A solid-state light–matter interface at the single-photon level

Stable organic radical qubits and their applications in quantum information science

The past century has witnessed the flourishing of organic radical chemistry. Stable organic radicals are highly valuable for quantum technologies thanks to their inherent room temperature quantum coherence, atomic-level designability, and fine tunability. In this comprehensive review, we highlight the potential of stable organic radicals as high-temperature qubits and explore their applications in quantum information science, which remain largely underexplored. Firstly, we summarize known spin dynamic properties of stable organic radicals and examine factors that influence their electron spin relaxation and decoherence times. This examination reveals their design principles and optimal operating conditions. We further discuss their integration in solid-state materials and surface structures, and present their state-of-the-art applications in quantum computing, quantum memory, and quantum sensing. Finally, we analyze the primary challenges associated with stable organic radical qubits and provide tentative insights to future research directions.

Nuclear quantum memory for hard x-ray photon wave packets

Optical quantum memories are key elements in modern quantum technologies to reliably store and retrieve quantum information. At present, they are conceptually limited to the optical wavelength regime. Recent advancements in x-ray quantum optics render an extension of optical quantum memory protocols to ultrashort wavelengths possible, thereby establishing quantum photonics at x-ray energies. Here, we introduce an x-ray quantum memory protocol that utilizes mechanically driven nuclear resonant 57Fe absorbers to form a comb structure in the nuclear absorption spectrum by using the Doppler effect. This room-temperature nuclear frequency comb enables us to control the waveform of x-ray photon wave packets to a high level of accuracy and fidelity using solely mechanical motions. This tunable, robust, and highly flexible system offers a versatile platform for a compact solid-state quantum memory at room temperature for hard x-rays.

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.

Telecom-band-integrated multimode photonic quantum memory

Telecom-band-integrated quantum memory is an elementary building block for developing quantum networks compatible with fiber communication infrastructures. Toward such a network with large capacity, an integrated multimode photonic quantum memory at telecom band has yet been demonstrated. Here, we report a fiber-integrated multimode quantum storage of single photon at telecom band on a laser-written chip. The storage device is a fiber-pigtailed Er³⁺:LiNbO₃ waveguide and allows a storage of up to 330 temporal modes of heralded single photon with 4-GHz-wide bandwidth at 1532 nm and a 167-fold increasing of coincidence detection rate with respect to single mode. Our memory system with all-fiber addressing is performed using telecom-band fiber-integrated and on-chip components. The results represent an important step for the future quantum networks using integrated photonics devices.

Integrated Multiresonator Quantum Memory

We develop an integrated efficient multiresonator quantum memory scheme based on a system of three interacting resonators coupled through a common resonator to an external waveguide via switchable coupler. It is shown that high-precision parameter matching based on step-by-step optimization makes it possible to efficiently store the signal field and enables on-demand retrieval of the signal at specified time moments. Possible experimental implementations and practical applications of the proposed quantum memory scheme are discussed.

Controlling single rare earth ion emission in an electro-optical nanocavity

Rare earth emitters enable critical quantum resources including spin qubits, single photon sources, and quantum memories. Yet, probing of single ions remains challenging due to low emission rate of their intra-4f optical transitions. One feasible approach is through Purcell-enhanced emission in optical cavities. The ability to modulate cavity-ion coupling in real-time will further elevate the capacity of such systems. Here, we demonstrate direct control of single ion emission by embedding erbium dopants in an electro-optically active photonic crystal cavity patterned from thin-film lithium niobate. Purcell factor over 170 enables single ion detection, which is verified by second-order autocorrelation measurement. Dynamic control of emission rate is realized by leveraging electro-optic tuning of resonance frequency. Using this feature, storage, and retrieval of single ion excitation is further demonstrated, without perturbing the emission characteristics. These results promise new opportunities for controllable single-photon sources and efficient spin-photon interfaces.

Cavity-enhanced and temporally multiplexed atom-photon entanglement interface

Practical realization of quantum repeaters requires quantum memories with high retrieval efficiency, multi-mode storage capacities, and long lifetimes. Here, we report a high-retrieval-efficiency and temporally multiplexed atom-photon entanglement source. A train of 12 write pulses in time is applied to a cold atomic ensemble along different directions, which generates temporally multiplexed pairs of Stokes photons and spin waves via Duan-Lukin-Cirac-Zoller processes. The two arms of a polarization interferometer are used to encode photonic qubits of 12 Stokes temporal modes. The multiplexed spin-wave qubits, each of which is entangled with one Stokes qubit, are stored in a "clock" coherence. A ring cavity that resonates simultaneously with the two arms of the interferometer is used to enhance retrieval from the spin-wave qubits, with the intrinsic retrieval efficiency reaching 70.4%. The multiplexed source gives rise to a ∼12.1-fold increase in atom-photon entanglement-generation probability compared to the single-mode source. The measured Bell parameter for the multiplexed atom-photon entanglement is 2.21(2), along with a memory lifetime of up to ∼125 µs.

Analysis of Imperfect Rephasing in Photon Echo-Based Quantum Memories

Over the last two decades, quantum memories have been intensively studied for potential applications of quantum repeaters in quantum networks. Various protocols have also been developed. To satisfy no noise echoes caused by spontaneous emission processes, a conventional two-pulse photon-echo scheme has been modified. The resulting methods include double-rephasing, ac Stark, dc Stark, controlled echo, and atomic frequency comb methods. In these methods, the main purpose of modification is to remove any chance of a population residual on the excited state during the rephasing process. Here, we investigate a typical Gaussian rephasing pulse-based double-rephasing photon-echo scheme. For a complete understanding of the coherence leakage by the Gaussian pulse itself, ensemble atoms are thoroughly investigated for all temporal components of the Gaussian pulse, whose maximum echo efficiency is 26% in amplitude, which is unacceptable for quantum memory applications.

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.

Toward a Quantum Memory in a Fiber Cavity Controlled by Intracavity Frequency Translation

We propose a quantum memory protocol based on trapping photons in a fiber-integrated cavity, comprised of a birefringent fiber with dichroic reflective end facets. Photons are switched into resonance with the fiber cavity by intracavity Bragg-scattering frequency translation, driven by ancillary control pulses. After the storage delay, photons are switched out of resonance with the cavity, again by intracavity frequency translation. We demonstrate storage of quantum-level THz-bandwidth coherent states for a lifetime up to 16 cavity round trips, or 200 ns, and a maximum overall efficiency of 73%.

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.

Periodic Cavity State Revivals from Atomic Frequency Combs

Spin ensembles with a comb-shaped spectrum have shown exciting properties as efficient quantum memories. Here, we present a rigorous theoretical study of such atomic frequency combs in the strong coupling limit of cavity QED, based on a full quantum treatment using tensor-network methods. Our results demonstrate that arbitrary multiphoton states in the cavity are almost perfectly absorbed by the spin ensemble and reemitted as parity-flipped states at periodic time intervals. Fidelity values near unity are achieved in these revived states by compensating for energy shifts induced by the strong spin-cavity coupling through adjustments of individual coupling values of the teeth in the atomic frequency comb.

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.

On-Demand Storage and Retrieval of Microwave Photons Using a Superconducting Multiresonator Quantum Memory

We realize on-demand storage and retrieval of weak coherent microwave photon pulses at the single-photon level. A superconducting multiresonator system which is composed of a set of frequency-tunable coplanar waveguide resonators is implemented as the quantum memory. By dynamically tuning the resonant frequencies of the resonators, we achieve tunable memory bandwidth from 10 to 55 MHz, with well preserved phase coherence. We further demonstrate on-demand storage and retrieval of a time-bin flying qubit. This result opens up a prospect to integrate our chip-based quantum memory with the state-of-the-art superconducting quantum circuit technology for quantum information processing.

Room temperature atomic frequency comb storage for light

We demonstrate coherent storage and retrieval of pulsed light using the atomic frequency comb protocol in a room temperature alkali vapor. We utilize velocity-selective optical pumping to prepare multiple velocity classes in the F=4 hyperfine ground state of cesium. The frequency spacing of the classes is chosen to coincide with the F^'=4-F^'=5 hyperfine splitting of the 6²P_3/2 excited state, resulting in a broadband periodic absorbing structure consisting of two usually Doppler-broadened optical transitions. Weak coherent states of duration 2ns are mapped into this atomic frequency comb with pre-programmed recall times of 8ns and 12ns, with multi-temporal mode storage and recall demonstrated. Utilizing two transitions in the comb leads to an additional interference effect upon rephasing that enhances the recall efficiency.

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.

Telecom-heralded entanglement between multimode solid-state quantum memories

Future quantum networks will enable the distribution of entanglement between distant locations and allow applications in quantum communication, quantum sensing and distributed quantum computation¹. At the core of this network lies the ability to generate and store entanglement at remote, interconnected quantum nodes². Although various remote physical systems have been successfully entangled^3-12, none of these realizations encompassed all of the requirements for network operation, such as compatibility with telecommunication (telecom) wavelengths and multimode operation. Here we report the demonstration of heralded entanglement between two spatially separated quantum nodes, where the entanglement is stored in multimode solid-state quantum memories. At each node a praseodymium-doped crystal^13,14 stores a photon of a correlated pair¹⁵, with the second photon at telecom wavelengths. Entanglement between quantum memories placed in different laboratories is heralded by the detection of a telecom photon at a rate up to 1.4 kilohertz, and the entanglement is stored in the crystals for a pre-determined storage time up to 25 microseconds. We also show that the generated entanglement is robust against loss in the heralding path, and demonstrate temporally multiplexed operation, with 62 temporal modes. Our realization is extendable to entanglement over longer distances and provides a viable route towards field-deployed, multiplexed quantum repeaters based on solid-state resources.

Studying the effect of fluctuating environment on intra-atomic frequency comb based quantum memory

In this article, we study the effect of various environmental factors on intra-atomic frequency comb (I-AFC) based quantum memory. The effect of the environment is incorporated as random fluctuations and non-uniformity in the parameters such as comb spacing and the optical depth, of the frequency comb. We found that the I-AFC is viable for photon storage even for very large fluctuations in the parameters of the frequency comb, which makes I-AFC a robust platform for photon storage. Furthermore, we show that the non-uniform frequency combs without any fluctuations in the comb parameters can also yield efficient quantum memory. Since the intra-atomic frequency combs found in natural atomic systems are often non-uniform, our results suggest that a large class of these systems can be used for I-AFC based efficient quantum memory.

One-hour coherent optical storage in an atomic frequency comb memory

Photon loss in optical fibers prevents long-distance distribution of quantum information on the ground. Quantum repeater is proposed to overcome this problem, but the communication distance is still limited so far because of the system complexity of the quantum repeater scheme. Alternative solutions include transportable quantum memory and quantum-memory-equipped satellites, where long-lived optical quantum memories are the key components to realize global quantum communication. However, the longest storage time of the optical memories demonstrated so far is approximately 1 minute. Here, by employing a zero-first-order-Zeeman magnetic field and dynamical decoupling to protect the spin coherence in a solid, we demonstrate coherent storage of light in an atomic frequency comb memory over 1 hour, leading to a promising future for large-scale quantum communication based on long-lived solid-state quantum memories.

Quantum memories are key components for quantum communication, but current storage times are still too short. Here, the authors use the atomic frequency comb protocol in a zero-first-order-Zeeman field to coherently store an optical pulse for an hour in a cryogenically cooled rare-earth doped crystal.

Optical spin-state polarization in a binuclear europium complex towards molecule-based coherent light-spin interfaces

The success of the emerging field of solid-state optical quantum information processing (QIP) critically depends on the access to resonant optical materials. Rare-earth ion (REI)-based molecular systems, whose quantum properties could be tuned taking advantage of molecular engineering strategies, are one of the systems actively pursued for the implementation of QIP schemes. Herein, we demonstrate the efficient polarization of ground-state nuclear spins-a fundamental requirement for all-optical spin initialization and addressing-in a binuclear Eu(III) complex, featuring inhomogeneously broadened ⁵D₀ →⁷F₀ optical transition. At 1.4 K, long-lived spectral holes have been burnt in the transition: homogeneous linewidth (Γ_h) = 22 ± 1 MHz, which translates as optical coherence lifetime (T_2opt) = 14.5 ± 0.7 ns, and ground-state spin population lifetime (T_1spin) = 1.6 ± 0.4 s have been obtained. The results presented in this study could be a progressive step towards the realization of molecule-based coherent light-spin QIP interfaces.

Using an injection-locked VCSEL to produce Fourier-transform-limited optical pulses

In this Letter, we present Fourier-transform-limited, nanosecond scale optical pulses from a vertical cavity surface emitting laser (VCSEL) using injection locking with a narrow-band seed laser. We examine two different injection-locking architectures and show that we can achieve an effective injection-locking range of over 8 GHz with an extinction ratio of 20,000:1. These results indicate that injection-locked VCSELs could become a key component of large-scale photonic quantum networks.

Coherent control of collective nuclear quantum states via transient magnons

Ultrafast and precise control of quantum systems at x-ray energies involves photons with oscillation periods below 1 as. Coherent dynamic control of quantum systems at these energies is one of the major challenges in hard x-ray quantum optics. Here, we demonstrate that the phase of a quantum system embedded in a solid can be coherently controlled via a quasi-particle with subattosecond accuracy. In particular, we tune the quantum phase of a collectively excited nuclear state via transient magnons with a precision of 1 zs and a timing stability below 50 ys. These small temporal shifts are monitored interferometrically via quantum beats between different hyperfine-split levels. The experiment demonstrates zeptosecond interferometry and shows that transient quasi-particles enable accurate control of quantum systems embedded in condensed matter environments.

On-Demand Quantum Storage of Photonic Qubits in an On-Chip Waveguide

Photonic quantum memory is the core element in quantum information processing (QIP). For the scalable and convenient practical applications, great efforts have been devoted to the integrated quantum memory based on various waveguides fabricated in solids. However, on-demand storage of qubits, which is an essential requirement for QIP, is still challenging to be implemented using such integrated quantum memory. Here we report the on-demand storage of time-bin qubits in an on-chip waveguide memory fabricated on the surface of a ^{151}Eu^{3+}:Y_{2}SiO_{5} crystal, utilizing the Stark-modulated atomic frequency comb protocol. A qubit storage fidelity of 99.3%±0.2% is obtained with single-photon-level coherent pulses, far beyond the highest fidelity achievable using the classical measure-and-prepare strategy. The developed integrated quantum memory with the on-demand retrieval capability represents an important step toward practical applications of integrated quantum nodes in quantum networks.

Analysis of Controlled Rabi Flopping in a Double Rephasing Photon Echo Scheme for Quantum Memories

A double rephasing scheme of a photon echo is analyzed for inversion-free photon echo-based quantum memories using controlled Rabi flopping, where the Rabi flopping is used for phase control of collective atom coherence. Unlike the rephasing-caused π-phase shift in a single rephasing scheme, the control Rabi flopping between the excited state and an auxiliary third state induces coherence inversion. Thus, the absorptive photon echo in a double rephasing scheme can be manipulated to be emissive. Here, we present a quantum coherence control of atom phases in a double rephasing photon echo scheme for emissive photon echoes for quantum memory applications.

Understanding of Collective Atom Phase Control in Modified Photon Echoes for a Near-Perfect Storage Time-Extended Quantum Memory

A near-perfect storage time-extended photon echo-based quantum memory protocol has been analyzed by solving the Maxwell–Bloch equations for a backward scheme in a three-level system. The backward photon echo scheme is combined with a controlled coherence conversion process via controlled Rabi flopping to a third state, where the control Rabi flopping collectively shifts the phase of the ensemble coherence. The propagation direction of photon echoes is coherently determined by the phase-matching condition between the data (quantum) and the control (classical) pulses. Herein, we discuss the classical controllability of a quantum state for both phase and propagation direction by manipulating the control pulses in both single and double rephasing photon echo schemes of a three-level system. Compared with the well-understood uses of two-level photon echoes, the Maxwell–Bloch equations for a three-level system have a critical limitation regarding the phase change when interacting with an arbitrary control pulse area.

Electric field manipulation enhanced by strong spin-orbit coupling: promoting rare-earth ions as qubits

Quantum information processing based on magnetic ions has potential for applications as the ions can be modified in their electronic properties and assembled by a variety of chemical methods. For these systems to achieve individual spin addressability and high energy efficiency, we exploited the electric field as a tool to manipulate the quantum behaviours of the rare-earth ion which has strong spin-orbit coupling. A Ce:YAG single crystal was employed with considerations to the dynamics and the symmetry requirements. The Stark effect of the Ce³⁺ ion was observed and measured. When demonstrated as a quantum phase gate, the electric field manipulation exhibited high efficiency which allowed up to 57 π/2 operations before decoherence with optimized field direction. It was also utilized to carry out quantum bang-bang control, as a method of dynamic decoupling, and the refined Deutsch-Jozsa algorithm. Our experiments highlighted rare-earth ions as potentially applicable qubits because they offer enhanced spin-electric coupling which enables high-efficiency quantum manipulation.

Cold-Atom Temporally Multiplexed Quantum Memory with Cavity-Enhanced Noise Suppression

Future quantum repeater architectures, capable of efficiently distributing information encoded in quantum states of light over large distances, will benefit from multiplexed photonic quantum memories. In this work we demonstrate a temporally multiplexed quantum repeater node in a laser-cooled cloud of ^{87}Rb atoms. We employ the Duan-Lukin-Cirac-Zoller protocol where pairs of photons and single collective spin excitations (so-called spin waves) are created in several temporal modes using a train of write pulses. To make the spin waves created in different temporal modes distinguishable and enable selective readout, we control the dephasing and rephasing of the spin waves by a magnetic field gradient, which induces a controlled reversible inhomogeneous broadening of the involved atomic hyperfine levels. We demonstrate that by embedding the atomic ensemble inside a low finesse optical cavity, the additional noise generated in multimode operation is strongly suppressed. By employing feed forward readout, we demonstrate distinguishable retrieval of up to 10 temporal modes. For each mode, we prove nonclassical correlations between the first and second photon. Furthermore, an enhancement in rates of correlated photon pairs is observed as we increase the number of temporal modes stored in the memory. The reported capability is a key element of a quantum repeater architecture based on multiplexed quantum memories.

Optical Spin-Wave Storage in a Solid-State Hybridized Electron-Nuclear Spin Ensemble

Solid-state impurity spins with optical control are currently investigated for quantum networks and repeaters. Among these, rare-earth-ion doped crystals are promising as quantum memories for light, with potentially long storage time, high multimode capacity, and high bandwidth. However, with spins there is often a tradeoff between bandwidth, which favors electronic spin, and memory time, which favors nuclear spins. Here, we present optical storage experiments using highly hybridized electron-nuclear hyperfine states in ^{171}Yb^{3+}:Y_{2}SiO_{5}, where the hybridization can potentially offer both long storage time and high bandwidth. We reach a storage time of 1.2 ms and an optical storage bandwidth of 10 MHz that is currently only limited by the Rabi frequency of the optical control pulses. The memory efficiency in this proof-of-principle demonstration was about 3%. The experiment constitutes the first optical storage using spin states in any rare-earth ion with electronic spin. These results pave the way for rare-earth based quantum memories with high bandwidth, long storage time, and high multimode capacity, a key resource for quantum repeaters.

Cavity-enhanced and long-lived optical memories for two orthogonal polarizations in cold atoms

The storage and retrieval efficiency (SRE) and lifetime of optical quantum memories are two key performance indicators for scaling up quantum information processing. Here, we experimentally demonstrate a cavity-enhanced long-lived optical memory for two polarizations in a cold atomic ensemble. Using electromagnetically induced-transparency (EIT) dynamics, we demonstrate the storages of left-circularly and right-circularly polarized signal light pulses in the atoms, respectively. By making the signal and control beams collinearly pass through the atoms and storing the two polarizations of the signal light as two magnetic-field-insensitive spin waves, we achieve a long-lived (3.5 ms) memory. By placing a low-finesse optical ring cavity around the cold atoms, the coupling between the signal light and the atoms is enhanced, which leads to an increase in SRE. The presented cavity-enhanced storage shows that the SRE is ∼30%, corresponding to an intrinsic SRE of ∼45%.

Narrowband photon pairs with independent frequency tuning for quantum light-matter interactions

We describe a cavity-enhanced spontaneous parametric down-conversion (CE-SPDC) source for narrowband photon pairs with filters designed such that 97.7% of the correlated photons are in a single mode of 4.3(4) MHz bandwidth. Type-II phase matching, a tuneable-birefringence resonator, MHz-resolution pump tuning, and tuneable Fabry-Perot filters are used to achieve independent signal and idler tuning. We map the CE-SPDC spectrum using difference frequency generation to precisely locate the emission clusters, demonstrate CE-SPDC driven atomic spectroscopy, and measure a contribution from unwanted modes of 7.7%. The generated photon pairs efficiently interact with neutral rubidium, a well-developed system for quantum networking and quantum simulation. The techniques are readily extensible to other material systems.

Quantum Storage of Frequency-Multiplexed Heralded Single Photons

We report on the quantum storage of a heralded frequency-multiplexed single photon in an integrated laser-written rare-earth doped waveguide. The single photon contains 15 discrete frequency modes separated by 261 MHz and spanning across 4 GHz. It is obtained from a nondegenerate photon pair created via cavity-enhanced spontaneous down-conversion, where the heralding photon is at telecom wavelength and the heralded photon is at 606 nm. The frequency-multimode photon is stored in a praseodymium-doped waveguide using the atomic frequency comb (AFC) scheme, by creating multiple combs within the inhomogeneous broadening of the crystal. Thanks to the intrinsic temporal multimodality of the AFC scheme, each spectral bin includes 9 temporal modes, such that the total number of stored modes is about 130. We demonstrate that the storage preserves the nonclassical properties of the single photon, and its normalized frequency spectrum.

Extending Phenomenological Crystal-Field Methods to C_{1} Point-Group Symmetry: Characterization of the Optically Excited Hyperfine Structure of ^{167}Er^{3+}:Y_{2}SiO_{5}

We show that crystal-field calculations for C_{1} point-group symmetry are possible, and that such calculations can be performed with sufficient accuracy to have substantial utility for rare-earth based quantum information applications. In particular, we perform crystal-field fitting for a C_{1}-symmetry site in ^{167}Er^{3+}:Y_{2}SiO_{5}. The calculation simultaneously includes site-selective spectroscopic data up to 20 000  cm^{-1}, rotational Zeeman data, and ground- and excited-state hyperfine structure determined from high-resolution Raman-heterodyne spectroscopy on the 1.5  μm telecom transition. We achieve an agreement of better than 50 MHz for assigned hyperfine transitions. The success of this analysis opens the possibility of systematically evaluating the coherence properties, as well as transition energies and intensities, of any rare-earth ion doped into Y_{2}SiO_{5}.

Spectral-Topological Superefficient Quantum Memory

In this work, we propose a universal (spectral-topological) approach towards the realization of the quantum memory, consisting of a small number of controlled absorbers, providing a super-high quantum efficiency of more than 99.9% required for practical quantum information science. In this way, we have found a series of spectral-topological matching conditions for the spectroscopic parameters of the absorbers which ensure the maximal efficiency in the broadband spectral range due to controlling the relative position (topology) of the eigenfrequencies in the absorbers spectrum. We also discuss the implementation of the proposed approach using the modern microwave and optical technologies.

Demonstration of stimulated photon echo isolation using interferometric cancellation

An alternative to phase-matched angled beam spatial-spectral holographic grating geometries for separating stimulated photon echoes (SPEs) from the probing pulse is proposed and demonstrated. By use of a Mach-Zehnder geometry with inhomogeneously broadened medium in both paths, the SPE can be interferometrically isolated from the generating probe pulse. This interferometric-based technique is well suited to waveguide geometries, which have benefits for future quantum and classical optical signal processing applications such as quantum memories, correlation, and efficient cryogenic microwave-to-optical conversion. Experimental demonstrations showing interferometric-based isolation in Tm³⁺-doped LiNbO₃ at 3.2 K are performed and analyzed.

Optically Addressing Single Rare-Earth Ions in a Nanophotonic Cavity

We demonstrate optical probing of spectrally resolved single Nd^{3+} rare-earth ions in yttrium orthovanadate. The ions are coupled to a photonic crystal resonator and show strong enhancement of the optical emission rate via the Purcell effect, resulting in near radiatively limited single photon emission. The measured high coupling cooperativity between a single photon and the ion allows for the observation of coherent optical Rabi oscillations. This could enable optically controlled spin qubits, quantum logic gates, and spin-photon interfaces for future quantum networks.

Variational Renormalization Group for Dissipative Spin-Cavity Systems: Periodic Pulses of Nonclassical Photons from Mesoscopic Spin Ensembles

Mesoscopic spin ensembles coupled to a cavity offer the exciting prospect of observing complex nonclassical phenomena that pool the microscopic features from a few spins with those of macroscopic spin ensembles. Here, we demonstrate how the collective interactions in an ensemble of as many as a hundred spins can be harnessed to obtain a periodic pulse train of nonclassical light. To unravel the full quantum dynamics and photon statistics, we develop a time-adaptive variational renormalization group method that accurately captures the underlying Lindbladian dynamics of the mesoscopic spin-cavity system.

Quantum Nonlinear Optics in Atomically Thin Materials

We show that a nonlinear optical response associated with a resonant, atomically thin material can be dramatically enhanced by placing it in front of a partially reflecting mirror, rendering otherwise weakly nonlinear systems suitable for experiments and applications involving quantum nonlinear optics. Our approach exploits the nonlinear response of long-lived polariton resonances that arise at particular distances between the material and the mirror. The scheme is entirely based on free-space optics, eliminating the need for cavities or complex nanophotonic structures. We analyze a specific implementation based on exciton-polariton resonances in two-dimensional semiconductors and discuss the role of imperfections and loss.

A wavelength-convertible quantum memory: Controlled echo

Quantum coherence control is reinvestigated for a new physical insight in quantum nonlinear optics and applied for a wavelength-convertible quantum memory in a solid ensemble whose spin states are inhomogeneously broadened. Unlike typical atomic media whose spin decays are homogeneous, a spin inhomogeneously broadened solid ensemble requires a counter-intuitive quantum coherence control to avoid spontaneous emission-caused quantum noises. Such a quantum coherence control in a solid ensemble satisfying both near perfect retrieval efficiency and ultralong photon storage offers a solid framework to quantum repeaters, scalable qubit generations, quantum cryptography, and highly sensitive magnetometry. Here, the basic physics of the counter-intuitive quantum coherence control is presented not only for a fundamental understanding of collective ensemble phase control but also for a coherence conversion mechanism between optical and spin states involving Raman rephasing.

Photonic quantum state transfer between a cold atomic gas and a crystal

Interfacing fundamentally different quantum systems is key to building future hybrid quantum networks. Such heterogeneous networks offer capabilities superior to those of their homogeneous counterparts, as they merge the individual advantages of disparate quantum nodes in a single network architecture. However, few investigations of optical hybrid interconnections have been carried out, owing to fundamental and technological challenges such as wavelength and bandwidth matching of the interfacing photons. Here we report optical quantum interconnection of two disparate matter quantum systems with photon storage capabilities. We show that a quantum state can be transferred faithfully between a cold atomic ensemble and a rare-earth-doped crystal by means of a single photon at 1,552  nanometre telecommunication wavelength, using cascaded quantum frequency conversion. We demonstrate that quantum correlations between a photon and a single collective spin excitation in the cold atomic ensemble can be transferred to the solid-state system. We also show that single-photon time-bin qubits generated in the cold atomic ensemble can be converted, stored and retrieved from the crystal with a conditional qubit fidelity of more than 85 per cent. Our results open up the prospect of optically connecting quantum nodes with different capabilities and represent an important step towards the realization of large-scale hybrid quantum networks.

Experimental entanglement of 25 individually accessible atomic quantum interfaces

A quantum interface links the stationary qubits in a quantum memory with flying photonic qubits in optical transmission channels and constitutes a critical element for the future quantum internet. Entanglement of quantum interfaces is an important step for the realization of quantum networks. Through heralded detection of photon interference, we generate multipartite entanglement between 25 (or 9) individually addressable quantum interfaces in a multiplexed atomic quantum memory array and confirm genuine 22-partite (or 9-partite) entanglement. This experimental entanglement of a record-high number of individually addressable quantum interfaces makes an important step toward the realization of quantum networks, long-distance quantum communication, and multipartite quantum information processing.

Broadband multiresonator quantum memory-interface

In this paper we experimentally demonstrated a broadband scheme of the multiresonator quantum memory-interface. The microwave photonic scheme consists of the system of mini-resonators strongly interacting with a common broadband resonator coupled with the external waveguide. We have implemented the impedance matched quantum storage in this scheme via controllable tuning of the mini-resonator frequencies and coupling of the common resonator with the external waveguide. Proof-of-principal experiment has been demonstrated for broadband microwave pulses when the quantum efficiency of 16.3% was achieved at room temperature. By using the obtained experimental spectroscopic data, the dynamics of the signal retrieval has been simulated and promising results were found for high-Q mini-resonators in microwave and optical frequency ranges. The results pave the way for the experimental implementation of broadband quantum memory-interface with quite high efficiency η > 0.99 on the basis of modern technologies, including optical quantum memory at room temperature.

Fast, noise-free memory for photon synchronization at room temperature

Future quantum photonic networks require coherent optical memories for synchronizing quantum sources and gates of probabilistic nature. We demonstrate a fast ladder memory (FLAME) mapping the optical field onto the superposition between electronic orbitals of rubidium vapor. Using a ladder-level system of orbital transitions with nearly degenerate frequencies simultaneously enables high bandwidth, low noise, and long memory lifetime. We store and retrieve 1.7-ns-long pulses, containing 0.5 photons on average, and observe short-time external efficiency of 25%, memory lifetime (1/e) of 86 ns, and below 10-4 added noise photons. Consequently, coupling this memory to a probabilistic source would enhance the on-demand photon generation probability by a factor of 12, the highest number yet reported for a noise-free, room temperature memory. This paves the way toward the controlled production of large quantum states of light from probabilistic photon sources.

Environment spectrum and coherence behaviours in a rare-earth doped crystal for quantum memory

We theoretically investigate the dynamics of environment and coherence behaviours of the central ion in a quantum memory based on a rare-earth doped crystal. The interactions between the central ion and the bath spins suppress the flip-flop rate of the neighbour bath spins and yield a specific environment spectral density S(ω). Under dynamical decoupling pulses, this spectrum provides a general scaling for the coherence envelope and coherence time, which significantly extend over a range on an hour-long time scale. The characterized environment spectrum with ultra-long coherence time can be used to implement various quantum communication and information processing protocols.

Entanglement between more than two hundred macroscopic atomic ensembles in a solid

There are both fundamental and practical motivations for studying whether quantum entanglement can exist in macroscopic systems. However, multiparty entanglement is generally fragile and difficult to quantify. Dicke states are multiparty entangled states where a single excitation is delocalized over many systems. Building on previous work on quantum memories for photons, we create a Dicke state in a solid by storing a single photon in a crystal that contains many large atomic ensembles with distinct resonance frequencies. The photon is re-emitted at a well-defined time due to an interference effect analogous to multi-slit diffraction. We derive a lower bound for the number of entangled ensembles based on the contrast of the interference and the single-photon character of the input, and we experimentally demonstrate entanglement between over two hundred ensembles, each containing a billion atoms. We also illustrate the fact that each individual ensemble contains further entanglement.

Multipartite entanglement is of both fundamental and practical interest, but is notoriously difficult to witness and characterise. Here, Zarkeshian et al. demonstrate multipartite entanglement in an atomic frequency comb storing a single photon in a Dicke state spread over a macroscopic ensemble.

Nanophotonic rare-earth quantum memory with optically controlled retrieval

Optical quantum memories are essential elements in quantum networks for long-distance distribution of quantum entanglement. Scalable development of quantum network nodes requires on-chip qubit storage functionality with control of the readout time. We demonstrate a high-fidelity nanophotonic quantum memory based on a mesoscopic neodymium ensemble coupled to a photonic crystal cavity. The nanocavity enables >95% spin polarization for efficient initialization of the atomic frequency comb memory and time bin-selective readout through an enhanced optical Stark shift of the comb frequencies. Our solid-state memory is integrable with other chip-scale photon source and detector devices for multiplexed quantum and classical information processing at the network nodes.