Optically addressable nuclear spins in a solid with a six-hour coherence time

Impact of Zeeman and hyperfine interactions on the magnetic properties of paramagnetic metal Ions: I. Local interactions of the electron spin

The anisotropic Zeeman interaction of an ion, and the strong hyperfine interaction with its own nucleus, can significantly influence its interactions with the local environment. These effects, including the reduction of the effective magnetic moment of the electron spin and the phase memory decay rate, are studied theoretically. Analytical expressions describing the mean magnetic moment of the electron spin are obtained. The results of the theoretical analysis and accompanying numerical computations show that the strong hyperfine interaction of the ion reduces its effective magnetic moment. In particular, a 7% reduction is found for the scandium endofullerene Sc2@C80(CH2Ph) under conditions typical of an X-band EPR experiment.

Coherent Erbium Spin Defects in Colloidal Nanocrystal Hosts

We demonstrate nearly a microsecond of spin coherence in Er3+ ions doped in cerium dioxide nanocrystal hosts, despite a large gyromagnetic ratio and nanometric proximity of the spin defect to the nanocrystal surface. The long spin coherence is enabled by reducing the dopant density below the instantaneous diffusion limit in a nuclear spin-free host material, reaching the limit of a single erbium spin defect per nanocrystal. We observe a large Orbach energy in a highly symmetric cubic site, further protecting the coherence in a qubit that would otherwise rapidly decohere. Spatially correlated electron spectroscopy measurements reveal the presence of Ce3+ at the nanocrystal surface, which likely acts as extraneous paramagnetic spin noise. Even with these factors, defect-embedded nanocrystal hosts show tremendous promise for quantum sensing and quantum communication applications, with multiple avenues, including core-shell fabrication, redox tuning of oxygen vacancies, and organic surfactant modification, available to further enhance their spin coherence and functionality in the future.

Remote and controlled quantum teleportation network of the polarization squeezed state

Quantum teleportation is a building block in quantum computation and quantum communication. The continuous-variable polarization squeezed state is a key resource in quantum networks, offering advantages for long-distance distribution and direct interfacing of quantum nodes. Although polarization squeezed state has been generated and distributed between remote users, it is a long-standing goal to implement controlled quantum teleportation of the polarization squeezed state with multiple remote users. Here, we propose a feasible scheme to teleport a polarization squeezed state among multiple remote users under control. The polarization state is transferred between different remote quantum networks, and the controlled quantum teleportation of the polarization state can be implemented in one quantum network involving multiple remote users. The results show that such a controlled quantum teleportation can be realized with 36 users through about 6-km free-space or fiber quantum channels, where the fidelity of 0.352 is achieved beyond the classical limit of 0.349 with an input squeezing variance of 0.25. This scheme provides a direct reference for the experimental implementation of remote and controlled quantum teleportation of polarization states, thus enabling more teleportation-based quantum network protocols.

The Asymmetry Observed between the Effects of Photon-Phonon Coupling and Crystal Field on the Fine Structure of Fluorescence and Spontaneous Four-Wave Mixing in Ion-Doped Microcrystals

In this paper, we explore the asymmetry observed between the effects of photon-phonon coupling (nested-dressing) and a crystal field (CF) on the fine structure of fluorescence (FL) and spontaneous four-wave mixing (SFWM) in Eu3+: BiPO4 and Eu3+: NaYF4. The competition between the CF and the strong photon-phonon dressing leads to dynamic splitting in two directions. The CF leads to static splitting in one direction under weak phonon dressing. The evolution from strong dressing to weak dressing results in spectral asymmetry. This spectral asymmetry includes out-of-phase FL and in-phase SFWM. Further, the large ratio between the dressing Rabi frequency and the de-phase rate leads to strong FL and SFWM asymmetry due to photon-phonon constructive dressing. Moreover, the experimental results suggest the analogy of a spectra asymmetry router with a channel equalization ratio of 96.6%.

Nanocavity-Mediated Purcell Enhancement of Er in TiO2 Thin Films Grown via Atomic Layer Deposition

The use of trivalent erbium (Er3+), typically embedded as an atomic defect in the solid-state, has widespread adoption as a dopant in telecommunication devices and shows promise as a spin-based quantum memory for quantum communication. In particular, its natural telecom C-band optical transition and spin-photon interface make it an ideal candidate for integration into existing optical fiber networks without the need for quantum frequency conversion. However, successful scaling requires a host material with few intrinsic nuclear spins, compatibility with semiconductor foundry processes, and straightforward integration with silicon photonics. Here, we present Er-doped titanium dioxide (TiO2) thin film growth on silicon substrates using a foundry-scalable atomic layer deposition process with a wide range of doping controls over the Er concentration. Even though the as-grown films are amorphous after oxygen annealing, they exhibit relatively large crystalline grains, and the embedded Er ions exhibit the characteristic optical emission spectrum from anatase TiO2. Critically, this growth and annealing process maintains the low surface roughness required for nanophotonic integration. Finally, we interface Er ensembles with high quality factor Si nanophotonic cavities via evanescent coupling and demonstrate a large Purcell enhancement (≈300) of their optical lifetime. Our findings demonstrate a low-temperature, nondestructive, and substrate-independent process for integrating Er-doped materials with silicon photonics. At high doping densities this platform can enable integrated photonic components such as on-chip amplifiers and lasers, while dilute concentrations can realize single ion quantum memories.

Post-quantum cryptography and the quantum future of cybersecurity

We review the current status of efforts to develop and deploy post-quantum cryptography on the Internet. Then we suggest specific ways in which quantum technologies might be used to enhance cybersecurity in the near future and beyond. We focus on two goals: protecting the secret keys that are used in classical cryptography, and ensuring the trustworthiness of quantum computations. These goals may soon be within reach, thanks to recent progress in both theory and experiment. This progress includes interactive protocols for testing quantumness as well as for performing uncloneable cryptographic computations; and experimental demonstrations of device-independent random number generators, device-independent quantum key distribution, quantum memories, and analog quantum simulators.

Suppression of Pulsed Dynamic Nuclear Polarization by Many-Body Spin Dynamics

We study a mechanism by which nuclear hyperpolarization due to the polarization transfer from a microwave-pulse-controlled electron spin is suppressed. From analytical and numerical calculations of the unitary dynamics of multiple nuclear spins, we uncover that, combined with the formation of the dark state within a cluster of nuclei, coherent higher-order nuclear spin dynamics impose limits on the efficiency of the polarization transfer even in the absence of mundane depolarization processes such as nuclear spin diffusion and relaxation. Furthermore, we show that the influence of the dark state can be partly mitigated by introducing a disentangling operation. Our analysis is applied to the nuclear polarizations observed in ^{13}C nuclei coupled with a single nitrogen-vacancy center in diamond [Randall et al., Science 374, 1474 (2021)SCIEAS0036-807510.1126/science.abk0603]. Our Letter sheds light on collective engineering of nuclear spins as well as future designs of pulsed dynamic nuclear polarization protocols.

Qudit-Based Spectroscopy for Measurement and Control of Nuclear-Spin Qubits in Silicon Carbide

Nuclear spins with hyperfine coupling to single electron spins are highly valuable quantum bits. Here we probe and characterize the particularly rich nuclear-spin environment around single silicon vacancy color centers (V2) in 4H-SiC. By using the electron spin-3/2 qudit as a four level sensor, we identify several sets of ^{29}Si and ^{13}C nuclear spins through their hyperfine interaction. We extract the major components of their hyperfine coupling via optical detected nuclear magnetic resonance, and assign them to shells in the crystal via the density function theory simulations. We utilize the ground-state level anticrossing of the electron spin for dynamic nuclear polarization and achieve a nuclear-spin polarization of up to 98±6%. We show that this scheme can be used to detect the nuclear magnetic resonance signal of individual spins and demonstrate their coherent control. Our work provides a detailed set of parameters and first steps for future use of SiC as a multiqubit memory and quantum computing platform.

Twisted van der Waals Quantum Materials: Fundamentals, Tunability, and Applications

Twisted van der Waals (vdW) quantum materials have emerged as a rapidly developing field of two-dimensional (2D) semiconductors. These materials establish a new central research area and provide a promising platform for studying quantum phenomena and investigating the engineering of novel optoelectronic properties such as single photon emission, nonlinear optical response, magnon physics, and topological superconductivity. These captivating electronic and optical properties result from, and can be tailored by, the interlayer coupling using moiré patterns formed by vertically stacking atomic layers with controlled angle misorientation or lattice mismatch. Their outstanding properties and the high degree of tunability position them as compelling building blocks for both compact quantum-enabled devices and classical optoelectronics. This paper offers a comprehensive review of recent advancements in the understanding and manipulation of twisted van der Waals structures and presents a survey of the state-of-the-art research on moiré superlattices, encompassing interdisciplinary interests. It delves into fundamental theories, synthesis and fabrication, and visualization techniques, and the wide range of novel physical phenomena exhibited by these structures, with a focus on their potential for practical device integration in applications ranging from quantum information to biosensors, and including classical optoelectronics such as modulators, light emitting diodes, lasers, and photodetectors. It highlights the unique ability of moiré superlattices to connect multiple disciplines, covering chemistry, electronics, optics, photonics, magnetism, topological and quantum physics. This comprehensive review provides a valuable resource for researchers interested in moiré superlattices, shedding light on their fundamental characteristics and their potential for transformative applications in various fields.

Design Rules, Accurate Enthalpy Prediction, and Synthesis of Stoichiometric Eu3+ Quantum Memory Candidates

Stoichiometric Eu3+ compounds have recently shown promise for building dense, optically addressable quantum memory as the cations' long nuclear spin coherence times and shielded 4f electron optical transitions provide reliable memory platforms. Implementing such a system, though, requires ultranarrow, inhomogeneous linewidth compounds. Finding this rare linewidth behavior within a wide range of potential chemical spaces remains difficult, and while exploratory synthesis is often guided by density functional theory (DFT) calculations, lanthanides' 4f electrons pose unique challenges for stability predictions. Here, we report DFT procedures that reliably reproduce known phase diagrams and correctly predict two experimentally realized quantum memory candidates. We are the first to synthesize the double perovskite halide Cs2NaEuF6. It is an air-stable compound with a calculated band gap of 5.0 eV that surrounds Eu3+ with mononuclidic elements, which are desirable for avoiding inhomogeneous linewidth broadening. We also analyze computational database entries to identify phosphates and iodates as the next generation of chemical spaces for stoichiometric quantum memory system studies. This work identifies new candidate platforms for exploring chemical effects on quantum memory candidates' inhomogeneous linewidth while also providing a framework for screening Eu3+ compound stability with DFT.

Rare isotope-containing diamond colour centres for fundamental symmetry tests

Detecting a non-zero electric dipole moment in a particle would unambiguously signify physics beyond the Standard Model. A potential pathway towards this is the detection of a nuclear Schiff moment, the magnitude of which is enhanced by the presence of nuclear octupole deformation. However, due to the low production rate of isotopes featuring such 'pear-shaped' nuclei, capturing, detecting and manipulating them efficiently is a crucial prerequisite. Incorporating them into synthetic diamond optical crystals can produce defects with defined, molecule-like structures and isolated electronic states within the diamond band gap, increasing capture efficiency, enabling repeated probing of even a single atom and producing narrow optical linewidths. In this study, we used density functional theory to investigate the formation, structure and electronic properties of crystal defects in diamond containing [Formula: see text], a rare isotope that is predicted to have an exceptionally strong nuclear octupole deformation. In addition, we identified and studied stable lanthanide-containing defects with similar electronic structures as non-radioactive proxies to aid in experimental methods. Our findings hold promise for the existence of such defects and can contribute to the development of a quantum information processing-inspired toolbox of techniques for studying rare isotopes. This article is part of the Theo Murphy meeting issue 'Diamond for quantum applications'.

Spectral and temporal atomic coherence interaction in Eu3+ : NaYF4 and Eu3+ : BiPO4

We investigate the spectral and temporal atomic coherence interaction based on out-of-phase fluorescence (FL) and spontaneous parametric four-wave mixing (SFWM) from the hexagonal phase of Eu3+ : NaYF4 and different phases of Eu3+ : BiPO4. Spectral and temporal interactions are interrelated and reduced by about 2 times due to two-photon nested dressing in contrast to the sum of each laser excitation. As the lifetime of photons increases, off-resonance profile cross-interaction decreases because cross-interaction reverses the signal at the near time gate position and keeps it consistent at the far time gate position. Moreover, the thermal phonon dressing at 300 K exhibits 6 times more eminent and obvious temporal interaction than that at 77 K. In a different phase of Eu3+ : BiPO4, there are three dark dips having stronger self-interaction; however, Eu3+ : NaYF4 has two dark dips as Eu3+ : BiPO4 has two phonon dressing. Further, the pure hexagonal phase of Eu3+ : BiPO4 demonstrates the strongest cross-interaction and longest coherent time under the dressing effect due to the smallest dressing phonon detuning and off-resonance profile cross-interaction at PMT2 because the angle quantization is the strongest. Such results can be used for designing novel quantum devices and have potential applications in quantum memory devices.

Germanium Vacancy in Diamond Quantum Memory Exceeding 20 ms

Negatively charged group-IV defects in diamond show great potential as quantum network nodes due to their efficient spin-photon interface. However, reaching sufficiently long coherence times remains a challenge. In this work, we demonstrate coherent control of germanium vacancy center (GeV) at millikelvin temperatures and extend its coherence time by several orders of magnitude to more than 20 ms. We model the magnetic and amplitude noise as an Ornstein-Uhlenbeck process, reproducing the experimental results well. The utilized method paves the way to optimized coherence times of group-IV defects in various experimental conditions and their successful applications in quantum technologies.

Future Paths in Cryogenic Single-Molecule Fluorescence Spectroscopy

In the last three decades, cryogenic single-molecule fluorescence spectroscopy has provided average-free understanding of the photophysics and of fundamental interactions at molecular scales. Furthermore, they propose original pathways and applications in the treatment and storage of quantum information. The ultranarrow lifetime-limited zero-phonon line acts as an excellent sensor to local perturbations caused either by intrinsic dynamical degrees of freedom, or by external perturbations, such as those caused by electric fields, elastic and acoustic deformations, or light-induced dynamics. Single aromatic hydrocarbon molecules, being sensitive to nanoscale probing at nanometer scales, are potential miniaturized platforms for integrated quantum photonics. In this Perspective, we look back at some of the past advances in cryogenic optical microscopy and propose some perspectives for future development.

Superradiant Detection of Microscopic Optical Dipolar Interactions

The interaction between light and cold atoms is a complex phenomenon potentially featuring many-body resonant dipole interactions. A major obstacle toward exploring these quantum resources of the system is macroscopic light propagation effects, which not only limit the available time for the microscopic correlations to locally build up, but also create a directional, superradiant emission background whose variations can overwhelm the microscopic effects. In this Letter, we demonstrate a method to perform "background-free" detection of the microscopic optical dynamics in a laser-cooled atomic ensemble. This is made possible by transiently suppressing the macroscopic optical propagation over a substantial time, before a recall of superradiance that imprints the effect of the accumulated microscopic dynamics onto an efficiently detectable outgoing field. We apply this technique to unveil and precisely characterize a density-dependent, microscopic dipolar dephasing effect that generally limits the lifetime of optical spin-wave order in ensemble-based atom-light interfaces.

Single-molecule electron spin resonance by means of atomic force microscopy

Understanding and controlling decoherence in open quantum systems is of fundamental interest in science, whereas achieving long coherence times is critical for quantum information processing1. Although great progress was made for individual systems, and electron spin resonance (ESR) of single spins with nanoscale resolution has been demonstrated2-4, the understanding of decoherence in many complex solid-state quantum systems requires ultimately controlling the environment down to atomic scales, as potentially enabled by scanning probe microscopy with its atomic and molecular characterization and manipulation capabilities. Consequently, the recent implementation of ESR in scanning tunnelling microscopy5-8 represents a milestone towards this goal and was quickly followed by the demonstration of coherent oscillations9,10 and access to nuclear spins11 with real-space atomic resolution. Atomic manipulation even fuelled the ambition to realize the first artificial atomic-scale quantum devices12. However, the current-based sensing inherent to this method limits coherence times12,13. Here we demonstrate pump-probe ESR atomic force microscopy (AFM) detection of electron spin transitions between non-equilibrium triplet states of individual pentacene molecules. Spectra of these transitions exhibit sub-nanoelectronvolt spectral resolution, allowing local discrimination of molecules that only differ in their isotopic configuration. Furthermore, the electron spins can be coherently manipulated over tens of microseconds. We anticipate that single-molecule ESR-AFM can be combined with atomic manipulation and characterization and thereby paves the way to learn about the atomistic origins of decoherence in atomically well-defined quantum elements and for fundamental quantum-sensing experiments.

Quantum storage of entangled photons at telecom wavelengths in a crystal

Quantum storage and distribution of entanglement are the key ingredients for realizing a global quantum internet. Compatible with existing fiber networks, telecom-wavelength entangled photons and corresponding quantum memories are of central interest. Recently, 167Er3+ ions have been identified as a promising candidate for an efficient telecom quantum memory. However, to date, no storage of entangled photons, the crucial step of quantum memory using these promising ions, 167Er3+, has been reported. Here, we demonstrate the storage and retrieval of the entangled state of two telecom photons generated from an integrated photonic chip. Combining the natural narrow linewidth of the entangled photons and long storage time of 167Er3+ ions, we achieve storage time of 1.936 μs, more than 387 times longer than in previous works. Successful storage of entanglement in the crystal is certified using entanglement witness measurements. These results pave the way for realizing quantum networks based on solid-state devices.

Frequency Tunable, Cavity-Enhanced Single Erbium Quantum Emitter in the Telecom Band

Single quantum emitters embedded in solid-state hosts are an ideal platform for realizing quantum information processors and quantum network nodes. Among the currently investigated candidates, Er^{3+} ions are particularly appealing due to their 1.5  μm optical transition in the telecom band as well as their long spin coherence times. However, the long lifetimes of the excited state-generally in excess of 1 ms-along with the inhomogeneous broadening of the optical transition result in significant challenges. Photon emission rates are prohibitively small, and different emitters generally create photons with distinct spectra, thereby preventing multiphoton interference-a requirement for building large-scale, multinode quantum networks. Here we solve this challenge by demonstrating for the first time linear Stark tuning of the emission frequency of a single Er^{3+} ion. Our ions are embedded in a lithium niobate crystal and couple evanescently to a silicon nanophotonic crystal cavity that provides a strong increase of the measured decay rate. By applying an electric field along the crystal c axis, we achieve a Stark tuning greater than the ion's linewidth without changing the single-photon emission statistics of the ion. These results are a key step towards rare earth ion-based quantum networks.

X-ray Spectroscopy of a Rare-Earth Molecular System Measured at the Single Atom Limit at Room Temperature

We investigate the limit of X-ray detection at room temperature on rare-earth molecular films using lanthanum and a pyridine-based dicarboxamide organic linker as a model system. Synchrotron X-ray scanning tunneling microscopy is used to probe the molecules with different coverages on a HOPG substrate. X-ray-induced photocurrent intensities are measured as a function of molecular coverage on the sample, allowing a correlation of the amount of La ions with the photocurrent signal strength. X-ray absorption spectroscopy shows cogent M4,5 absorption edges of the lanthanum ion originated by the transitions from the 3d3/2 and 3d5/2 to 4f orbitals. X-ray absorption spectra measured in the tunneling regime further reveal an X-ray excited tunneling current produced at the M4,5 absorption edge of the La ion down to the ultimate atomic limit at room temperature.

Iterative Adaptive Spectroscopy of Short Signals

We develop an iterative, adaptive frequency sensing protocol based on Ramsey interferometry of a two-level system. Our scheme allows one to estimate unknown frequencies with a high precision from short, finite signals consisting of only a small number of Ramsey fringes. It avoids several issues related to processing of decaying signals and reduces the experimental overhead related to sampling. High precision is achieved by enhancing the Ramsey sequence to prepare with high fidelity both the sensing and readout state and by using an iterative procedure built to mitigate systematic errors when estimating frequencies from Fourier transforms. A comparison with state-of-the-art dynamical decoupling techniques reveals a significant speedup of the frequency estimation without loss of precision.

Indistinguishable telecom band photons from a single Er ion in the solid state

Atomic defects in the solid state are a key component of quantum repeater networks for long-distance quantum communication1. Recently, there has been significant interest in rare earth ions2-4, in particular Er3+ for its telecom band optical transition5-7 that allows long-distance transmission in optical fibres. However, the development of repeater nodes based on rare earth ions has been hampered by optical spectral diffusion, precluding indistinguishable single-photon generation. Here, we implant Er3+ into CaWO4, a material that combines a non-polar site symmetry, low decoherence from nuclear spins8 and is free of background rare earth ions, to realize significantly reduced optical spectral diffusion. For shallow implanted ions coupled to nanophotonic cavities with large Purcell factor, we observe single-scan optical linewidths of 150 kHz and long-term spectral diffusion of 63 kHz, both close to the Purcell-enhanced radiative linewidth of 21 kHz. This enables the observation of Hong-Ou-Mandel interference9 between successively emitted photons with a visibility of V = 80(4)%, measured after a 36 km delay line. We also observe spin relaxation times T1,s = 3.7 s and T2,s > 200 μs, with the latter limited by paramagnetic impurities in the crystal instead of nuclear spins. This represents a notable step towards the construction of telecom band quantum repeater networks with single Er3+ ions.

Erbium emitters in commercially fabricated nanophotonic silicon waveguides

Quantum memories integrated into nanophotonic silicon devices are a promising platform for large quantum networks and scalable photonic quantum computers. In this context, erbium dopants are particularly attractive, as they combine optical transitions in the telecommunications frequency band with the potential for second-long coherence time. Here, we show that these emitters can be reliably integrated into commercially fabricated low-loss waveguides. We investigate several integration procedures and obtain ensembles of many emitters with an inhomogeneous broadening of <2 GHz and a homogeneous linewidth of <30 kHz. We further observe the splitting of the electronic spin states in a magnetic field up to 9 T that freezes paramagnetic impurities. Our findings are an important step toward long-lived quantum memories that can be fabricated on a wafer-scale using CMOS technology.

Entangling microwaves with light

Quantum entanglement is a key resource in currently developed quantum technologies. Sharing this fragile property between superconducting microwave circuits and optical or atomic systems would enable new functionalities, but this has been hindered by an energy scale mismatch of >10⁴ and the resulting mutually imposed loss and noise. In this work, we created and verified entanglement between microwave and optical fields in a millikelvin environment. Using an optically pulsed superconducting electro-optical device, we show entanglement between propagating microwave and optical fields in the continuous variable domain. This achievement not only paves the way for entanglement between superconducting circuits and telecom wavelength light, but also has wide-ranging implications for hybrid quantum networks in the context of modularization, scaling, sensing, and cross-platform verification.

Zeeman spectroscopy and crystal-field analysis of low symmetry centres in Nd3+doped Y2SiO5

We report on infrared to visible Zeeman absorption spectroscopy and parameterised crystal-field modelling of Nd³⁺centres in Y₂SiO₅through the use of experimentally inferred crystal-field energy levels and Zeeman directional electronicgvalues. We demonstrate that good agreement between the calculated and experimental crystal-field energy levels as well as directional Zeemangvalues along all three crystallographic axes can be obtained. Further, we demonstrate that the addition of correlation crystal field effects successfully account for discrepancies that arise between the calculated and experimental values relevant to the²H11/2(2) multiplet in a one-electron crystal field model.

Electron and nuclear magnetic properties near ZEFOZ region

In the vicinity of spin level anti-crossings, electron-nuclear spin systems reveal characteristic features that have been investigated by electron paramagnetic resonance (EPR) methods, including electron spin echo envelope modulation (ESEEM). The spectral properties depend considerably on the difference, ΔB, between the magnetic field and the critical field at which the zero first-order Zeeman shift (ZEFOZ) occurs. To analyze the characteristic features near the ZEFOZ point, analytical expressions for the behavior of EPR spectra and ESEEM traces as a function of ΔB are obtained. It is shown that the influence of hyperfine interactions (HFI) decreases linearly when approaching the ZEFOZ point. The HFI splitting of the EPR lines is essentially independent of ΔB near the ZEFOZ point, while the depth of the ESEEM signal has an approximately quadratic dependence on ΔB with a small cubic asymmetry due to the Zeeman interaction of the nuclear spin.

Probing many-body dynamics in a two-dimensional dipolar spin ensemble

The most direct approach for characterizing the quantum dynamics of a strongly interacting system is to measure the time evolution of its full many-body state. Despite the conceptual simplicity of this approach, it quickly becomes intractable as the system size grows. An alternate approach is to think of the many-body dynamics as generating noise, which can be measured by the decoherence of a probe qubit. Here we investigate what the decoherence dynamics of such a probe tells us about the many-body system. In particular, we utilize optically addressable probe spins to experimentally characterize both static and dynamical properties of strongly interacting magnetic dipoles. Our experimental platform consists of two types of spin defects in nitrogen delta-doped diamond: nitrogen-vacancy colour centres, which we use as probe spins, and a many-body ensemble of substitutional nitrogen impurities. We demonstrate that the many-body system's dimensionality, dynamics and disorder are naturally encoded in the probe spins' decoherence profile. Furthermore, we obtain direct control over the spectral properties of the many-body system, with potential applications in quantum sensing and simulation.

Deterministic manipulation of steering between distant quantum network nodes

Multipartite Einstein-Podolsky-Rosen (EPR) steering is a key resource in a quantum network. Although EPR steering between spatially separated regions of ultracold atomic systems has been observed, deterministic manipulation of steering between distant quantum network nodes is required for a secure quantum communication network. Here, we propose a feasible scheme to deterministically generate, store, and manipulate one-way EPR steering between distant atomic cells by a cavity-enhanced quantum memory approach. While optical cavities effectively suppress the unavoidable noises in electromagnetically induced transparency, three atomic cells are in a strong Greenberger-Horne-Zeilinger state by faithfully storing three spatially separated entangled optical modes. In this way, the strong quantum correlation of atomic cells guarantees one-to-two node EPR steering is achieved, and can perserve the stored EPR steering in these quantum nodes. Furthermore, the steerability can be actively manipulated by the temperature of the atomic cell. This scheme provides the direct reference for experimental implementation for one-way multipartite steerable states, which enables an asymmetric quantum network protocol.

An electrically driven single-atom "flip-flop" qubit

The spins of atoms and atom-like systems are among the most coherent objects in which to store quantum information. However, the need to address them using oscillating magnetic fields hinders their integration with quantum electronic devices. Here, we circumvent this hurdle by operating a single-atom "flip-flop" qubit in silicon, where quantum information is encoded in the electron-nuclear states of a phosphorus donor. The qubit is controlled using local electric fields at microwave frequencies, produced within a metal-oxide-semiconductor device. The electrical drive is mediated by the modulation of the electron-nuclear hyperfine coupling, a method that can be extended to many other atomic and molecular systems and to the hyperpolarization of nuclear spin ensembles. These results pave the way to the construction of solid-state quantum processors where dense arrays of atoms can be controlled using only local electric fields.

Quantum face recognition protocol with ghost imaging

Face recognition is one of the most ubiquitous examples of pattern recognition in machine learning, with numerous applications in security, access control, and law enforcement, among many others. Pattern recognition with classical algorithms requires significant computational resources, especially when dealing with high-resolution images in an extensive database. Quantum algorithms have been shown to improve the efficiency and speed of many computational tasks, and as such, they could also potentially improve the complexity of the face recognition process. Here, we propose a quantum machine learning algorithm for pattern recognition based on quantum principal component analysis, and quantum independent component analysis. A novel quantum algorithm for finding dissimilarity in the faces based on the computation of trace and determinant of a matrix (image) is also proposed. The overall complexity of our pattern recognition algorithm is [Formula: see text]-N is the image dimension. As an input to these pattern recognition algorithms, we consider experimental images obtained from quantum imaging techniques with correlated photons, e.g. "interaction-free" imaging or "ghost" imaging. Interfacing these imaging techniques with our quantum pattern recognition processor provides input images that possess a better signal-to-noise ratio, lower exposures, and higher resolution, thus speeding up the machine learning process further. Our fully quantum pattern recognition system with quantum algorithm and quantum inputs promises a much-improved image acquisition and identification system with potential applications extending beyond face recognition, e.g., in medical imaging for diagnosing sensitive tissues or biology for protein identification.

The deep space quantum link: prospective fundamental physics experiments using long-baseline quantum optics

The National Aeronautics and Space Administration's Deep Space Quantum Link mission concept enables a unique set of science experiments by establishing robust quantum optical links across extremely long baselines. Potential mission configurations include establishing a quantum link between the Lunar Gateway moon-orbiting space station and nodes on or near the Earth. This publication summarizes the principal experimental goals of the Deep Space Quantum Link. These goals, identified through a multi-year design study conducted by the authors, include long-range teleportation, tests of gravitational coupling to quantum states, and advanced tests of quantum nonlocality.

Structural, Optical, and Magnetic Properties of Erbium-Substituted Yttrium Iron Garnets

We synthesized a series of slightly erbium-substituted yttrium iron garnets (Er:YIG), Y3-x Er x Fe5O12 at different Er concentrations (x = 0, 0.01, 0.05, 0.10, and 0.20) using a solid-state reaction and investigated their structural, magnetic, and optical properties as a function of Er concentration. The volume of the unit cell slightly increased with Er concentration and Er atoms predominately replaced Y atoms in the dodecahedrons of YIG. The optical properties exhibited certain decreases in reflectance in the 1500-1600 nm wavelength range due to the presence of Er3+. Despite the many unpaired 4f electrons in Er3+, the total magnetic moments of Er:YIG showed similar trends with temperatures and magnetic fields above 30 K. An X-ray magnetic circular dichroism study confirmed the robust Fe 3d magnetic moments. However, the magnetic moments suddenly decreased to below 30 K with Er substitution, and the residual magnetism (M R) and coercive field (H C) in the magnetic hysteresis loops decreased to below 30 K with Er substitution. This implies that Er substitution in YIG has a negligible effect on magnetic properties over a wide temperature range except below 30 K where the Er 4f spins are coupled antiparallel to the majority Fe 3d spins. Our studies demonstrated that above 30 K the magnetic properties of YIG are retained even with Er substitution, which is evidence that the Er doping scheme is applicable for YIG-based magneto-optical devices in the mid-infrared regime.

First-principles study of the electronic and optical properties of Ho[Formula: see text] impurities in single-layer tungsten disulfide

The electronic and optical properties of single-layer (SL) tungsten disulfide (WS[Formula: see text]) in the presence of substitutional Holmium impurities (Ho[Formula: see text]) are studied. Although Ho is much larger than W, density functional theory (DFT) including spin-orbit coupling is used to show that Ho:SL WS[Formula: see text] is stable. The magnetic moment of the Ho impurity is found to be 4.75[Formula: see text] using spin-dependent DFT. The optical selection rules identified in the optical spectrum match exactly the optical selection rules derived by means of group theory. The presence of neutral Ho[Formula: see text] impurities gives rise to localized impurity states (LIS) with f-orbital character in the band structure. Using the Kubo-Greenwood formula and Kohn-Sham orbitals we obtain atom-like sharp transitions in the in-plane and out-of-plane components of the susceptibility tensor, Im[Formula: see text] and Im[Formula: see text]. The optical resonances are in good agreement with experimental data.

Zeeman and laser site selective spectroscopy of C1point group symmetry Sm3+centres in Y2SiO5: a parametrized crystal-field analysis for the 4f5configuration

Parametrized crystal-field analyses are presented for both the six and seven fold coordinated, C₁symmetry Sm³⁺centres in Y₂SiO₅, based on extensive spectroscopic data spanning the infrared to optical regions. Laser site-selective excitation and fluorescence spectroscopy as well as Zeeman absorption spectroscopy performed along multiple crystallographic directions has been utilized, in addition to previously determinedgtensors for the⁶H_5/2Z₁and⁴G_5/2A₁states. The resultant analyses give good approximation to the experimental energy levels and magnetic splittings, yielding crystal-field parameters consistent with the few other lanthanide ions for which such analyses are available.

On-Demand Integrated Quantum Memory for Polarization Qubits

Photonic polarization qubits are widely used in quantum computation and quantum communication due to the robustness in transmission and the easy qubit manipulation. An integrated quantum memory for polarization qubits is a useful building block for large-scale integrated quantum networks. However, on-demand storing polarization qubits in an integrated quantum memory is a long-standing challenge due to the anisotropic absorption of solids and the polarization-dependent features of microstructures. Here we demonstrate a reliable on-demand quantum memory for polarization qubits, using a depressed-cladding waveguide fabricated in a ^{151}Eu^{3+}:Y_{2}SiO_{5} crystal. The site-2 ^{151}Eu^{3+} ions in Y_{2}SiO_{5} crystal provides a near-uniform absorption for arbitrary polarization states and a new pump sequence is developed to prepare a wideband and enhanced absorption profile. A fidelity of 99.4±0.6% is obtained for the qubit storage process with an input of 0.32 photons per pulse, together with a storage bandwidth of 10 MHz. This reliable integrated quantum memory for polarization qubits reveals the potential for use in the construction of integrated quantum networks.

High-performance cavity-enhanced quantum memory with warm atomic cell

High-performance quantum memory for quantized states of light is a prerequisite building block of quantum information technology. Despite great progresses of optical quantum memories based on interactions of light and atoms, physical features of these memories still cannot satisfy requirements for applications in practical quantum information systems, since all of them suffer from trade-off between memory efficiency and excess noise. Here, we report a high-performance cavity-enhanced electromagnetically-induced-transparency memory with warm atomic cell in which a scheme of optimizing the spatial and temporal modes based on the time-reversal approach is applied. The memory efficiency up to 67 ± 1% is directly measured and a noise level close to quantum noise limit is simultaneously reached. It has been experimentally demonstrated that the average fidelities for a set of input coherent states with different phases and amplitudes within a Gaussian distribution have exceeded the classical benchmark fidelities. Thus the realized quantum memory platform has been capable of preserving quantized optical states, and is ready to be applied in quantum information systems, such as distributed quantum logic gates and quantum-enhanced atomic magnetometry.

Superior atomic coherence time controlled by crystal phase transition and optical dressing

We compare the atomic coherence time of doped ion crystals, i.e., BiPO₄: Eu³⁺, YPO₄: Eu³⁺, YPO₄: Pr³⁺, and Y₂SiO₅: Pr^3 +crystals. Such atomic coherence time is controlled by crystal field splitting (CF-splitting) and optical (photon and phonon) dressing. Compared with the other doped ion crystals, BiPO₄: Eu³⁺ exhibits the longest coherence time. By controlling thermal phonon, phase-transition phonon, broadband or narrowband excitation, and fluorescence (FL) or spontaneous four-wave-mixing ratio (S-FWM), a superior atomic coherence time of up to 10 ± 0.6 ms is achieved in the pure hexagonal (0.5:1) phase of BiPO₄: Eu³⁺. Furthermore, the relationship between TAT-splitting and spectral Autler-Townes (SAT)-splitting was investigated. This superior atomic coherence time has potential applications in quantum memory devices.

Ultra-narrow optical linewidths in rare-earth molecular crystals

Rare-earth ions (REIs) are promising solid-state systems for building light-matter interfaces at the quantum level^1,2. This relies on their potential to show narrow optical and spin homogeneous linewidths, or, equivalently, long-lived quantum states. This enables the use of REIs for photonic quantum technologies such as memories for light, optical-microwave transduction and computing^3-5. However, so far, few crystalline materials have shown an environment quiet enough to fully exploit REI properties. This hinders further progress, in particular towards REI-containing integrated nanophotonics devices^6,7. Molecular systems can provide such capability but generally lack spin states. If, however, molecular systems do have spin states, they show broad optical lines that severely limit optical-to-spin coherent interfacing^8-10. Here we report on europium molecular crystals that exhibit linewidths in the tens of kilohertz range, orders of magnitude narrower than those of other molecular systems. We harness this property to demonstrate efficient optical spin initialization, coherent storage of light using an atomic frequency comb, and optical control of ion-ion interactions towards implementation of quantum gates. These results illustrate the utility of rare-earth molecular crystals as a new platform for photonic quantum technologies that combines highly coherent emitters with the unmatched versatility in composition, structure and integration capability of molecular materials.

Precision tomography of a three-qubit donor quantum processor in silicon

Nuclear spins were among the first physical platforms to be considered for quantum information processing^1,2, because of their exceptional quantum coherence³ and atomic-scale footprint. However, their full potential for quantum computing has not yet been realized, owing to the lack of methods with which to link nuclear qubits within a scalable device combined with multi-qubit operations with sufficient fidelity to sustain fault-tolerant quantum computation. Here we demonstrate universal quantum logic operations using a pair of ion-implanted ³¹P donor nuclei in a silicon nanoelectronic device. A nuclear two-qubit controlled-Z gate is obtained by imparting a geometric phase to a shared electron spin⁴, and used to prepare entangled Bell states with fidelities up to 94.2(2.7)%. The quantum operations are precisely characterized using gate set tomography (GST)⁵, yielding one-qubit average gate fidelities up to 99.95(2)%, two-qubit average gate fidelity of 99.37(11)% and two-qubit preparation/measurement fidelities of 98.95(4)%. These three metrics indicate that nuclear spins in silicon are approaching the performance demanded in fault-tolerant quantum processors⁶. We then demonstrate entanglement between the two nuclei and the shared electron by producing a Greenberger-Horne-Zeilinger three-qubit state with 92.5(1.0)% fidelity. Because electron spin qubits in semiconductors can be further coupled to other electrons^7-9 or physically shuttled across different locations^10,11, these results establish a viable route for scalable quantum information processing using donor nuclear and electron spins.

Time-Resolved Photoionization Detection of a Single Er3+ Ion in Silicon

The detection of charge trap ionization induced by resonant excitation enables spectroscopy on single Er³⁺ ions in silicon nanotransistors. In this work, a time-resolved detection method is developed to investigate the resonant excitation and relaxation of a single Er³⁺ ion in silicon. The time-resolved detection is based on a long-lived current signal with a tunable reset and allows the measurement under stronger and shorter resonant excitation in comparison to time-averaged detection. Specifically, the short-pulse study gives an upper bound of 23.7 μs on the decay time of the ⁴I_13/2 state of the Er³⁺ ion. The fast decay and the tunable reset allow faster repetition of the single-ion detection, which is attractive for implementing this method in large-scale quantum systems of single optical centers. The findings on the detection mechanism and dynamics also provide an important basis for applying this technique to detect other single optical centers in solids.

Harnessing the Quantum Behavior of Spins on Surfaces

The desire to control and measure individual quantum systems such as atoms and ions in a vacuum has led to significant scientific and engineering developments in the past decades that form the basis of today's quantum information science. Single atoms and molecules on surfaces, on the other hand, are heavily investigated by physicists, chemists, and material scientists in search of novel electronic and magnetic functionalities. These two paths crossed in 2015 when it was first clearly demonstrated that individual spins on a surface can be coherently controlled and read out in an all-electrical fashion. The enabling technique is a combination of scanning tunneling microscopy (STM) and electron spin resonance, which offers unprecedented coherent controllability at the Angstrom length scale. This review aims to illustrate the essential ingredients that allow the quantum operations of single spins on surfaces. Three domains of applications of surface spins, namely quantum sensing, quantum control, and quantum simulation, are discussed with physical principles explained and examples presented. Enabled by the atomically-precise fabrication capability of STM, single spins on surfaces might one day lead to the realization of quantum nanodevices and artificial quantum materials at the atomic scale.

Optomechanical Anti-Lasing with Infinite Group Delay at a Phase Singularity

Singularities which symbolize abrupt changes and exhibit extraordinary behavior are of a broad interest. We experimentally study optomechanically induced singularities in a compound system consisting of a three-dimensional aluminum superconducting cavity and a metalized high-coherence silicon nitride membrane resonator. Mechanically induced coherent perfect absorption and anti-lasing occur simultaneously under a critical optomechanical coupling strength. Meanwhile, the phase around the cavity resonance undergoes an abrupt π-phase transition, which further flips the phase slope in the frequency dependence. The observed infinite discontinuity in the phase slope defines a singularity, at which the group velocity is dramatically changed. Around the singularity, an abrupt transition from an infinite group advance to delay is demonstrated by measuring a Gaussian-shaped waveform propagating. Our experiment may broaden the scope of realizing extremely long group delays by taking advantage of singularities.

Twenty-three-millisecond electron spin coherence of erbium ions in a natural-abundance crystal

Erbium ions embedded in crystals have unique properties for quantum information processing, because of their optical transition at 1.5 μm and of the large magnetic moment of their effective spin-1/2 electronic ground state. Most applications of erbium require, however, long electron spin coherence times, and this has so far been missing. Here, by selecting a host matrix with a low nuclear-spin density (CaWO4) and by quenching the spectral diffusion due to residual paramagnetic impurities at millikelvin temperatures, we obtain a 23-ms coherence time on the Er3+ electron spin transition. This is the longest Hahn echo electron spin coherence time measured in a material with a natural abundance of nuclear spins and on a magnetically sensitive transition. Our results establish Er3+:CaWO4 as a potential platform for quantum networks.

Quantum-coherent nanoscience

For the past three decades nanoscience has widely affected many areas in physics, chemistry and engineering, and has led to numerous fundamental discoveries, as well as applications and products. Concurrently, quantum science and technology has developed into a cross-disciplinary research endeavour connecting these same areas and holds burgeoning commercial promise. Although quantum physics dictates the behaviour of nanoscale objects, quantum coherence, which is central to quantum information, communication and sensing, has not played an explicit role in much of nanoscience. This Review describes fundamental principles and practical applications of quantum coherence in nanoscale systems, a research area we call quantum-coherent nanoscience. We structure this Review according to specific degrees of freedom that can be quantum-coherently controlled in a given nanoscale system, such as charge, spin, mechanical motion and photons. We review the current state of the art and focus on outstanding challenges and opportunities unlocked by the merging of nanoscience and coherent quantum operations.

Observation of Symmetry-Protected Selection Rules in Periodically Driven Quantum Systems

Periodically driven (Floquet) quantum systems have recently been a focus of nonequilibrium physics by virtue of their rich dynamics. Time-periodic systems not only exhibit symmetries that resemble those in spatially periodic systems, but also display novel behavior that arises from symmetry breaking. Characterization of such dynamical symmetries is crucial, but often challenging due to limited driving strength and lack of an experimentally accessible characterization technique. Here, we show how to reveal dynamical symmetries, namely, parity, rotation, and particle-hole symmetries, by observing symmetry-induced Floquet selection rules. Notably, we exploit modulated driving to reach the strong light-matter coupling regime, and we introduce a protocol to experimentally extract the transition matrix elements between Floquet states from the system coherent evolution. By using nitrogen-vacancy centers in diamond as an experimental test bed, we execute our protocol to observe symmetry-protected dark states and dark bands, and coherent destruction of tunneling. Our work shows how one can exploit the quantum control toolkit to study dynamical symmetries that arise in the topological phases of strongly driven Floquet systems.

Precise spectroscopy of 167Er:Y2SiO5 based on laser frequency stabilization using a fiber laser comb

Precise spectroscopy of the hyperfine level system of ¹⁶⁷Er-doped Y₂SiO₅ was achieved in the frequency domain. By using an optical frequency comb to stabilize the light source frequency to an accuracy on the order of hertz on a long-term scale, Allan deviation < 10 Hz was achieved for an integration time of 180 s. As a result, spectral hole-burning experiments yielded a more accurate hole spectrum with a narrow homogeneous linewidth. The method opens the way to the straightforward exploration of relaxation mechanisms in the frequency domain by simple steady-state measurements.

Elimination of noise in optically rephased photon echoes

Photon echo is a fundamental tool for the manipulation of electromagnetic fields. Unavoidable spontaneous emission noise is generated in this process due to the strong rephasing pulse, which limits the achievable signal-to-noise ratio and represents a fundamental obstacle towards their applications in the quantum regime. Here we propose a noiseless photon-echo protocol based on a four-level atomic system. We implement this protocol in a Eu³⁺:Y₂SiO₅ crystal to serve as an optical quantum memory. A storage fidelity of 0.952 ± 0.018 is obtained for time-bin qubits encoded with single-photon-level coherent pulses, which is far beyond the maximal fidelity achievable using the classical measure-and-prepare strategy. In this work, the demonstrated noiseless photon-echo quantum memory features spin-wave storage, easy operation and high storage fidelity, which should be easily extended to other physical systems.

Dynamical Decoupling of Spin Ensembles with Strong Anisotropic Interactions

Ensembles of dopants have widespread applications in quantum technology. The miniaturization of corresponding devices is however hampered by dipolar interactions that reduce the coherence at increased dopant density. We theoretically and experimentally investigate this limitation. We find that dynamical decoupling can alleviate, but not fully eliminate, the decoherence in crystals with strong anisotropic spin-spin interactions that originate from an anisotropic g tensor. Our findings can be generalized to many quantum systems used for quantum sensing, microwave-to-optical conversion, and quantum memory.

Dynamic control of Purcell enhanced emission of erbium ions in nanoparticles

The interaction of single quantum emitters with an optical cavity enables the realization of efficient spin-photon interfaces, an essential resource for quantum networks. The dynamical control of the spontaneous emission rate of quantum emitters in cavities has important implications in quantum technologies, e.g., for shaping the emitted photons’ waveform or for driving coherently the optical transition while preventing photon emission. Here we demonstrate the dynamical control of the Purcell enhanced emission of a small ensemble of erbium ions doped into a nanoparticle. By embedding the nanoparticles into a fully tunable high finesse fiber based optical microcavity, we demonstrate a median Purcell factor of 15 for the ensemble of ions. We also show that we can dynamically control the Purcell enhanced emission by tuning the cavity on and out of resonance, by controlling its length with sub-nanometer precision on a time scale more than two orders of magnitude faster than the natural lifetime of the erbium ions. This capability opens prospects for the realization of efficient nanoscale quantum interfaces between solid-state spins and single telecom photons with controllable waveform, for non-destructive detection of photonic qubits, and for the realization of quantum gates between rare-earth ion qubits coupled to an optical cavity.

Control of quantum emitters is needed in order to enable many applications. Here, the authors demonstrate enhancement and dynamical control of the Purcell emission from erbium ions doped in a nanoparticle within a fiber-based microcavity.