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A hybrid interface of solid state single-photon sources and atomic quantum memories is a long sought-after goal in photonic quantum technologies. Here we demonstrate deterministic storage and retrieval of photons from a semiconductor quantum dot in an atomic ensemble quantum memory at telecommunications wavelengths. We store single photons from an InAs quantum dot in a high-bandwidth rubidium vapour based quantum memory, with a total internal memory efficiency of $(12.9 \pm 0.4) \%$. The signal-to-noise ratio of the retrieved photons is $18.2\pm 0.6$, limited only by detector dark counts. This demonstration paves the way to quantum technologies that rely on distributed entanglement, and is especially suited for photonic quantum networks.

The efficient storage and on-demand retrieval of quantum optical states that are compatible with the telecommunications C-band is a requirement for future terrestrial-based quantum optical networking. Spectrum in the C-band minimises optical fiber-propagation losses, and broad optical bandwidth facilitates high-speed networking protocols. Here we report on a telecommunication wavelength and bandwidth compatible quantum memory. Using the Off-Resonant Cascaded Absorption protocol in hot $^{87}$Rb vapour, we demonstrate a total memory efficiency of $20.90(1)\,\%$ with a Doppler-limited storage time of $1.10(2)\,$ns. We characterise the memory performance with weak coherent states, demonstrating signal-to-noise ratios greater than unity for mean photon number inputs above $4.5(6)\times10^{-6}$ per pulse.

Gaussian Boson Sampling (GBS) is a quantum computing concept based on drawing samples from a multimode nonclassical Gaussian state using photon-number resolving detectors. It was initially posed as a near-term approach aiming to achieve quantum advantage, but several applications have been proposed ever since, such as the calculation of graph features or molecular vibronic spectra, among others. For the first time, we use a time-bin encoded interferometer to implement GBS experimentally and extract samples to enhance the search for dense subgraphs in a graph. Our results indicate an improvement over classical methods for subgraphs of sizes three and four in a graph containing ten nodes. In addition, we numerically explore the role of imperfections in the optical circuit and on the performance of the algorithm., Comment: 11 pages, 8 figures. Improved readibility

Gaussian boson sampling (GBS) is quantum sampling task in which one has to draw samples from the photon-number distribution of a large-dimensional nonclassical squeezed state of light. In an effort to make this task intractable for a classical computer, experiments building GBS machines have mainly focused on increasing the dimensionality and squeezing strength of the nonclassical light. However, no experiment has yet demonstrated the ability to displace the squeezed state in phase-space, which is generally required for practical applications of GBS. In this work, we build a GBS machine which achieves the displacement by injecting a laser beam alongside a two-mode squeezed vacuum state into a 15-mode interferometer. We focus on two new capabilities. Firstly, we use the displacement to reconstruct the multimode Gaussian state at the output of the interferometer. Our reconstruction technique is in situ and requires only three measurements settings regardless of the state dimension. Secondly, we study how the addition of classical laser light in our GBS machine affects the complexity of sampling its output photon statistics. We introduce and validate approximate semi-classical models which reduce the computational cost when a significant fraction of the detected light is classical., Comment: 11 pages, 11 figures

One of the core questions of quantum physics is how to reconcile the unitary evolution of quantum states, which is information-preserving and time-reversible, with evolution following the second law of thermodynamics, which, in general, is neither. The resolution to this paradox is to recognize that global unitary evolution of a multi-partite quantum state causes the state of local subsystems to evolve towards maximum-entropy states. In this work, we experimentally demonstrate this effect in linear quantum optics by simultaneously showing the convergence of local quantum states to a generalized Gibbs ensemble constituting a maximum-entropy state under precisely controlled conditions, while introducing an efficient certification method to demonstrate that the state retains global purity. Our quantum states are manipulated by a programmable integrated quantum photonic processor, which simulates arbitrary non-interacting Hamiltonians, demonstrating the universality of this phenomenon. Our results show the potential of photonic devices for quantum simulations involving non-Gaussian states., Comment: 9+12 pages, 12 figures, replaced with final version

Multiphoton contributions pose a significant challenge for the realisation of heralded single-photon sources (HSPS) based on nonlinear processes. In this work, we improve the quality of single photons generated in this way by harnessing the photon-number resolving (PNR) capabilities of commercial superconducting nanowire single-photon detectors (SNSPDs). We report a $13 \pm 0.4 \%$ reduction in the intensity correlation function $g^{(2)}(0)$ even with a collection efficiency in the photon source of only $29.6\%$. Our work demonstrates the first application of the PNR capabilities of SNSPDs and shows improvement in the quality of an HSPS with widely available technology., Comment: 10 pages, 4 figures

The ability to manipulate and measure the time-frequency structure of quantum light is useful for information processing and metrology. Measuring this structure is also important when developing quantum light sources with high modal purity that can interfere with other independent sources. Here, we present and experimentally demonstrate a scheme based on intensity interferometry to measure the joint spectral mode of photon pairs produced by spontaneous parametric down-conversion. We observe correlations in the spectral phase of the photons due to chirp in the pump. We show that our scheme can be combined with stimulated emission tomography to quickly measure their mode using bright classical light. Our scheme does not require phase stability, nonlinearities, or spectral shaping, and thus is an experimentally simple way of measuring the modal structure of quantum light., Comment: 8 pages, 6 figures; includes Supplemental Material

We experimentally study a broadband implementation of the atomic frequency comb (AFC) rephasing protocol with a cryogenically cooled Pr$^{3+}$:Y$_2$SiO$_5$ crystal. To allow for storage of broadband pulses, we explore a novel regime where the input photonic bandwidth closely matches the inhomogeneous broadening of the material $(\sim5\,\textrm{GHz})$, thereby significantly exceeding the hyperfine ground and excited state splitting $(\sim10\,\textrm{MHz})$. Through an investigation of different AFC preparation parameters, we measure a maximum efficiency of $10\%$ after a rephasing time of $12.5\,$ns. With a suboptimal AFC, we witness up to 12 rephased temporal modes.

The discrimination of coherent states is a key task in optical communication and quantum key distribution protocols. In this work, we use a photon-number-resolving detector, the transition-edge sensor, to discriminate binary-phase-shifted coherent states at a telecom wavelength. Owing to its dynamic range and high efficiency, we achieve a bit error probability that unconditionally exceeds the standard quantum limit (SQL) by up to 7.7 dB. The improvement to the SQL persists for signals containing up to approximately seven photons on average and is achieved in a single shot (i.e. without measurement feedback), thus making our approach compatible with larger bandwidths., Comment: 4 pages, 3 figures

Quantum memories are a crucial technology for enabling large-scale quantum networks through synchronisation of probabilistic operations. Such networks impose strict requirements on quantum memory, such as storage time, retrieval efficiency, bandwidth, and scalability. On- and off-resonant ladder protocols on warm atomic vapour platforms are promising candidates, combining efficient high-bandwidth operation with low-noise on-demand retrieval. However, their storage time is severely limited by motion-induced dephasing caused by the broad velocity distribution of atoms comprising the vapour. In this paper, we demonstrate velocity selective optical pumping to overcome this decoherence mechanism. This will increase the achievable memory storage time of vapour memories. This technique can also be used for preparing arbitrarily shaped absorption profiles, for instance, preparing an atomic frequency comb absorption feature.

We demonstrate coherent storage and retrieval of pulsed light using the atomic frequency comb quantum memory protocol in a room temperature alkali vapour. We utilise velocity-selective optical pumping to prepare multiple velocity classes in the $F=4$ hyperfine ground state of caesium. The frequency spacing of the classes is chosen to coincide with the $F'=4 - F'=5$ hyperfine splitting of the $6^2$P$_{3/2}$ excited state resulting in a broadband periodic absorbing structure consisting of two usually Doppler-broadened optical transitions. Weak coherent states of duration $2\,\mathrm{ns}$ are mapped into this atomic frequency comb with pre-programmed recall times of $8\,\mathrm{ns}$ and $12\,\mathrm{ns}$, with multi-temporal mode storage and recall demonstrated. Utilising two transitions in the comb leads to an additional interference effect upon rephasing that enhances the recall efficiency.

Quantum phenomena such as entanglement can improve fundamental limits on the sensitivity of a measurement probe. In optical interferometry, a probe consisting of $N$ entangled photons provides up to a $\sqrt{N}$ enhancement in phase sensitivity compared to a classical probe of the same energy. Here, we employ high-gain parametric down-conversion sources and photon-number-resolving detectors to perform interferometry with heralded quantum probes of sizes up to $N=8$ (i.e. measuring up to 16-photon coincidences). Our probes are created by injecting heralded photon-number states into an interferometer, and in principle provide quantum-enhanced phase sensitivity even in the presence of significant optical loss. Our work paves the way towards quantum-enhanced interferometry using large entangled photonic states., Comment: 15 pages, 9 figures; includes Supplemental Material

Electro-optic modulators within Mach--Zehnder interferometers are a common construction for optical switches in integrated photonics. A challenge faced when operating at high switching speeds is that noise from the electronic drive signals will effect switching performance. Inspired by the Mach--Zehnder lattice switching devices of Van Campenhout et al. [Opt. Express, 17, 23793 (2009)] and techniques from the field of Nuclear Magnetic Resonance known as composite pulses, we present switches which offer protection against drive-noise in both the on and off state of the switch for both the phase and intensity information encoded in the switched optical mode., Comment: 8 pages, 4 figures

When two equal photon-number states are combined on a balanced beam splitter, both output ports of the beam splitter contain only even numbers of photons. Consider the time-reversal of this interference phenomenon: the probability that a pair of photon-number-resolving detectors at the output ports of a beam splitter both detect the same number of photons depends on the overlap between the input state of the beam splitter and a state containing only even photon numbers. Here, we propose using this even-parity detection to engineer quantum states containing only even photon-number terms. As an example, we demonstrate the ability to prepare superpositions of two coherent states with opposite amplitudes, i.e. two-component Schr\"odinger cat states. Our scheme can prepare cat states of arbitrary size with nearly perfect fidelity. Moreover, we investigate engineering more complex even-parity states such as four-component cat states by iteratively applying our even-parity detector., Comment: 8 pages, 5 figures

Variable measurement operators enable the optimization of strategies for testing quantum properties and the preparation of a range of quantum states. Here, we experimentally implement a weak-field homodyne detector that can continuously tune between measuring photon numbers and field quadratures. We combine a quantum signal with a coherent state on a balanced beam splitter and detect light at both output ports using photon-number-resolving transition edge sensors. We observe that the discrete difference statistics converge to the quadrature distribution of the signal as we increase the coherent state amplitude. Moreover, in a proof-of-principle demonstration of state engineering, we show the ability to control the photon-number distribution of a state that is heralded using our weak-field homodyne detector., Comment: 12 pages, 10 figures; includes Supplemental Material

We demonstrate multiphoton interference using a resource-efficient frequency multiplexing scheme, suitable for quantum information applications that demand multiple indistinguishable and pure single photons. In our source, frequency-correlated photon pairs are generated over a wide range of frequencies by pulsed parametric down conversion. Indistinguishable single photons of a predetermined frequency are prepared using frequency-resolved detection of one photon to control an electro-optic frequency shift applied to its partner. Measured photon statistics show multiplexing increases the probability of delivering a single photon, without a corresponding increase to multiphoton events. Interference of consecutive outputs is used to bound the single-photon purity and demonstrate the non-classical nature of the emitted light.

Quantum simulations are becoming an essential tool for studying complex phenomena, e.g. quantum topology, quantum information transfer, and relativistic wave equations, beyond the limitations of analytical computations and experimental observations. To date, the primary resources used in proof-of-principle experiments are collections of qubits, coherent states or multiple single-particle Fock states. Here we show the first quantum simulation performed using genuine higher-order Fock states, with two or more indistinguishable particles occupying the same bosonic mode. This was implemented by interfering pairs of Fock states with up to five photons on an interferometer, and measuring the output states with photon-number-resolving detectors. Already this resource-efficient demonstration reveals new topological matter, simulates non-linear systems and elucidates a perfect quantum transfer mechanism which can be used to transport Majorana fermions., Comment: New text and results. 19 pages, 13 figures, supplementary material

The representation of quantum states via phase-space functions constitutes an intuitive technique to characterize light. However, the reconstruction of such distributions is challenging as it demands specific types of detectors and detailed models thereof to account for their particular properties and imperfections. To overcome these obstacles, we derive and implement a measurement scheme that enables a reconstruction of phase-space distributions for arbitrary states whose functionality does not depend on the knowledge of the detectors, thus defining the notion of detector-agnostic phase-space distributions. Our theory presents a generalization of well-known phase-space quasiprobability distributions, such as the Wigner function. We implement our measurement protocol, using state-of-the-art transition-edge sensors without performing a detector characterization. Based on our approach, we reveal the characteristic features of heralded single- and two-photon states in phase space and certify their nonclassicality with high statistical significance.

We introduce a filter using a noise-free quantum buffer with large optical bandwidth that can both filter temporal-spectral modes, as well as inter-convert them and change their frequency. We show that such quantum buffers optimally filter out temporal-spectral noise; producing identical single-photons from many distinguishable noisy single-photon sources with the minimum required reduction in brightness. We then experimentally demonstrate a noise-free quantum buffer in a warm atomic system that is well matched to quantum dots and can outperform all intensity (incoherent) filtering schemes for increasing indistinguishability., Comment: 5 pages, 4 Figures

The quasiprobability representation of quantum states addresses two main concerns, the identification of nonclassical features and the decomposition of the density operator. While the former aspect is a main focus of current research, the latter decomposition property has been studied less frequently. In this contribution, we introduce a method for the generalized expansion of quantum states in terms of so-called quasistates. In contrast to the quasiprobability decomposition through nonclassical distributions and pure-state operators, our technique results in classical probabilities and nonpositive semidefinite operators, defining the notion of quasistates, that carry the information about the nonclassical characteristics of the system. Therefore, our method presents a complementary approach to prominent quasiprobability representations. We explore the usefulness of our technique with several examples, including applications for quantum state reconstruction and the representation of nonclassical light. In addition, using our framework, we also demonstrate that inseparable quantum correlations can be described in terms of classical joint probabilities and tensor-product quasistates for an unambiguous identification of quantum entanglement.

Achieving cavity-optomechanical strong coupling with high-frequency phonons provides a rich avenue for quantum technology development including quantum state-transfer, memory, and transduction, as well as enabling several fundamental studies of macroscopic phononic degrees-of-freedom. Reaching such coupling with GHz mechanical modes however has proved challenging, with a prominent hindrance being material- and surface-induced-optical absorption in many materials. Here, we circumvent these challenges and report the observation of optomechanical strong coupling to a high frequency (11 GHz) mechanical mode of a fused-silica whispering-gallery microresonator via the electrostrictive Brillouin interaction. Using an optical heterodyne detection scheme, the anti-Stokes light backscattered from the resonator is measured and normal-mode splitting and an avoided crossing are observed in the recorded spectra, providing unambiguous signatures of strong coupling. The optomechanical coupling rate reaches values as high as $G/2\pi = 39 \ \text{MHz}$ through the use of an auxiliary pump resonance, where the coupling dominates both the optical ($\kappa/2\pi = 3 \ \text{MHz}$) and the mechanical ($\gamma_\text{m}/2\pi = 21 \ \text{MHz}$) amplitude decay rates. Our findings provide a promising new approach for optical quantum control using light and sound., Comment: 16 pages, 5 figures, includes supplementary, accepted in Optica

Gaussian boson sampling is a promising scheme for demonstrating a quantum computational advantage using photonic states that are accessible in a laboratory and, thus, offer scalable sources of quantum light. In this contribution, we study two-point photon-number correlation functions to gain insight into the interference of Gaussian states in optical networks. We investigate the characteristic features of statistical signatures which enable us to distinguish classical from quantum interference. In contrast to the typical implementation of boson sampling, we find additional contributions to the correlators under study which stem from the phase dependence of Gaussian states and which are not observable when Fock states interfere. Using the first three moments, we formulate the tools required to experimentally observe signatures of quantum interference of Gaussian states using two outputs only. By considering the current architectural limitations in realistic experiments, we further show that a statistically significant discrimination between quantum and classical interference is possible even in the presence of loss, noise, and a finite photon-number resolution. Therefore, we formulate and apply a theoretical framework to benchmark the quantum features of Gaussian boson sampling under realistic conditions.

It is an open question how fast information processing can be performed and whether quantum effects can speed up the best existing solutions. Signal extraction, analysis and compression in diagnostics, astronomy, chemistry and broadcasting builds on the discrete Fourier transform. It is implemented with the Fast Fourier Transform (FFT) algorithm that assumes a periodic input of specific lengths, which rarely holds true. A less-known transform, the Kravchuk-Fourier (KT), allows one to operate on finite strings of arbitrary length. It is of high demand in digital image processing and computer vision, but features a prohibitive runtime. Here, we report a one-step computation of a fractional quantum KT. A quantum $d$-nary (qudit) architecture we use comprises only one gate and offers processing time independent of the input size. The gate may employ a multiphoton Hong-Ou-Mandel effect. Existing quantum technologies may scale it up towards diverse applications., Comment: Accepted for publication in Science Advances; 51 pages, 10 figures

We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state. Conversely, quantum phenomena are certified in terms of signed distributions, i.e., quasiprobabilities, and a residual component unaccessible via classical states. Our unifying method combines well-established concepts, such as phase-space distributions in quantum optics, with resources of quantumness relevant for quantum technologies. We apply our approach to analyze various forms of quantum coherence in different physical systems. Moreover, our framework renders it possible to uncover complex quantum correlations between systems, for example, via quasiprobability representations of multipartite entanglement., Comment: revised version

We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first place. For this reason, we derive from first principles equations of motions that describe the classical propagation in quantum systems. A comparison of this classical model with the actual temporal quantum behavior enables us to identify quantum phenomena in the system's dynamics and distinguish them from static quantum features at individual points in time. For instance, we show how Newton's second law emerges as a special case of our general treatment, connecting it to a Schr\"odinger-type equation. As applications of our universal technique, we analyze nonlinear optical processes, semiclassical models, and the multipartite entanglement dynamics of macroscopic ensembles., Comment: extended version, close to published paper

We demonstrate a monolithic III-V photonic circuit combining a heralded single photon source with a beamsplitter, at room temperature and telecom wavelength. Pulsed parametric down-conversion in an AlGaAs waveguide generates counterpropagating photons, one of which is used to herald the injection of its twin into the beamsplitter. We use this configuration to implement an integrated Hanbury-Brown and Twiss experiment, yielding a heralded second-order correlation $g^{(2)}_{\rm her}(0)=0.10 \pm 0.02$ that confirms single-photon operation. The demonstrated generation and manipulation of quantum states on a single III-V semiconductor chip opens promising avenues towards real-world applications in quantum information.

The dynamical behavior of interacting systems plays a fundamental role for determining quantum correlations, such as entanglement. In this Letter, we describe temporal quantum effects of the inseparable evolution of composite quantum states by comparing the trajectories to their classically correlated counterparts. For this reason, we introduce equations of motions describing the separable propagation of any interacting quantum system, which are derived by requiring separability for all times. The resulting Schroedinger-type equations allow for comparing the trajectories in a separable configuration with the actual behavior of the system and, thereby, identifying inseparable and time-dependent quantum properties. As an example, we study bipartite discrete- and continuous-variable interacting systems. The generalization of our developed technique to multipartite scenarios is also provided., Comment: close to published version

Quantum networks promise to revolutionise computing, simulation, and communication. Light is the ideal information carrier for quantum networks, as its properties are not degraded by noise in ambient conditions, and it can support large bandwidths enabling fast operations and a large information capacity. Quantum memories, devices that store, manipulate, and release on demand quantum light, have been identified as critical components of photonic quantum networks, because they facilitate scalability. However, any noise introduced by the memory can render the device classical by destroying the quantum character of the light. Here we introduce an intrinsically noise-free memory protocol based on two-photon off-resonant cascaded absorption (ORCA). We consequently demonstrate for the first time successful storage of GHz-bandwidth heralded single photons in a warm atomic vapour with no added noise; confirmed by the unaltered photon statistics upon recall. Our ORCA memory platform meets the stringent noise-requirements for quantum memories whilst offering technical simplicity and high-speed operation, and therefore is immediately applicable to low-latency quantum networks.

We study emerging notions of quantum correlations in compound systems. Based on different definitions of quantumness in individual subsystems, we investigate how they extend to the joint description of a composite system. Especially, we study the bipartite case and the connection of two typically applied and distinctively different concepts of nonclassicality in quantum optics and quantum information. Our investigation includes the representation of correlated states in terms of quasiprobability matrices, a comparative study of joint and conditional quantum correlations, and an entanglement characterization. It is, for example, shown that our composition approach always includes entanglement as one form of quantum correlations. Yet, other forms of quantum correlations can also occur without entanglement. Finally, we give an outlook towards multimode systems and temporal correlations.

In a recent contribution, we introduced and applied a detector-independent method to uncover nonclassicality. Here, we extend those techniques and give more details on the performed analysis. We derive a general theory of the positive-operator-valued measure that describes multiplexing layouts with arbitrary detectors. From the resulting quantum version of a multinomial statistics, we infer nonclassicality probes based on a matrix of normally ordered moments. We discuss these criteria and apply the theory to our data which are measured with superconducting transition-edge sensors. Our experiment produces heralded multi-photon states from a parametric down-conversion light source. We show that the known notions of sub-Poisson and sub-binomial light can be deduced from our general approach, and we establish the concept of sub-multinomial light, which is shown to outperform the former two concepts of nonclassicality for our data., Comment: close to published version

We introduce a method for the verification of nonclassical light which is independent of the complex interaction between the generated light and the material of the detectors. This is accomplished by means of a multiplexing arrangement. Its theoretical description yields that the coincidence statistics of this measurement layout is a mixture of multinomial distributions for any classical light field and any type of detector. This allows us to formulate bounds on the statistical properties of classical states. We apply our directly accessible method to heralded multiphoton states which are detected with a single multiplexing step only and two detectors, which are in our work superconducting transition-edge sensors. The nonclassicality of the generated light is verified and characterized through the violation of the classical bounds without the need for characterizing the used detectors., Comment: close to published version

We present a theoretical study of entanglement in ensembles consisting of an arbitrary number of particles. Multipartite entanglement criteria in terms of observables are formulated for a fixed number of particles as well as for systems with a fluctuating particle number. To access the quality of the verified entanglement, the operational measure of the entanglement visibility is introduced. As an example, we perform an analytical characterization of quantum systems composed of interacting harmonic oscillators and witness the entanglement via energy measurements. Our analysis shows that the detectable entanglement decays for macroscopic particle numbers without the need for decoherence processes and for all considered coupling regimes. We further study thermal states of the given correlated system together with the temperature dependence of entanglement.

Raman interactions in alkali vapours are used in applications such as atomic clocks, optical signal processing, generation of squeezed light and Raman quantum memories for temporal multiplexing. To achieve a strong interaction the alkali ensemble needs both a large optical depth and a high level of spin-polarisation. We implement a technique known as quenching using a molecular buffer gas which allows near-perfect spin-polarisation of over $99.5\%$ in caesium vapour at high optical depths of up to $\sim 2 \times 10^5$; a factor of 4 higher than can be achieved without quenching. We use this system to explore efficient light storage with high gain in a GHz bandwidth Raman memory., Comment: 11 pages, 6 figures

We demonstrate the fabrication of sub-micron layers of single-crystal diamond suitable for subsequent processing as demonstrated by this test ring structure. This method is a significant enabling technology for nanomechanical and photonic structures incorporating colour-centres. The process uses a novel double implant process, annealing and chemical etching to produce membranes of diamond from single-crystal starting material, the thinnest layers achieved to date are 210 nm thick., Comment: 21 pages, 4 figures

We demonstrate a platform for implementing quantum walks that overcomes many of the barriers associated with photonic implementations. We use coupled fiber-optic cavities to implement time-bin encoded walks in an integrated system. We show that this platform can achieve very low losses combined with high-fidelity operations, enabling an unprecedented large number of steps in a passive system, as required for scenarios with multiple walkers. Furthermore the platform is reconfigurable, enabling variation of the coin, and readily extends to multidimensional lattices. We demonstrate variation of the coin bias experimentally for three different values.

We study, in theory and experiment, the quantum properties of correlated light fields measured with click-counting detectors providing incomplete information on the photon statistics. We establish a correlation parameter for the conditional statistics, and we derive the corresponding nonclassicality criteria for detecting conditional quantum correlations. Classical bounds for Pearson's correlation parameter are formulated that allow us, once they are violated, to determine nonclassical correlations via the joint statistics. On the one hand, we demonstrate nonclassical correlations in terms of the joint click statistics of light produced by a parametric down conversion source. On the other hand, we verify quantum correlations of a heralded, split single-photon state via the conditional click statistics together with a generalization to higher-order moments. We discuss the performance of the presented nonclassicality criteria to successfully discern joint and conditional quantum correlations. Remarkably, our results are obtained without making any assumptions on the response function, quantum efficiency, and dark-count rate of the photodetectors.

Quantum memories, capable of storing single photons or other quantum states of light, to be retrieved on-demand, offer a route to large-scale quantum information processing with light. A promising class of memories is based on far-off-resonant Raman absorption in ensembles of $\Lambda$-type atoms. However at room temperature these systems exhibit unwanted four-wave mixing, which is prohibitive for applications at the single-photon level. Here we show how this noise can be suppressed by placing the storage medium inside a moderate-finesse optical cavity, thereby removing the main roadblock hindering this approach to quantum memory., Comment: 10 pages, 3 figures. This paper provides the theoretical background to our recent experimental demonstration of noise suppression in a cavity-enhanced Raman-type memory ( arXiv:1510.04625 ). See also the related paper arXiv:1511.05448, which describes numerical modelling of an atom-filled cavity. Comments welcome

A means for precise experimental characterization of the dielectric susceptibility of an atomic gas inside and optical cavity is important for design and operation of quantum light matter interfaces, particularly in the context of quantum information processing. Here we present a numerically optimised theoretical model to predict the spectral response of an atom-filled cavity, accounting for both homogeneous and inhomogeneous broadening at high optical densities. We investigate the regime where the two broadening mechanisms are of similar magnitude, which makes the use of common approximations invalid. Our model agrees with an experimental implementation with warm caesium vapour in a ring cavity. From the cavity response, we are able to extract important experimental parameters, for instance the ground state populations, total number density and the magnitudes of both homogeneous and inhomogeneous broadening., Comment: Author accepted version

Broadband quantum memories hold great promise as multiplexing elements in future photonic quantum information protocols. Alkali vapour Raman memories combine high-bandwidth storage, on-demand read-out, and operation at room temperature without collisional fluorescence noise. However, previous implementations have required large control pulse energies and suffered from four-wave mixing noise. Here we present a Raman memory where the storage interaction is enhanced by a low-finesse birefringent cavity tuned into simultaneous resonance with the signal and control fields, dramatically reducing the energy required to drive the memory. By engineering anti-resonance for the anti-Stokes field, we also suppress the four-wave mixing noise and report the lowest unconditional noise floor yet achieved in a Raman-type warm vapour memory, $(15\pm2)\times10^{-3}$ photons per pulse, with a total efficiency of $(9.5\pm0.5)$%.

It is proposed that the ground-state manifold of the neutral nitrogen-vacancy center in diamond could be used as a quantum two-level system in a solid-state-based implementation of a broadband, noise-free quantum optical memory. The proposal is based on the same-spin $\Lambda$-type three-level system created between the two E orbital ground states and the A$_1$ orbital excited state of the center, and the cross-linear polarization selection rules obtained with the application of transverse electric field or uniaxial stress. Possible decay and decoherence mechanisms of this system are discussed, and it is shown that high-efficiency, noise-free storage of photons as short as a few tens of picoseconds for at least a few nanoseconds could be possible at low temperature., Comment: Revised version. 11 pages, 5 figures, 2 appendices, 22 equations

Photonics is a promising platform for quantum technologies. However, photon sources and two-photon gates currently only operate probabilistically. Large-scale photonic processing will therefore be impossible without a multiplexing strategy to actively select successful events. High time-bandwidth-product quantum memories - devices that store and retrieve single photons on-demand - provide an efficient remedy via active synchronisation. Here we interface a GHz-bandwidth heralded single-photon source and a room-temperature Raman memory with a time-bandwidth product exceeding 1000. We store heralded single photons and observe a clear influence of the input photon statistics on the retrieved light, which agrees with our theoretical model. The preservation of the stored field's statistics is limited by four-wave-mixing noise, which we identify as the key remaining challenge in the development of practical memories for scalable photonic information processing.

We introduce a novel time-frequency quantum key distribution (TFQKD) scheme based on photon pairs entangled in these two conjugate degrees of freedom. The scheme uses spectral detection and phase modulation to enable measurements in the temporal basis by means of time-to-frequency conversion. This allows large-alphabet encoding to be implemented with realistic components. A general security analysis for TFQKD with binned measurements reveals a close connection with finite-dimensional QKD protocols and enables analysis of the effects of dark counts on the secure key size., Comment: 14 pages, 3 figures, submitted

Single photons are a vital resource for optical quantum information processing. Efficient and deterministic single photon sources do not yet exist, however. To date, experimental demonstrations of quantum processing primitives have been implemented using non-deterministic sources combined with heralding and/or postselection. Unfortunately, even for eight photons, the data rates are already so low as to make most experiments impracticable. It is well known that quantum memories, capable of storing photons until they are needed, are a potential solution to this `scaling catastrophe'. Here, we analyze in detail the benefits of quantum memories for producing multiphoton states, showing how the production rates can be enhanced by many orders of magnitude. We identify the quantity $\eta B$ as the most important figure of merit in this connection, where $\eta$ and $B$ are the efficiency and time-bandwidth product of the memories, respectively., Comment: Just over 4 pages, 2 figures

Conventional tomographic techniques are becoming increasingly infeasible for reconstructing the operators of quantum devices of growing sophistication. We describe a novel tomographic procedure using coherent states which begins by reconstructing the diagonals of the operator, and then each successive off-diagonal in a recursive manner. Each recursion is considerably more efficient than reconstructing the operator in its entirety, and each successive recursion involves fewer parameters. We apply our technique to reconstruct the positive-operator-valued measure (POVM) corresponding to a recently developed coherent optical detector with phase sensitivity and number resolution. We discuss the effect of various parameters on the reconstruction accuracy. The results show the efficiency of the method and its robustness to experimental noise., Comment: 23 pages, 5 figures. Minor changes

Quantum memories are vital to the scalability of photonic quantum information processing (PQIP), since the storage of photons enables repeat-until-success strategies. On the other hand the key element of all PQIP architectures is the beam splitter, which allows to coherently couple optical modes. Here we show how to combine these crucial functionalities by addressing a Raman quantum memory with multiple control pulses. The result is a coherent optical storage device with an extremely large time-bandwidth product, that functions as an array of dynamically configurable beam splitters, and that can be read out with arbitrarily high efficiency. Networks of such devices would allow fully scalable PQIP, with applications in quantum computation, long-distance quantum communications and quantum metrology., Comment: 4 pages, 3 figures

We demonstrate a dual-rail optical Raman memory inside a polarization interferometer; this enables us to store polarization-encoded information at GHz bandwidths in a room-temperature atomic ensemble. By performing full process tomography on the system we measure up to 97\pm1% process fidelity for the storage and retrieval process. At longer storage times, the process fidelity remains high, despite a loss of efficiency. The fidelity is 86\pm4% for 1.5 \mu s storage time, which is 5,000 times the pulse duration. Hence high fidelity is combined with a large time-bandwidth product. This high performance, with an experimentally simple setup, demonstrates the suitability of the Raman memory for integration into large-scale quantum networks., Comment: 10 pages, 4 figures. Accepted for publication in Journal of Physics B

Quantum memories capable of storing single photons are essential building blocks for quantum information processing, enabling the storage and transfer of quantum information over long distances. Devices operating at room temperature can be deployed on a large scale and integrated into existing photonic networks, but so far warm quantum memories have been susceptible to noise at the single photon level. This problem is circumvented in cold atomic ensembles, but these are bulky and technically complex. Here we demonstrate controllable, broadband and efficient storage and retrieval of weak coherent light pulses at the single-photon level in warm atomic caesium vapour using the far off-resonant Raman memory scheme. The unconditional noise floor is found to be low enough to operate the memory in the quantum regime at room temperature., Comment: 7 pages, 3 figures

Arrays of atoms trapped in optical lattices are appealing as storage media for photons, since motional dephasing of the atoms is eliminated. The regular lattice is also associated with band structure in the dispersion experienced by incident photons. Here we study the influence of this band structure on the efficiency of quantum memories based on electromagnetically induced transparency (EIT) and on Raman absorption. We observe a number of interesting effects, such as both reduced and superluminal group velocities, enhanced atom-photon coupling and anomalous transmission. These effects are ultimately deleterious to the memory efficiency, but they are easily avoided by tuning the optical fields away from the band edges., Comment: 6 pages, 5 figures, accepted for publication in PRA

We perform a review of various approaches to the implementation of quantum memories, with an emphasis on activities within the quantum memory sub-project of the EU Integrated Project "Qubit Applications". We begin with a brief overview over different applications for quantum memories and different types of quantum memories. We discuss the most important criteria for assessing quantum memory performance and the most important physical requirements. Then we review the different approaches represented in "Qubit Applications" in some detail. They include solid-state atomic ensembles, NV centers, quantum dots, single atoms, atomic gases and optical phonons in diamond. We compare the different approaches using the discussed criteria., Comment: 22 pages, 12 figures

Quantum memories, capable of controllably storing and releasing a photon, are a crucial component for quantum computers and quantum communications. So far, quantum memories have operated with bandwidths that limit data rates to MHz. Here we report the coherent storage and retrieval of sub-nanosecond low intensity light pulses with spectral bandwidths exceeding 1 GHz in cesium vapor. The novel memory interaction takes place via a far off-resonant two-photon transition in which the memory bandwidth is dynamically generated by a strong control field. This allows for an increase in data rates by a factor of almost 1000 compared to existing quantum memories. The memory works with a total efficiency of 15% and its coherence is demonstrated by directly interfering the stored and retrieved pulses. Coherence times in hot atomic vapors are on the order of microsecond - the expected storage time limit for this memory., Comment: 13 pages, 5 figures