Quantum state reconstruction of the single-photon Fock state

Gouy phase and quantum interference with cross-Wigner functions for matter-waves

The Gouy phase is essential for accurately describing various wave phenomena, ranging from classical electromagnetic waves to matter waves and quantum optics. In this work, we employ phase-space methods based on the cross-Wigner transformation to analyze spatial and temporal interference in the evolution of matter waves characterized initially by a correlated Gaussian wave packet. First, we consider the cross-Wigner of the initial wave function with its free evolution, and second for the evolution through a double-slit arrangement. Different from the wave function which acquires a global Gouy phase, we find that the cross-Wigner acquires a Gouy phase difference due to different evolution times. The results suggest that temporal like-Gouy phase difference is important for an accurate description of temporal interference. Furthermore, we propose a technique based on the Wigner function to reconstruct the cross-Wigner from the spatial intensity interference term in a double-slit experiment with matter waves.

A Bi-CMOS electronic photonic integrated circuit quantum light detector

Complimentary metal-oxide semiconductor (CMOS) integration of quantum technology provides a route to manufacture at volume, simplify assembly, reduce footprint, and increase performance. Quantum noise-limited homodyne detectors have applications across quantum technologies, and they comprise photonics and electronics. Here, we report a quantum noise-limited monolithic electronic-photonic integrated homodyne detector, with a footprint of 80 micrometers by 220 micrometers, fabricated in a 250-nanometer lithography bipolar CMOS process. We measure a 15.3-gigahertz 3-decibel bandwidth with a maximum shot noise clearance of 12 decibels and shot noise clearance out to 26.5 gigahertz, when measured with a 9-decibel-milliwatt power local oscillator. This performance is enabled by monolithic electronic-photonic integration, which goes below the capacitance limits of devices made up of separate integrated chips or discrete components. It exceeds the bandwidth of quantum detectors with macroscopic electronic interconnects, including wire and flip chip bonding. This demonstrates electronic-photonic integration enhancing quantum photonic device performance.

Remote switch for Schrödinger's cat state using Einstein-Podolsky-Rosen entanglement

We propose a 'remote switch' for Schrödinger's cat state (SCS). Resorting to nonlocal correlations, we demonstrate that an approximate SCS can be heralded at one mode of an Einstein-Podolsky-Rosen entangled state, via a conditional 'hybrid projective measurement' (HPM) performed on the other one mode. The HPM is able to fully manipulate both size and parity of the generated SCS. Here, the HPM consists of both photon number measurement and homodyne conditioning. Such a remote switch for SCS will open up new ideas in subsequent protocols, including fundamental tests and nonlocal manipulation of non-Gaussian states.

Ponderomotive Squeezing of Light by a Levitated Nanoparticle in Free Space

A mechanically compliant element can be set into motion by the interaction with light. In turn, this light-driven motion can give rise to ponderomotive correlations in the electromagnetic field. In optomechanical systems, cavities are often employed to enhance these correlations up to the point where they generate quantum squeezing of light. In free-space scenarios, where no cavity is used, observation of squeezing remains possible but challenging due to the weakness of the interaction, and has not been reported so far. Here, we measure the ponderomotively squeezed state of light scattered by a nanoparticle levitated in a free-space optical tweezer. We observe a reduction of the optical fluctuations by up to 25% below the vacuum level, in a bandwidth of about 15 kHz. Our results are explained well by a linearized dipole interaction between the nanoparticle and the electromagnetic continuum. These ponderomotive correlations open the door to quantum-enhanced sensing and metrology with levitated systems, such as force measurements below the standard quantum limit.

Remote preparation and manipulation of squeezed light

Remote state preparation enables one to create and manipulate a quantum state based on the shared entanglement between distant nodes. Here, we experimentally demonstrate remote preparation and manipulation of squeezed light. By performing a homodyne projective measurement on one mode of the continuous variable entangled state at Alice's station, a squeezed state is created at Bob's station. Moreover, rotation and displacement operations are applied on the prepared squeezed state by changing the projective parameters on Alice's state. We also show that the remotely prepared squeezed state is robust against loss and N - 1 squeezed states can be remotely prepared based on an N-mode continuous variable Greenberger-Horne-Zeilinger-like state. Our results verify the entanglement-based model used in security analysis of quantum key distribution with continuous variables and have potential application in remote quantum information processing.

Measuring the Joint Spectral Mode of Photon Pairs Using Intensity Interferometry

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.

Non-Gaussian Mechanical Motion via Single and Multiphonon Subtraction from a Thermal State

Quantum optical measurement techniques offer a rich avenue for quantum control of mechanical oscillators via cavity optomechanics. In particular, a powerful yet little explored combination utilizes optical measurements to perform heralded non-Gaussian mechanical state preparation followed by tomography to determine the mechanical phase-space distribution. Here, we experimentally perform heralded single-phonon and multiphonon subtraction via photon counting to a laser-cooled mechanical thermal state with a Brillouin optomechanical system at room temperature and use optical heterodyne detection to measure the s-parametrized Wigner distribution of the non-Gaussian mechanical states generated. The techniques developed here advance the state of the art for optics-based tomography of mechanical states and will be useful for a broad range of applied and fundamental studies that utilize mechanical quantum-state engineering and tomography.

Room-Temperature Mechanical Resonator with a Single Added or Subtracted Phonon

A room-temperature mechanical oscillator undergoes thermal Brownian motion with an amplitude much larger than the amplitude associated with a single phonon of excitation. This motion can be read out and manipulated using laser light using a cavity-optomechanical approach. By performing a strong quantum measurement (i.e., counting single photons in the sidebands imparted on a laser), we herald the addition and subtraction of single phonons on the 300 K thermal motional state of a 4 GHz mechanical oscillator. To understand the resulting mechanical state, we implement a tomography scheme and observe highly non-Gaussian phase-space distributions. Using a maximum likelihood method, we infer the density matrix of the oscillator, and we confirm the counterintuitive doubling of the mean phonon number resulting from phonon addition and subtraction.

Coherent Superpositions of Photon Creation Operations and Their Application to Multimode States of Light

We present a concise review of recent experimental results concerning the conditional implementation of coherent superpositions of single-photon additions onto distinct field modes. Such a basic operation is seen to give rise to a wealth of interesting and useful effects, from the generation of a tunable degree of entanglement to the birth of peculiar correlations in the photon numbers and the quadratures of multimode, multiphoton, states of light. The experimental investigation of these properties will have an impact both on fundamental studies concerning, for example, the quantumness and entanglement of macroscopic states, and for possible applications in the realm of quantum-enhanced technologies.

Direct Tomography of High-Dimensional Density Matrices for General Quantum States of Photons

Quantum-state tomography is the conventional method used to characterize density matrices for general quantum states. However, the data acquisition time generally scales linearly with the dimension of the Hilbert space, hindering the possibility of dynamic monitoring of a high-dimensional quantum system. Here, we demonstrate a direct tomography protocol to measure density matrices of photons in the position basis through the use of a polarization-resolving camera, where the dimension of density matrices can be as large as 580×580 in our experiment. The use of the polarization-resolving camera enables parallel measurements in the position and polarization basis and as a result, the data acquisition time of our protocol does not increase with the dimension of the Hilbert space and is solely determined by the camera exposure time (on the order of 10 ms). Our method is potentially useful for the real-time monitoring of the dynamics of quantum states and paves the way for the development of high-dimensional, time-efficient quantum metrology techniques.

Direct Experimental Certification of Quantum Non-Gaussian Character and Wigner Function Negativity of Single-Photon Detectors

Highly nonclassical character of optical quantum detectors, such as single-photon detectors, is essential for preparation of quantum states of light and a vast majority of applications in quantum metrology and quantum information processing. Therefore, it is both fundamentally interesting and practically relevant to investigate the nonclassical features of optical quantum measurements. Here we propose and experimentally demonstrate a procedure for direct certification of quantum non-Gaussianity and Wigner function negativity, two crucial nonclassicality levels, of photonic quantum detectors. Remarkably, we characterize the highly nonclassical properties of the detector by probing it with only two classical thermal states and a vacuum state. We experimentally demonstrate the quantum non-Gaussianity of a single-photon avalanche diode even under the presence of background noise, and we also certify the negativity of the Wigner function of this detector. Our results open the way for direct benchmarking of photonic quantum detectors with a few measurements on classical states.

Experimental Certification of Nonclassicality via Phase-Space Inequalities

In spite of its fundamental importance in quantum science and technology, the experimental certification of nonclassicality is still a challenging task, especially in realistic scenarios where losses and noise imbue the system. Here, we present the first experimental implementation of the recently introduced phase-space inequalities for nonclassicality certification, which conceptually unite phase-space representations with correlation conditions. We demonstrate the practicality and sensitivity of this approach by studying nonclassicality of a family of noisy and lossy quantum states of light. To this end, we experimentally generate single-photon-added thermal states with various thermal mean photon numbers and detect them at different loss levels. Based on the reconstructed Wigner and Husimi Q functions, the inequality conditions detect nonclassicality despite the fact that the involved distributions are nonnegative, which includes cases of high losses (93%) and cases where other established methods do not reveal nonclassicality. We show the advantages of the implemented approach and discuss possible extensions that assure a wide applicability for quantum science and technologies.

Spatial Wavefunction Characterization of Femtosecond Pulses at Single-Photon Level

Reading quantum information of single photons is commonly realized by quantum tomography or the direct (weak) measurement approach. However, these methods are time-consuming and face enormous challenges in characterizing single photons from an ultrafast light source due to the stringent temporal mode matching requirements. Here, we retrieve the spatial wavefunction of indistinguishable single photons from both a continuous wave source and a femtosecond light source using a self-referencing interferometer. Our method only requires nine ensemble-averaged measurements. This technique simplifies the measurement procedure of single-photon wavefunction and automatically mode matches each self-interfering single photon temporally, which enables the measurement of the spatial wavefunction of single photons from an ultrafast light source.

Phase-Space Inequalities Beyond Negativities

We derive a family of inequalities involving different phase-space distributions of a quantum state which have to be fulfilled by any classical state. The violation of these inequalities is a clear signature of nonclassicality. Our approach combines the characterization of nonclassical effects via negativities in phase-space distributions with inequality conditions usually being formulated for moments of physical observables. Importantly, the obtained criteria certify nonclassicality even when the involved phase-space distributions are non-negative. Moreover, we show how these inequalities are related to correlation measurements. The strength of the derived conditions is demonstrated by different examples, including squeezed states, lossy single-photon states, and even coherent states.

Single-photon sources: Approaching the ideal through multiplexing

We review the rapid recent progress in single-photon sources based on multiplexing multiple probabilistic photon-creation events. Such multiplexing allows higher single-photon probabilities and lower contamination from higher-order photon states. We study the requirements for multiplexed sources and compare various approaches to multiplexing using different degrees of freedom.

Detector-Agnostic Phase-Space Distributions

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.

Critical Response of a Quantum van der Pol Oscillator

Classical dynamical systems close to a critical point are known to act as efficient sensors due to a strongly nonlinear response. We explore such systems in the quantum regime by modeling a quantum version of a driven van der Pol oscillator. We find the classical response survives down to one excitation quantum. At very weak drives, genuine quantum features arise, including diverging and negative susceptibilities. Further, the linear response is greatly enhanced by using a strong incoherent pump. These results are largely generic and can be probed in current experimental platforms suited for quantum sensing.

Measurement of Motion beyond the Quantum Limit by Transient Amplification

Through simultaneous but unequal electromechanical amplification and cooling processes, we create a method for a nearly noiseless pulsed measurement of mechanical motion. We use transient electromechanical amplification (TEA) to monitor a single motional quadrature with a total added noise -8.5±2.0  dB relative to the zero-point motion of the oscillator, or equivalently the quantum limit for simultaneous measurement of both mechanical quadratures. We demonstrate that TEA can be used to resolve fine structure in the phase space of a mechanical oscillator by tomographically reconstructing the density matrix of a squeezed state of motion. Without any inference or subtraction of noise, we directly observe a squeezed variance 2.8±0.3  dB below the oscillator's zero-point motion.

Benchmarking Maximum-Likelihood State Estimation with an Entangled Two-Cavity State

The efficient quantum state reconstruction algorithm described by Six et al. [Phys. Rev. A 93, 012109 (2016)PLRAAN2469-992610.1103/PhysRevA.93.012109] is experimentally implemented on the nonlocal state of two microwave cavities entangled by a circular Rydberg atom. We use information provided by long sequences of measurements performed by resonant and dispersive probe atoms over timescales involving the system decoherence. Moreover, we benefit from the consolidation, in the same reconstruction, of different measurement protocols providing complementary information. Finally, we obtain realistic error bars for the matrix elements of the reconstructed density operator. These results demonstrate the pertinence and precision of the method, directly applicable to any complex quantum system.

Faithful Hierarchy of Genuine n-Photon Quantum Non-Gaussian Light

Light is an essential tool for connections between quantum devices and for diagnostic processes in quantum technology. Both applications deal with advanced nonclassical states beyond Gaussian coherent and squeezed states. Current development requires a loss-tolerant diagnostic of such nonclassical aspects. We propose and experimentally verify a faithful hierarchy of genuine n-photon quantum non-Gaussian light. We conclusively witnessed three-photon quantum non-Gaussian light in the experiment. Measured data demonstrate a direct applicability of the hierarchy for a large class of real states.

Quantum fidelity measures for mixed states

Applications of quantum technology often require fidelities to quantify performance. These provide a fundamental yardstick for the comparison of two quantum states. While this is straightforward in the case of pure states, it is much more subtle for the more general case of mixed quantum states often found in practice. A large number of different proposals exist. In this review, we summarize the required properties of a quantum fidelity measure, and compare them, to determine which properties each of the different measures has. We show that there are large classes of measures that satisfy all the required properties of a fidelity measure, just as there are many norms of Hilbert space operators, and many measures of entropy. We compare these fidelities, with detailed proofs of their properties. We also summarize briefly the applications of these measures in teleportation, quantum memories and quantum computers, quantum communications, and quantum phase-space simulations.

Quantum Storage of Single-Photon and Two-Photon Fock States with an All-Optical Quantum Memory

Quantum memories are a crucial element toward efficient quantum protocols. In the continuous variables domain, such memories need to provide high fidelity with an efficiency set to one. Moreover, one needs to store complex quantum states exhibiting negative Wigner functions after storage. We report the storage of single- and two-photon Fock states in an all-optical quantum memory. The Wigner functions of these states show negativity after a storage time of several hundred nanoseconds. This is, to our knowledge, the first demonstration of the storage in the optical domain of non-Gaussian states with more than one photon, captured from an external source and characterized with homodyne detection.

Rigorous characterization method for photon-number statistics

Characterization of photon statistics of a light source is one of the most basic tools in quantum optics. Existing methods rely on an implicit and unverifiable assumption that the source never emits too many photons to stay within the measuring range of the detectors. As a result, they fail to fulfill the demand arising from emerging applications of quantum information such as quantum cryptography. Here, we propose a characterization method using a conventional Hanbury-Brown-Twiss setup to produce rigorous bounds on emission probabilities of low photon numbers from an unknown source. As an application, we show that our characterization method can be used for a practical light source in a quantum key distribution protocol to forsake the commonly used a priori assumption without significant change in efficiency. Our versatile and flexible formula for rigorous bounds will make an essential contribution to the optics toolbox in the era of quantum information.

High production rate of single-photon and two-photon Fock states for quantum state engineering

We report the implementation of a high-rate source of single- and two-photon states. By combining the advantages of short pulses and cavities, heralding rates as high as 200 kHz have been obtained for the single photons, as well as 250 Hz for the two-photon states. In this setup, homodyne measurements are conditioned by the heralding of the quantum states thanks to the introduction of a low-loss optical delay line in the heralded states path. This enables the detection of most of the heralded events, and fidelities reaching 68.5% (91% with correction for detection efficiency) and 50.4% (85% with correction) were obtained for the single- and two-photon states, respectively. Such high rates and fidelities in the generation of elementary Fock states may open the path for the production of complex quantum states.

Incomplete Detection of Nonclassical Phase-Space Distributions

We implement the direct sampling of negative phase-space functions via unbalanced homodyne measurement using click-counting detectors. The negativities significantly certify nonclassical light in the high-loss regime using a small number of detectors which cannot resolve individual photons. We apply our method to heralded single-photon states and experimentally demonstrate the most significant certification of nonclassicality for only two detection bins. By contrast, the frequently applied Wigner function fails to directly indicate such quantum characteristics for the quantum efficiencies present in our setup without applying additional reconstruction algorithms. Therefore, we realize a robust and reliable approach to characterize nonclassical light in phase space under realistic conditions.

Cross-Kerr Nonlinearity for Phonon Counting

State measurement of a quantum harmonic oscillator is essential in quantum optics and quantum information processing. In a system of trapped ions, we experimentally demonstrate the projective measurement of the state of the ions' motional mode via an effective cross-Kerr coupling to another motional mode. This coupling is induced by the intrinsic nonlinearity of the Coulomb interaction between the ions. We spectroscopically resolve the frequency shift of the motional sideband of the first mode due to the presence of single phonons in the second mode and use it to reconstruct the phonon number distribution of the second mode.

Pulsed quantum continuous-variable optoelectromechanical transducer

We propose a setup allowing to entangle two directly non-interacting radiation modes applying four sequential pulsed quantum resonant interactions with a noisy vibrational mode of a mechanical oscillator which plays the role of the mediator. We analyze Gaussian entanglement of the radiation modes generated by the transducer and confirm that the noisy mechanical mode can mediate generation of entanglement. The entanglement, however, is limited if the interaction gains are not individually optimized. We prove the robustness of the transducer to optical losses and the influence of the mechanical bath and propose the ways to achieve maximal performance through the individual optimization.

Controlling quantum interference in phase space with amplitude

We experimentally show a quantum interference in phase space by interrogating photon number probabilities (n = 2, 3, and 4) of a displaced squeezed state, which is generated by an optical parametric amplifier and whose displacement is controlled by amplitude of injected coherent light. It is found that the probabilities exhibit oscillations of interference effect depending upon the amplitude of the controlling light field. This phenomenon is attributed to quantum interference in phase space and indicates the capability of controlling quantum interference using amplitude. This remarkably contrasts with the oscillations of interference effects being usually controlled by relative phase in classical optics.

Multi-copy quantifiers for single-photon states

Single-photon states are basic resources for hybrid quantum technology with non-Gaussian states of light. Accelerating quantum technology is already able to produce high-quality single-photon states. These states can be used for hybrid quantum information processing, based on a nonclassical phase-space interference represented by negativity of a Wigner function. Therefore, new quantifiers, capable of evaluating such high-quality single-photon states, are required. We propose and analyze quantifiers which process multiple estimates of single-photon state’s statistics. The quantifiers simulate basic capability of single photons to conditionally bunch into a single mode and form a Fock state. This state exhibits complex nonclassical phase-space interference effects making its Wigner function negative in multiple areas. The quantifiers directly evaluate a presence of the multiple negativities corresponding to the Fock state. We verify applicability of the quantifiers by using them to single-photon states from recent experiments. The quantifiers can be further extended to also test indistinguishability of single-photon states. It allows to verify quantum interference of light from single-photon emitters more sensitively than in the traditional Hong-Ou-Mandel test. Besides quantum optics, the multi-copy quantifiers can be also applied to experiments with atomic memories and mechanical oscillators.

Quantum Teleportation Between Discrete and Continuous Encodings of an Optical Qubit

The transfer of quantum information between physical systems of a different nature is a central matter in quantum technologies. Particularly challenging is the transfer between discrete and continuous degrees of freedom of various harmonic oscillator systems. Here we implement a protocol for teleporting a continuous-variable optical qubit, encoded by means of low-amplitude coherent states, onto a discrete-variable, single-rail qubit-a superposition of the vacuum and single-photon optical states-via a hybrid entangled resource. We test our protocol on a one-dimensional manifold of the input qubit space and demonstrate the mapping onto the equator of the teleported qubit's Bloch sphere with an average fidelity of 0.83±0.04. Our work opens up the way to the wide application of quantum information processing techniques where discrete- and continuous-variable encodings are combined within the same optical circuit.

Revealing nonclassicality beyond Gaussian states via a single marginal distribution

A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum-state tomography. We theoretically propose and experimentally demonstrate a general framework to manifest nonclassicality by observing a single marginal distribution only, which provides a unique insight into nonclassicality and a practical applicability to various quantum systems. Our approach maps the 1D marginal distribution into a factorized 2D distribution by multiplying the measured distribution or the vacuum-state distribution along an orthogonal axis. The resulting fictitious Wigner function becomes unphysical only for a nonclassical state; thus the negativity of the corresponding density operator provides evidence of nonclassicality. Furthermore, the negativity measured this way yields a lower bound for entanglement potential-a measure of entanglement generated using a nonclassical state with a beam-splitter setting that is a prototypical model to produce continuous-variable (CV) entangled states. Our approach detects both Gaussian and non-Gaussian nonclassical states in a reliable and efficient manner. Remarkably, it works regardless of measurement axis for all non-Gaussian states in finite-dimensional Fock space of any size, also extending to infinite-dimensional states of experimental relevance for CV quantum informatics. We experimentally illustrate the power of our criterion for motional states of a trapped ion, confirming their nonclassicality in a measurement-axis-independent manner. We also address an extension of our approach combined with phase-shift operations, which leads to a stronger test of nonclassicality, that is, detection of genuine non-Gaussianity under a CV measurement.

High-efficiency WSi superconducting nanowire single-photon detectors for quantum state engineering in the near infrared

We report on high-efficiency superconducting nanowire single-photon detectors based on amorphous tungsten silicide and optimized at 1064 nm. At an operating temperature of 1.8 K, we demonstrated a 93% system detection efficiency at this wavelength with a dark noise of a few counts per second. Combined with cavity-enhanced spontaneous parametric downconversion, this fiber-coupled detector enabled us to generate narrowband single photons with a heralding efficiency greater than 90% and a high spectral brightness of 0.6×10⁴ photons/(s·mW·MHz). Beyond single-photon generation at large rate, such high-efficiency detectors open the path to efficient multiple-photon heralding and complex quantum state engineering.

Loss-tolerant state engineering for quantum-enhanced metrology via the reverse Hong-Ou-Mandel effect

Highly entangled quantum states, shared by remote parties, are vital for quantum communications and metrology. Particularly promising are the N00N states-entangled N-photon wavepackets delocalized between two different locations-which outperform coherent states in measurement sensitivity. However, these states are notoriously vulnerable to losses, making them difficult to both share them between remote locations and recombine in order to exploit interference effects. Here we address this challenge by utilizing the reverse Hong-Ou-Mandel effect to prepare a high-fidelity two-photon N00N state shared between two parties connected by a lossy optical medium. We measure the prepared state by two-mode homodyne tomography, thereby demonstrating that the enhanced phase sensitivity can be exploited without recombining the two parts of the N00N state. Finally, we demonstrate the application of our method to remotely prepare superpositions of coherent states, known as Schrödinger's cat states.

Real-Time Quadrature Measurement of a Single-Photon Wave Packet with Continuous Temporal-Mode Matching

Real-time controls based on quantum measurements are powerful tools for various quantum protocols. However, their experimental realization has been limited by mode mismatch between the temporal mode of quadrature measurement and that heralded by photon detection. Here, we demonstrate real-time quadrature measurement of a single-photon wave packet induced by photon detection by utilizing continuous temporal-mode matching between homodyne detection and an exponentially rising temporal mode. Single photons in exponentially rising modes are also expected to be useful resources for interactions with other quantum systems.

Synchronization of optical photons for quantum information processing

A fundamental element of quantum information processing with photonic qubits is the nonclassical quantum interference between two photons when they bunch together via the Hong-Ou-Mandel (HOM) effect. Ultimately, many such photons must be processed in complex interferometric networks. For this purpose, it is essential to synchronize the arrival times of the flying photons and to keep their purities high. On the basis of the recent experimental success of single-photon storage with high purity, we demonstrate for the first time the HOM interference of two heralded, nearly pure optical photons synchronized through two independent quantum memories. Controlled storage times of up to 1.8 μs for about 90 events per second were achieved with purities that were sufficiently high for a negative Wigner function confirmed with homodyne measurements.

Nonclassical light revealed by the joint statistics of simultaneous measurements

Nonclassicality cannot be a single-observable property, since the statistics of any quantum observable is compatible with classical physics. We develop a general procedure to reveal nonclassical behavior of light states from the joint statistics arising in the practical measurement of multiple observables. Beside embracing previous approaches, this protocol can disclose nonclassical features for standard examples of classical-like behavior, such as SU(2) and Glauber coherent states. When combined with other criteria, this would imply that every light state is nonclassical.

Wigner Distribution of Twisted Photons

We present the first experimental characterization of the azimuthal Wigner distribution of a photon. Our protocol fully characterizes the transverse structure of a photon in conjugate bases of orbital angular momentum (OAM) and azimuthal angle. We provide a test of our protocol by characterizing pure superpositions and incoherent mixtures of OAM modes in a seven-dimensional space. The time required for performing measurements in our scheme scales only linearly with the dimension size of the state under investigation. This time scaling makes our technique suitable for quantum information applications involving a large number of OAM states.

Double-heralded generation of two-photon-states by spontaneous four-wave-mixing in the presence of noise

We present an experimental method for creating and verifying photon-number states created by non-degenerate, third-order nonlinear-optical photon-pair sources. By using spatially multiplexed, thresholding single-photon detectors and inverting a conditional probability matrix, we determine the photon-number probabilities created through heralded spontaneous four-wave-mixing. The deleterious effects of noise photons on reliable heralding are investigated and shown to degrade the conditional preparation of two-photon number states more than they degrade conditional single-photon states. We derive the equivalence between the presence of unwanted noise in the herald channel and loss in the signal channel of heralded experiments. A procedure for characterizing the noise-photon contributions, and a means of estimating the herald noise-free photon-number distribution is demonstrated.

Universal Continuous-Variable State Orthogonalizer and Qubit Generator

We experimentally demonstrate a universal strategy for producing a quantum state that is orthogonal to an arbitrary, infinite-dimensional, pure input one, even if only a limited amount of information about the latter is available. Arbitrary coherent superpositions of the two mutually orthogonal states are then produced by a simple change in the experimental parameters. We use input coherent states of light to illustrate two variations of the method. However, we show that the scheme works equally well for arbitrary input fields and constitutes a universal procedure, which may thus prove a useful building block for quantum state engineering and quantum information processing with continuous-variable qubits.

Direct sampling of electric-field vacuum fluctuations

The ground state of quantum systems is characterized by zero-point motion. This motion, in the form of vacuum fluctuations, is generally considered to be an elusive phenomenon that manifests itself only indirectly. Here, we report direct detection of the vacuum fluctuations of electromagnetic radiation in free space. The ground-state electric-field variance is inversely proportional to the four-dimensional space-time volume, which we sampled electro-optically with tightly focused laser pulses lasting a few femtoseconds. Subcycle temporal readout and nonlinear coupling far from resonance provide signals from purely virtual photons without amplification. Our findings enable an extreme time-domain approach to quantum physics, with nondestructive access to the quantum state of light. Operating at multiterahertz frequencies, such techniques might also allow time-resolved studies of intrinsic fluctuations of elementary excitations in condensed matter.

Interaction-free measurements by quantum Zeno stabilization of ultracold atoms

Quantum mechanics predicts that our physical reality is influenced by events that can potentially happen but factually do not occur. Interaction-free measurements (IFMs) exploit this counterintuitive influence to detect the presence of an object without requiring any interaction with it. Here we propose and realize an IFM concept based on an unstable many-particle system. In our experiments, we employ an ultracold gas in an unstable spin configuration, which can undergo a rapid decay. The object—realized by a laser beam—prevents this decay because of the indirect quantum Zeno effect and thus, its presence can be detected without interacting with a single atom. Contrary to existing proposals, our IFM does not require single-particle sources and is only weakly affected by losses and decoherence. We demonstrate confidence levels of 90%, well beyond previous optical experiments.

The inherent strangeness of quantum mechanics means it is possible to detect objects using single-quantum particles even if they do not interact directly. Peise et al. realize such an ‘interaction-free measurement' by exploiting the quantum Zeno effect in a BEC, obviating the need for single-particle sources.

Measuring the biphoton temporal wave function with polarization-dependent and time-resolved two-photon interference

We propose and demonstrate an approach to measuring the biphoton temporal wave function with polarization-dependent and time-resolved two-photon interference. Through six sets of two-photon interference measurements projected onto different polarization subspaces, we can reconstruct the amplitude and phase functions of the biphoton temporal waveform. For the first time, we apply this technique to experimentally determine the temporal quantum states of the narrow-band biphotons generated from the spontaneous four-wave mixing in cold atoms.

Quantum non-Gaussian Depth of Single-Photon States

We introduce and experimentally explore the concept of the non-Gaussian depth of single-photon states with a positive Wigner function. The depth measures the robustness of a single-photon state against optical losses. The directly witnessed quantum non-Gaussianity withstands significant attenuation, exhibiting a depth of 18 dB, while the nonclassicality remains unchanged. Quantum non-Gaussian depth is an experimentally approachable quantity that is much more robust than the negativity of the Wigner function. Furthermore, we use it to reveal significant differences between otherwise strongly nonclassical single-photon sources.

Atomic filtering for hybrid continuous-variable/discrete-variable quantum optics

We demonstrate atomic filtering of frequency-degenerate photon pairs from a sub-threshold optical parametric oscillator (OPO). The filter, a modified Faraday anomalous dispersion optical filter (FADOF), achieves 70% peak transmission simultaneous with 57 dB out-of-band rejection and a 445 MHz transmission bandwidth. When applied to the OPO output, only the degenerate mode, containing one-mode squeezed vacuum, falls in the filter pass-band; all other modes are strongly suppressed. The high transmission preserves non-classical continuous-variable features, e.g. squeezing or non-gaussianity, while the high spectral purity allows reliable discrete-variable detection and heralding. Correlation and atomic absorption measurements indicate a spectral purity of 96% for the individual photons, and 98% for the photon pairs. These capabilities will enable generation of atom-resonant hybrid states, e.g. "Schrödinger kittens" obtained by photon subtraction from squeezed vacuum, making these exotic states available for quantum networking and atomic quantum metrology applications.

Quantum non-Gaussianity of frequency up-converted single photons

Nonclassical states of light are an important resource in today's quantum communication and metrology protocols. Quantum up-conversion of nonclassical states is a promising approach to overcome frequency differences between disparate subsystems within a quantum information network. Here, we present the generation of heralded narrowband single photons at 1550 nm via cavity enhanced spontaneous parametric down-conversion (SPDC) and their subsequent up-conversion to 532 nm. Quantum non-Gaussianity (QNG), which is an important feature for applications in quantum information science, was experimentally certified for the first time in frequency up-converted states.

Local mapping of detector response for reliable quantum state estimation

Improved measurement techniques are central to technological development and foundational scientific exploration. Quantum physics relies on detectors sensitive to non-classical features of systems, enabling precise tests of physical laws and quantum-enhanced technologies including precision measurement and secure communications. Accurate detector response calibration for quantum-scale inputs is key to future research and development in these cognate areas. To address this requirement, quantum detector tomography has been recently introduced. However, this technique becomes increasingly challenging as the complexity of the detector response and input space grow in a number of measurement outcomes and required probe states, leading to further demands on experiments and data analysis. Here we present an experimental implementation of a versatile, alternative characterization technique to address many-outcome quantum detectors that limits the input calibration region and does not involve numerical post processing. To demonstrate the applicability of this approach, the calibrated detector is subsequently used to estimate non-classical photon number states.

The successful realization of quantum information protocols relies on characterization of quantum states and measurements. Here, Cooper et al. experimentally demonstrate a technique enabling calibration of a detector with a sizeable number of outcomes using a limited amount of resources.