ion.

8. The rare-earth-doped crystal of claim 1, wherein the host lattice is antiferromagnetic below a Neel temperature of less than 20 Kelvin.

9. The rare-earth-doped crystal of claim 1 , wherein the host lattice is ferromagnetic below a Curie temperature.Docket no. 10872-0005-PCT10. The rare-earth-doped crystal of claim 1, wherein the crystal is configured for use in quantum communication, quantum sensing, or entanglement generation.

11. A system for achieving long optical coherence times, comprising: a rare-earth-doped crystal, the crystal including a host lattice comprising first rare earth ions, wherein the host lattice is antiferromagnetic below a Neel temperature or ferromagnetic below a Curie temperature, wherein the host lattice is doped with a second rare-earth ion; a cryogenic cooling apparatus configured to maintain the crystal at a temperature below the Neel temperature such that electron spins in the host lattice are magnetically ordered; and an optical source configured to excite optical transitions of the second rare-earth ion, wherein, in use, the system is configured to provide optical coherence times for the second rare-earth ion greater than 200 microseconds.

12. The system of claim 11, wherein the optical source is configured to selectively excite transitions between ground and excited states of the second rare-earth ion to enable quantum memory operations.

13. The system of claim 11, wherein the system is configured for use in quantum communication, quantum sensing, or entanglement generation.

14. The system of claim 11, wherein the host lattice is isotopically purified to reduce a nuclear spin background and further enhance an optical coherence time.

15. The system of claim 11, wherein the second rare-earth ion is erbium.

16. The system of claim 11, further comprising a superconducting magnet configured to apply a magnetic field to the rare-earth-doped crystal.

17. The system of claim 16, further comprising a microwave cavity resonator positioned to couple electromagnetic energy to magnon modes of the host lattice.Docket no. 10872-0005-PCT18. The system of claim 11, wherein the system is configured to enable coherent coupling between an optical transition of the second rare-earth ion and a magnon mode of the host lattice.

19. The system of claim 11, wherein the system is configured to generate entanglement using a rephased amplified spontaneous emission (RASE) protocol, comprising inverting a population of a rare-earth ion ensemble to produce amplified spontaneous emission, and applying a rephasing pulse sequence to emit a second optical field entangled with an original emission.

20. A method for achieving long optical coherence times in a rare-earth-doped crystal, the method comprising: cooling a host crystal to a temperature below a magnetic transition temperature of the host crystal such that electron spins in the host crystal are antiferromagnetically or ferromagnetically ordered; and providing an optical source to couple to an optical transition of rare-earth ion dopants in the host crystal.

21. The method of claim 20, wherein a concentration of the rare-earth ion dopant is between 10 and 1000 parts per million.

22. The method of claim 20, wherein the host crystal is cooled to a temperature below a Neel temperature of less than 20 Kelvin.

23. The method of claim 20, wherein the crystal exhibits optical coherence times for the rare-earth ion greater than 200 microseconds.

24. The method of claim 20, further comprising configuring a microwave cavity resonator positioned to couple electromagnetic energy to magnon modes of the host crystal.

25. The method of claim 20, further comprising performing transduction of quantum information between microwave and optical domains via the coherent coupling between the rare-earth ion and a magnon mode.

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