Light is a perfect candidate to carry out quantum information for applications to quantum computation, communication and metrology. Information can be encoded using observables with discrete spectrum (or DV for discrete variable encoding) as well as with continuous spectrum observables (or CV for continuous variable encoding). One of the most used states to encode a CV qubit is the so called optical Schrödinger cat state, i.e. a superposition of two coherent states with the same amplitude and opposite phases. Approximation of these states, named Schrödinger kittens, have been generated in an heralded fashion by subtraction of one or two photons from a degenerate single mode squeezed vacuum states. Experiments have been conducted in continuous wave regime generally using optical parametric oscillators as well as in the pulsed regime. The quality of Schrödinger kittens generated with this strategy, however, suffers from the impurity of the squeezing in the wave-packet of the heralded state. In the CW regime, it is shown theoretically and experimentally that a narrowband filtering of the heralding photon increase the purity of thegenerated state. We extend this study so as to describe also the pulsed regime where the squeezed vacuum state is in general spectrally multimode. We calculate and numerically simulate the state generated when subtracting a photon from an arbitrary multimode pulsed squeezed vacuum state. Inaddition, we investigate its homodyne detection by considering an arbitrary pulsed local oscillator. The fidelity between the heralded state and a perfect single mode photon subtracted squeezed state decreases when the number of modes excited in the multimode squeezed vacuum increases. We show how to increase this fidelity by using a narrowband filter in the heralding path. This study quantifies the effect of spectral filtering on the quality of the generated state using a multimode approach that can be applied to a wide variety of situations. We believe that it will have a major impact on realisation of non-Gaussian states in an heralded fashion.
Light is a perfect candidate to carry out quantum information for applications to quantum computation, communication and metrology. Information can be encoded using observables with discrete spectrum (or DV for discrete variable encoding) as well as with continuous spectrum observables (or CV for continuous variable encoding). One of the most used states to encode a CV qubit is the so called optical Schrödinger cat state, i.e. a superposition of two coherent states with the same amplitude and opposite phases. Approximation of these states, named Schrödinger kittens, have been generated in an heralded fashion by subtraction of one or two photons from a degenerate single mode squeezed vacuum states. Experiments have been conducted in continuous wave regime generally using optical parametric oscillators as well as in the pulsed regime. The quality of Schrödinger kittens generated with this strategy, however, suffers from the impurity of the squeezing in the wave-packet of the heralded state. In the CW regime, it is shown theoretically and experimentally that a narrowband filtering of the heralding photon increase the purity of thegenerated state. We extend this study so as to describe also the pulsed regime where the squeezed vacuum state is in general spectrally multimode. We calculate and numerically simulate the state generated when subtracting a photon from an arbitrary multimode pulsed squeezed vacuum state. Inaddition, we investigate its homodyne detection by considering an arbitrary pulsed local oscillator. The fidelity between the heralded state and a perfect single mode photon subtracted squeezed state decreases when the number of modes excited in the multimode squeezed vacuum increases. We show how to increase this fidelity by using a narrowband filter in the heralding path. This study quantifies the effect of spectral filtering on the quality of the generated state using a multimode approach that can be applied to a wide variety of situations. We believe that it will have a major impact on realisation of non-Gaussian states in an heralded fashion.
Optical "Schrödinger cat" states, the non-classical superposition of two quasi-classical coherent states, serve as a basis for gedanken experiments testing quantum physics on mesoscopic scales and are increasingly recognized as a resource for quantum information processing. Here, we report the first experimental realization of optical "Schrödinger cats" by adding a photon to a squeezed vacuum state, so far only photon-subtraction protocols have been realized. Photon-addition gives us the advantage of using heralded signal photons as experimental triggers, and we can generate "Schrödinger cats" at rates exceeding 8.5×104 counts per second; at least one order of magnitude higher than all previously reported realizations. Wigner distributions with pronounced negative parts are demonstrated at down to -8.89 dB squeezing, even when the initial squeezed vacuum input state has low purity. Benchmarking against such a degraded squeezed input state we report a maximum fidelity of more than 80% with a maximum cat amplitude of ∣α∣≈1.66. Our experiment uses photon-addition from pairs, one of those photons is used for monitoring, giving us enhanced control; moreover the pair production rates are high and should allow for repeated application of photon-addition via repeat-stages.
Schrödinger cat state is an important non-classical state, and it can be used in quantum teleportation, quantum computation and quantum repeater. Schrödinger cat state is usually obtained experimentally by subtracting one photon from a squeezed-vacuum state. The fidelity between a photon-subtracted squeezed state and a cat state can be very high under suitable parameters. However, the quality of the generated state will be affected by the imperfect experimental conditions. In this paper, the effect of imperfect experimental conditions on the generation of cat state is theoretically calculated and analyzed. The input squeezed-vacuum field is represented by Weyl characteristic function, which contains the fluctuation variance of the squeezed and amplified noises. The characteristic function of generated state is obtained by using the transmission matrix of beam splitter and the measurement operator of single-photon detector. We acquire the expression of Wigner function of generated state by the Fourier transform of the Weyl characteristic function. The fidelity is calculated by using the formula F=1/π∫d2ζC1(ζ)C|cat->(ζ), where C1(ζ) and C|cat->(ζ) represent Weyl characteristic function of the generated state and the Schrodinger cat state, respectively. The imperfection of the input squeezed state, the imperfection of the single-photon detector and the loss of the balanced homodyne detection are included in our theoretical model. We calculate the Wigner function at the phase-space origin W(0) and the fidelity in terms of different experimental parameters. The results show that the fidelity and negativity of W(0) decrease with squeezing purity decreasing. A pure squeezed-vacuum state is composed of even photon number states. In the case of impure squeezing, some odd photon number states appear in the photon number distribution. After subtracting one photon from the impure squeezing state, the generated state consists of not only odd photon number state but also even photon states, which degrades the fidelity of the generated state. The lower squeezing purity is required to meet the demand for W(0)<0 under the condition of higher squeezing degree. There is an optimal squeezing degree to maximize the fidelity of generated state with impure squeezing. The use of inefficient on-ff single-photon detector and the loss of the balanced homodyne detection will further reduce the fidelity of the generated state. Under the practical experimental condition:squeezing degree s=-3 dB, the squeezing purity μ=99% and the quantum efficiency of balanced homodyne detection η=98%, the fidelity of generated state can reach 0.88 with using a commercially available on-off single-photon detector. This work can provide theoretical guidance for generating a high-quality Schrödinger cat state.
Continuous-variable quantum networks constitute a valuable resource for a wide range of quantum communication and information protocols. While frequency- and fast time-multiplexing enable the implementation of scalable quantum architectures, a precise characterization of multimode squeezed-light sources is essential. In this work, we increase both the spectral resolution and the measured squeezing values. Both parameters are relevant for the improved generation of so-called cluster states, a key resource for measurement-based quantum computing. Our source is based on parametric down-conversion in a periodically poled KTP waveguide pumped by a pulsed laser. The source produces squeezed states over a specific set of optical spectra. Increased spectral resolution in spectrally resolved homodyne detection allowed us to enhance the squeezing per spectral mode, increasing it from 1 dB to more than 2.4 dB in the first mode when measuring with a homodyne detector with a bandwidth of a few MHz. Secondly, we implemented a pulse-by-pulse characterization of the resource using a fast homodyne detector with an electronic bandwidth on the order of the laser repetition rate (100 MHz). Using this approach, the fast measurements revealed squeezing values of up to 1.5 dB in the first few spectral modes. To fully access the multimode quantum resource and ultimately improve the amount of squeezing, a high quantum efficiency is required. To avoid limitations imposed by poor spatial mode matching between the quantum resource and the local oscillator in homodyne detection, we implemented a wavefront-shaping scheme to characterize and control both the intensity profile and phase of the local oscillator. In preliminary tests this approach increased the mode-matching between the reference beam and the quantum signal by more than 8% while simultaneously providing a detailed characterization of the beam shape and of the influence of waveguide transmission on the beam profile. To achieve a genuine advantage in quantum information processing over classical protocols, the generation of non-Gaussian states is necessary. We therefore present a complete scheme for the creation of non-Gaussian states in a multimode system via mode-selective single-photon addition and subtraction, implemented through nonlinear optical processes in second-order nonlinear materials. We introduce a simulation framework applied to our squeezing source, which can be adapted to other regimes as well. Based on this framework, we are able to predict specific waveguide configurations that enable full control over the generated quantum states while maintaining high purity, with each process exhibiting a Schmidt number close to K=1, corresponding to effective single-mode addressing. generated quantum states while maintaining high purity, with each process exhibiting a Schmidt number close to K=1, corresponding to effective single-mode addressing.
Optical non-Gaussian quantum states can be generated in a heralded manner by applying a photon subtraction operation to a Gaussian input state. In our work, we develop a theoretical framework to describe this operation in the case where the input state is spectrally multimode. This framework allows the optimal design of photon subtraction experiments. We give the exact expression of the generated non-Gaussian state in the general case. We apply this framework to the case of Schrodinger kitten state generation using a multimode squeezed vacuum as input state. We show that the quality of the generated state (in terms of fidelity and Wigner function negativity) can be enhanced by adapting the different experimental parameters.
In recent years, there has been an increased interest in the generation of superposition of coherent states with opposite phases, the so-called photonic Schrodinger-cat states. These experiments are very challenging and so far, cats involving small photon numbers only have been implemented. Here, we propose to consider two-mode squeezed states as examples of a Schrodinger-cat-like state. In particular, we are interested in several criteria aiming to identify quantum states that are macroscopic superpositions in a more general sense. We show how these criteria can be extended to continuous variable entangled states. We apply them to various squeezed states, argue that two-mode squeezed vacuum states belong to a class of general Schrodinger-cat states and compare the size of states obtained in several experiments. Our results not only promote two-mode squeezed states for exploring quantum effects at the macroscopic level but also provide direct measures to evaluate their usefulness for quantum metrology.
Nowadays, the realization of quantum computations and communications based on continuous variables has attracted a significant attention due to a substantial expansion of the system dimensionality. The main progress in this area is attributed to the implementation of multimode systems based on squeezed states of light. One of the simplest ways to generate such states relies upon their producing in a single-pass optical parametric amplifier (OPA) using ultrafast pumping. However, for homodyne detection of such multimode states, the profile of the local oscillator (LO) must perfectly match the profile of the measured mode. Usually, this is not the case; therefore a proper treatment of multimode squeezing is required. In this work, we study both theoretically and experimentally the multimode squeezed light generated in type-0 and type-II OPA. We characterize such sources and investigate the degree of squeezing in dependence on the LO spectral profile, employing a pulse shaping technique. The theoretical analysis is performed using the Schmidt-mode theory. This work might have a significant impact on the realization of multimode quantum protocols