The second-order Talbot effect is analyzed for a periodic object illuminated by entangled photon pairs in both the quantum imaging and quantum lithography configurations. The Klyshko picture is applied to describe the quantum imaging scheme, in which self-images of the object that may or may not be magnified can be observed nonlocally in the photon coincidences but not in the singles count rate. In the quantum lithography setup, we find that the second-order Talbot length is half that of the classical first-order case, thus the resolution may be improved by a factor of two.
Time-frequency Talbot effect as Clifford operations on entangled time-frequency GKP states
Télécom Paris-LTCI, Institut Polytechnique de Paris（巴黎电信学院-LTCI，巴黎理工学院）；Université Côte d’Azur, CNRS, Institut de physique de Nice（蔚蓝海岸大学，法国国家科学研究中心，尼斯物理研究所）
The Talbot effect in quantum physics is known to produce intricate patterns in the probability distribution of a particle, known as "quantum carpets", corresponding to the revival and replication of the initial wave function. Recently, it was shown that one can encode a $D$-level qudit, in such a way that the Talbot effect can be used to process the $D$-dimensional quantum information [Far\'ıas et al, PRA (2015)]. Here we introduce a scheme to produce free-propagating "entangled quantum carpets" with pairs of photons produced by spontaneous parametric down-conversion. First we introduce an opt…
The self-imaging, or Talbot Effect, that occurs with the propagation of periodically structured waves has enabled several unique applications in optical metrology, image processing, data transmission, and matter-wave interferometry. In this work, we report on the first demonstration of a Talbot Effect with single photons prepared in a lattice of orbital angular momentum (OAM) states. We observe that upon propagation, the wavefronts of the single photons manifest self-imaging whereby the OAM lattice intensity profile is recovered. Furthermore, we show that the intensity at fractional Talbot dis…
Single photon interference due to passage through a periodic grating is considered in a novel proposal for processing D-dimensional quantum systems (quDits) encoded in the spatial degrees of freedom of light. We show that free space propagation naturally implements basic single quDit gates by means of the Talbot effect: an intricate time-space carpet of light in the near field diffraction regime. Adding a diagonal phase gate, we show that a complete set of single quDit gates can be implemented. We then introduce a spatially-dependent beam splitter that allows implementation of controlled opera…
Recent theoretical investigations on tomographic entanglement indicators have showcased the advantages of the tomographic approach in the context of continuous-variable (CV), spin and hybrid quantum systems. Direct estimation of entanglement using experimental data from the IBM quantum computing platform and NMR experiments have also been carried out in earlier work. A similar investigation in the context of CV systems is necessary to fully assess the utility of our tomographic approach. In this paper, we highlight the advantages of our approach in the context of experiments reported in the li…
Wave propagation on the surface of cylinders exhibits interferometric self imaging, much like the Talbot effect in the near-field diffraction at periodic gratings. We report the experimental observation of the cylindrical Talbot carpet in weakly-guiding ring-core fibers for classical light fields. We further show that the ring-core fiber acts as a high-order optical beamsplitter for single photons, whose output can be controlled by the relative phase between the input light fields. By also demonstrating high-quality two-photon interference between indistinguishable photons sent into the ring-c…
We demonstrate the quantum Talbot effect using pairs of single photons produced by parametric down conversion. In contrast to the previous works, we use a programmable spatial light modulator to behave as a diffraction grating. Thus, the investigation of the Talbot diffraction patterns under the variation of grating structure can be easily performed. The influence of spectral bandwidth of the down-converted photons on the diffraction pattern is also investigated. A theoretical model based on the wave nature of photons is presented to explain the Talbot diffraction pattern under varying conditi…
Recent progress in matter-wave interferometry aims to directly probe the quantum properties of matter on ever increasing scales. However, in order to perform interferometric experiments with massive mesoscopic objects, taking into account the constraints on the experimental set-ups, the point-like particle approximation needs to be cast aside. In this work, we consider near-field interferometry based on the Talbot effects with a single optical grating for large spherical particles beyond the point-particle approximation. We account for the suppression of the coherent grating effect and, at the…
We show that complex PT-symmetric photonic lattices can lead to a new class of self-imaging Talbot effects. For this to occur, we find that the input field pattern, has to respect specific periodicities which are dictated by the symmetries of the system. While at the spontaneous PT-symmetry breaking point, the image revivals occur at Talbot lengths governed by the characteristics of the passive lattice, at the exact phase it depends on the gain and loss parameter thus allowing one to control the imaging process.
We present a scheme to produce an entangled four-photon state from two pairs of entangled two-photon states. Such entangled four-photon states are equivalent to the quantum state of two maximally entangled spin-1 particles. The scheme can also be generated to prepare an entangled 2N-photon state from N pairs of entangled two-photon states. Such multi-photon states play a crucial role in fundamental tests of quantum mechanics versus local realism and in many quantum information and quantum computation schemes.
A scheme to distinguish entangled two-photon-polarization states (ETP) from two independent entangled one-photon-polarization states (EOP) is proposed. Using this scheme, the experimental generation of ETP by parametric down-conversion is confirmed through the anti-correlations between three orthogonal two-photon-polarization states. The estimated fraction of ETP among the correlated photon pairs is 37% in the present experimental setup.
The generation and storage of entangled photons play important roles in quantum information technique. Spontaneous Raman scattering (SRS) in atomic ensembles provides a promising method to generate entangled photons capable of storage. In the past experiments, a spin-wave-photon entangled state is produced via SRS in an atomic ensemble, with which a pair of entangled photons is obtained. Here, we report a scheme of simultaneously generating two spin-wave-photon entangled states in an atomic ensemble by collecting Stokes photons at two different directions. Based on the obtained two atom-photon…
We extend entangled coincidence (ghost) imaging to fluorescent samples. Given the entangled photon correlation, one photon of the pair carries information on where the other photon has been absorbed and has produced fluorescence in a sample. Fluorescent molecules serve as ''detectors breaking'' the entanglement.
Entangled two-photon spectroscopy is expected to provide advantages compared with classical protocols. It is achieved by coherently controlling the spectral properties of energy-entangled photons. We present here an experimental setup that allows the spectral shaping of entangled photons with high resolution. We evaluate its performances by detecting sum frequency generation in a non-linear crystal. The efficiency of the process is compared when performed with classical or entangled light.
The general concept of entangled photon holes is based on a correlated absence of photon pairs in an otherwise constant optical background. Here we consider the specialized case when this background is confined to two well-defined time bins, which allows the formation of time-bin entangled photon holes. We show that when the typical coherent state background is replaced by a true single-photon (Fock state) background, the basic time-bin entangled photon-hole state becomes equivalent to one of the time-bin entangled photon-pair states. We experimentally demonstrate these ideas using a parametri…
We present a concentration and purification scheme for nonmaximally entangled pure and mixed porization entangled state. We firstly show that two distant parties Alice and Bob first start with two shared but less entangled photon pure states to produce a four photon GHZ state, and then perform a 45 polarization measurement onto one of the two photons at each location such that the remaining two photon are projected onto a maximally entangled state. We further show the scheme also can be used to purify a class of mixed polarization-entangled state.
In addition to photon pairs entangled in polarization or other variables, quantum mechanics also allows optical beams that are entangled through the absence of the photons themselves. These correlated absences, or ``entangled photon holes'', can lead to counter-intuitive nonlocal effects analogous to those of the more familiar entangled photon pairs. Here we report an experimental observation of photon holes generated using quantum interference effects to suppress the probability that two photons in a weak laser pulse will separate at an optical beam splitter.
I show that the photon pairs used in experimental tests of quantum non-locality based on Bell's theorem are not in the entangled quantum state. The correct quantum state of the ``entangled'' photon pairs is suggested. Two experiments for testing this quantum state are proposed.
The quantum interference of entangled photons forms a key phenomenon underlying various quantum-optical technologies. It is known that the quantum interference patterns of entangled photon pairs can be reconstructed classically by the time-reversal method; however, the time-reversal method has been applied only to time-frequency-entangled two-photon systems in previous experiments. Here, for the first time, we apply the time-reversal method to the position-wavevector-entangled two-photon systems: the two-photon Young interferometer and the two-photon beam focusing system. We experimentally dem…
We experimentally study entangled two-photon absorption in Rhodamine 6G as a function of the spatial properties of a high flux of broadband entangled photon pairs. We first demonstrate a key signature dependence of the entangled two-photon absorption rate on the type of entangled pair flux attenuation: linear, when the laser pump power is attenuated, and quadratic, when the pair flux itself experiences linear loss. We then perform a fluorescence-based Z-scan measurement to study the influence of beam waist size on the entangled two-photon absorption process and compare this to classical single…
An experimental scheme for concentrating entanglement in partially entangled photon pairs is proposed. In this scheme, two separated parties obtain one maximally entangled photon pair from previously shared two partially entangled photon pairs by local operations and classical communication. A practical realization of the proposed scheme is discussed, which uses imperfect photon detectors and spontaneous parametric down-conversion as a photon source. This scheme also works for purifying a class of mixed states.
We present an scheme to generate entangled state between two traveling modes for fixed number of photon, which is based on beam splitter transformation and conditional zero photon counters.
We discuss the possibility of synchronising two atomic clocks exchanging entangled photon pairs through a quantum channel. A proposal for implementing practically such a scheme is discussed.
We report on the the experimental realization of hyper-entangled two photon states, entangled in polarization and momentum. These states are produced by a high brilliance parametric source of entangled photon pairs with peculiar characteristics of flexibility in terms of state generation. The quality of the entanglement in the two degrees of freedom has been tested by multimode Hong-Ou-Mandel interferometry.
Entangled photons are a crucial resource for quantum communication and linear optical quantum computation. Unfortunately, the applicability of many photon-based schemes is limited due to the stochastic character of the photon sources. Therefore, a worldwide effort has focused in overcoming the limitation of probabilistic emission by generating two-photon entangled states conditioned on the detection of auxiliary photons. Here we present the first heralded generation of photon states that are maximally entangled in polarization with linear optics and standard photon detection from spontaneous p…
Entangled photons are crucial for quantum technologies, but generating arbitrary entangled photon states deterministically, efficiently, and with high fidelity remains a challenge. Here, we demonstrate how hybridization and dipole-dipole interactions -- potentially simultaneously available in colloidal quantum dots and molecular aggregates -- leveraged in conjunction can couple simple, well understood emitters into composite emitters with flexible control over the level structure. We show that cascade decay through carefully designed level structures can result in emission of frequency-entangl…
We construct an entangled photon polarimeter capable of monitoring a two-qubit quantum state in real time. Using this polarimeter, we record a nine frames-per-second video of a two-photon state's transition from separability to entanglement.
We present detailed instructions for constructing and operating an apparatus to produce and detect polarization-entangled photons. The source operates by type-I spontaneous parametric downconversion in a two-crystal geometry. Photons are detected in coincidence by single-photon counting modules and show strong angular and polarization correlations. We observe more than 100 entangled photon pairs per second. A test of a Bell inequality can be performed in an afternoon.
We present a feasible scheme to produce a polarization-entangled photon states $\frac{1}{\sqrt{2}}(|H>|V>+|V>|H>)$ in a controllable way. This scheme requires single-photon sources, linear optical elements and photon detectors. It generates the entanglement of spatially separated photons. The interaction takes place in the photon detectors. We also show that the same idea can be used to produce the entangled $N$-photon state $\frac{1}{\sqrt{2}}(|0,N>+|N,0>)$
We propose a simple scheme to produce the polarization entangled photon pairs without the type II phase match. The same scheme can also be used to produce the macroscopic entangled photon states in both photon number space and the polarization space(A. Lamas-Linares, J.C. Howell and D. Bouwmeester, Nature, 412887(2001)). Advantages and applications of our scheme in quantum key distribution are discussed.
We report on a method for optimizing the collection of entangled photon pairs in type-II parametric fluorescence. With this technique, we detected 360000 polarization-entangled photon pairs per second in the near-IR region in single-mode optical fibers. The entanglement of the photon pairs was verified by measuring polarization correlations in different bases of at least 96%.
We consider ramifications of the use of high speed light modulators to questions of correlation and measurement of time-energy entangled photons. Using phase modulators, we find that temporal modulation of one photon of an entangled pair, as measured by correlation in the frequency domain, may be negated or enhanced by modulation of the second photon. Using amplitude modulators we describe a Fourier technique for measurement of biphoton wave functions with slow detectors.
When basic tools of quantum information are applied to the quantum tomography data presented in Nature 439, 179 (2006), none of their devices appears to be a source of entangled photons.
Using the process of cavity-enhanced spontaneous parametric down-conversion (SPDC), we generate a narrow-band polarization-entangled photon pair resonant on the rubidium (Rb) D1 line (795 nm). The degenerate single-mode photon pair is selected by multiple temperature controlled etalons. The linewidth of generated polarization-entangled photon pairs is 15 MHz which matches the typical atomic memory bandwidth. The measured Bell parameter for the polarization-entangled photons S=2.73+-0.04 which violates the Bell-CHSH inequality by ~18 standard deviations. The presented entangled photon pair sour…
In this paper, an experiment of quantum diffraction of position-momentum entangled photons from a straight sharp edge is presented. Path of a single photon of an entangled pair is partially blocked by a sharp edge whereas the other photon is detected at a stationary location without revealing the which-path information of the other photon. Quantum diffraction pattern of the sharp edge is revealed only in the correlated conditional detection of spatially separated photons and no diffraction pattern is formed in local detections of individual photons. Theoretical analysis of the quantum diffract…
A novel method for preparation of a single photon in temporally-delocalized entangled modes is proposed and analyzed. We show that two single-photon pulses propagating in a driven nonabsorbing medium with different group velocities are temporally split under parametric interaction into well-separated pulses. In consequence, the single-photon "time-bin-entangled" states are generated with a programmable entanglement easily controlled by driving field intensity. The experimental study of nonclassical features and nonlocality of generated states by means of balanced homodyne tomography is discuss…
Remote state preparation (RSP) provides an indirect way of manipulating quantum information based on the nonlocal effect of quantum measurement. Although RSP has been demonstrated in recent years to remotely prepare multi-photon states, quantum measurement on the same number of photons was required, i.e., to prepare N-photon states via RSP, quantum measurement on the other N-photons was required, hence significantly limiting practicality and applicability of RSP. Here we report the first experimental demonstration of remote preparation of three-photon entangled states by measuring only a singl…
The properties of an entangled two-photon state antisymmetric in frequencies are studied. At a beam-splitter, two entangled photons are perfectly anti-correlated. In addition, they cannot be detected at the same time instant despite the fact that their detection times are confined to a narrow time window, i.e. they are temporally anti-bunched. Using nonlinear photonic-band-gap structures made of GaN/AlN, two schemes for generating such states are described.
Multi-dimensional entangled states have been proven to be more powerful in some quantum information process. In this paper, down-converted photons from spontaneous parametric down conversion(SPDC) are used to engineer multi-dimensional entangled states. A kind of multi-degree multi-dimensional Greenberger-Horne-Zeilinger(GHZ) state can also be generated. The hyper-entangled photons, which are entangled in energy-time, polarization and orbital angular momentum (OAM), is proved to be useful to increase the dimension of systems and investigate higher-dimensional entangled states.
A photon source based on postselection from entangled photon pairs produced by parametric frequency down-conversion is suggested. Its ability to provide good approximations of single-photon states is examined. Application of this source in quantum cryptography for quantum key distribution is discussed. Advantages of the source compared to other currently used sources are clarified. Future prospects of the photon source are outlined.
We report measurements of time-frequency entangled photon pairs and heralded single photons at telecommunications wavelengths, generated using a periodically-poled, lithium niobate on insulator (LNOI) waveguide pumped optically by a diode laser. We achieve a high Coincidences-to-Accidentals Ratio (CAR) at high pair brightness, a low value of the conditional self-correlation function [$g^{(2)}$(0)], and high two-photon energy-time Franson interferometric visibility, which demonstrate the high quality of the entangled photon pairs and heralded single photons.
We present a feasible and efficient scheme, and its proof-of-principle demonstration, of creating entangled photon pairs in an event-ready way using only simple linear optical elements and single photons. The quality of entangled photon pair produced in our experiment is confirmed by a strict violation of Bell's inequality. This scheme and the associated experimental techniques present an important step toward linear optics quantum computation.
Using a linear optical elements and post-selection, we construct an entangled polarization state of three photons in the same spatial mode. This state is analogous to a ``photon-number path entangled state'' and can be used for super-resolving interferometry. Measuring a birefringent phase shift, we demonstrate two- and three-fold improvements in phase resolution.
The dependence of one- and two-photon characteristics of pulsed entangled two-photon fields generated in spontaneous parametric down-conversion on the pump-pulse properties (shape of the pump-pulse spectrum and its internal structure) is examined. It is shown that entangled two-photon fields with defined properties can be generated. A general relation between the spectra of the down-converted fields is established. As a special case interference of two partially overlapping pulsed two-photon fields is studied. Fourth-order interference pattern of entangled two-photon fields is investigated in …
In this work we generate two-photon hybrid entangled states (HES), where the polarization of one photon is entangled with the transverse spatial degree of freedom of the second photon. The photon pair is created by parametric down-conversion in a polarization-entangled state. A birefringent double-slit couples the polarization and spatial degrees of freedom of these photons and finally, suitable spatial and polarization projections generate the HES. We investigate some interesting aspects of the two-photon hybrid interference, and present this study in the context of the complementarity relati…
We show that polarization entangled photons at x-ray energies can be generated via spontaneous parametric down conversion. Each of the four Bell states can be generated by choosing the angle of incidence and polarization of the pumping beam.
Entangled photon pairs are key to many novel applications in quantum technologies. Semiconductor quantum dots can be used as sources of on-demand, highly entangled photons. The fidelity to a fixed maximally entangled state is limited by the excitonic fine-structure splitting. This work demonstrates that, even if this splitting is absent, the degree of entanglement cannot reach unity when the excitation pulse in a two-photon resonance scheme has a finite duration. The degradation of the entanglement has its origin in a dynamically induced splitting of the exciton states caused by the laser puls…
We experimentally show that two-photon path-entangled states can be coherently manipulated by multi-mode interference in multi-mode waveguides. By measuring the output two-photon spatial correlation function versus the phase of the input state, we show that multi-mode waveguides perform as nearly-ideal multi-port beam splitters at the quantum level, creating a large variety of entangled and separable multi-path two-photon states.
We propose a feasible scheme to create $n$-party ($n\geq 2$) polarization-entangled photon states in a controllable way. The scheme requires only single-photon sources, single-photon quantum non-demolition measurement (SP-QNDM) and simple linear optical elements, usually with high perfections. The SP-QNDM acts as a non-destructive projection measurement onto the wanted entangled states and filters out the unwanted terms. Our scheme in fact realizes entanglement of non-interacting photons; the interaction occurs only implicitly in the optical elements and SP-QNDM. We also briefly consider purif…
We propose a scheme for the observation of micro-macro entanglement in photon number based on amplifying and de-amplifying a single-photon entangled state in combination with homodyne quantum state tomography. The created micro-macro entangled state, which exists between the amplification and de-amplification steps, is a superposition of two components with mean photon numbers that differ by approximately a factor of three. We show that for reasonable values of photon loss it should be possible to detect micro-macro photon-number entanglement where the macro system has a mean number of one hun…
We consider six-photon entangled state emitted from a single third-order parametric down-conversion process. In the regime of weak nonlinearities, we present a symmetry detector which is capable of analyzing the twin-beam six-photon symmetric states. By cascading the symmetry detectors, as an application, it is shown that one can purify the desired six-photon entangled state from an arbitrary twin-beam six-photon symmetric state. With linear optics we propose a fruitful scheme for exploring a class of multimode-photon entangled states from third-order parametric down-conversion process. Furthe…
A two-step quantum key distribution protocol using frequency and polarization doubly entangled photons is proposed. In this protocol, information is encoded by a unitary operation on each of the two doubly entangled photons and sent from Alice to Bob in two steps. State measurement device is designed. The security of the communication is analyzed.
We analyse the correlation properties of light in non-linear wave-guides and transmission lines, predict the position-momentum realization of EPR paradox for photon pairs in Kerr-type non-linear photonic circuits, and we show how two-photon entangled states can be generated and detected.
Entangled photons can be used to make measurements with an accuracy beyond that possible with classical light. While most implementations of quantum metrology have used states made up of a single colour of photons, we show that entangled states of two colours can show supersensitivity to optical phase and path-length by using a photonic crystal fibre source of photon pairs inside an interferometer. This setup is relatively simple and robust to experimental imperfections. We demonstrate sensitivity beyond the standard quantum limit and show super-resolved interference fringes using entangled st…
In this paper, we propose two protocols for generating super-resolving \textit{single-photon} path-entangled states from general maximally path-entangled N00N states. We also show that both protocols generate the desired state with different probabilities depending on the type of detectors being used. Such super-resolving single-photon path-entangled states preserve high resolving power but lack the requirement of a multi-photon absorbing resist, which makes this state a perfect candidate for quantum lithography.
Energy-time entangled photon holes are shown to be relatively insensitive to photon loss due to absorption by atoms whose coherence times are longer than the time delays typically employed in nonlocal interferometry (a fraction of a nanosecond). Roughly speaking, the excited atoms do not retain any significant "which-path" information regarding the time at which a photon was absorbed. High-intensity entangled photon holes can also be amplified under similar conditions. Decoherence does occur from losses at beam splitters, and these results show that photon loss cannot always be adequately mode…
We present a scheme to generate entangled photons using the NV centers in diamond. We show how the long-lived nuclear spin in diamond can mediate entanglement between multiple photons thereby increasing the length of entangled photon string. With the proposed scheme one could generate both n-photon GHZ and cluster states. We present an experimental scheme realizing the same and estimating the rate of entanglement generation both in the presence and absence of a cavity.
The mid-infrared (MIR) band entangled photon source is vital for the next generation of quantum communication, quantum imaging, and quantum sensing. However, the current entangled states are mainly prepared in visible or near-infrared bands. It is still lack of high-quality entangled photon sources in the MIR band. In this work, we optimize the poling sequence of lithium niobate to prepare two kinds of typical entangled states, the Hermit-Gaussian state and the comb-like entangled state at 3.2 $μ$m. We have also calculated the photon pair rates and estimated the effect of fabrication resolutio…
