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Physical Review Letters

Experimental Generation of Squeezed Cat States with an Operation Allowing Iterative Growth

Jean Etesse, Martin Bouillard, Bhaskar Kanseri, Rosa Tualle-Brouri

Published May 15, 2015• 125 citations
Publisher

Abstract

We present what is, to our knowledge, the first implementation of a "cat breeding" operation, which allows an iterative growth of cat states. We thus report the experimental generation of a squeezed cat state from two single photon Fock states, which can be seen as cat states with zero amplitude. These Fock states are mixed on a symmetrical beam splitter, and the generation is heralded by a homodyne measurement in one of the two output arms. The output state has a fidelity of 61% with an even squeezed cat state of amplitude α=1.63. This hybrid operation opens up new prospects in quantum optics, as the protocol depicted here can be iterated in order to produce new kinds of mesoscopic states.

DOI
10.1103/physrevlett.114.193602

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We present what is, to our knowledge, the first implementation of a "cat breeding" operation, which allows an iterative growth of cat states. We thus report the experimental generation of a squeezed cat state from two single photon Fock states, which can be seen as cat states with zero amplitude. These Fock states are mixed on a symmetrical beam splitter, and the generation is heralded by a homodyne measurement in one of the two output arms. The output state has a fidelity of 61% with an even squeezed cat state of amplitude α=1.63. This hybrid operation opens up new prospects in quantum optics, as the protocol depicted here can be iterated in order to produce new kinds of mesoscopic states.
We present what is to our knowledge the first implementation of a Schrödinger cat states "breeding" operation, which allows an iterative growth of these states. We thus report the experimental generation of a squeezed Schrödinger cat state from two single photon Fock states, which can be seen as cat states with zero amplitude. These Fock states are mixed on a symmetrical beamsplitter and the generation is heralded by a homodyne measurement in one of the two output arms. The output state has a fidelity of 61% with an even squeezed Schrödinger cat state of amplitude α=1.63α=1.63α=1.63. This hybrid operation opens up new prospects in quantum optics as the protocol depicted here can be iterated in order to produce new kind of mesoscopic states.
The generation of non-Gaussian quantum states is a key requirement for universal continuous-variable quantum information processing. We report the experimental generation of large-amplitude squeezed coherent-state superpositions (squeezed cat states) on free-space optical pulses, reaching an amplitude of α=2.47α= 2.47α=2.47, which, to our knowledge, exceeds all previously reported values. Our protocol relies on the controlled mixing of the Fock states ∣1⟩|1\rangle∣1⟩ and ∣2⟩|2\rangle∣2⟩ through a tunable beam splitter, followed by heralding via homodyne detection. The resulting state displays three well-resolved negative regions in its Wigner function and achieves a fidelity of 0.530.530.53 with the target state ∝S^(z)(∣α⟩−∣−α⟩)\propto \hat{S}(z)(|α\rangle - |-α\rangle)∝S^(z)(∣α⟩−∣−α⟩), with α=2.47α= 2.47α=2.47 and squeezing parameter z=0.56z = 0.56z=0.56. These results constitute a significant milestone for temporal breeding protocols and for the iterative generation of optical GKP states, opening new perspectives for scalable and fault-tolerant photonic quantum architectures.
Iterative CZC_ZCZ​-gate-based protocol for squeezed Schrödinger cat state engineering
Squeezed optical Schrödinger cat states constitute a key resource for both fundamental tests of quantum theory and up-to-date quantum technologies. We propose a measurement-assisted gate for the generation and manipulation of the cat states. In this scheme, an ancilla in the non-Gaussian small-amplitude (in general, squeezed) Schrödinger cat state and the target oscillator initially prepared in a squeezed vacuum (or coherent) state are subjected to a quantum nondemolition (QND) entangling operation followed by projective homodyne measurement. The proposed gate enables generation of high-fidelity squeezed Schrödinger cat states with controllable size and squeezing with tunable fidelity/success-probability trade-off. We also introduce an iterative, homodyne-conditioned CZC_ZCZ​-based protocol for cat-state amplification. The parameter regimes required to achieve the desired fidelity and the success probability are analyzed. The approach is well suited for applications in measurement-based quantum computing and hybrid quantum networks where non-Gaussian resources enhance computational and communication capabilities.
Coherent state superpositions, also known as Schrödinger cat states, are widely recognized as promising resources in quantum information, quantum metrology, as well as fundamental tests. These states are hard to produce deterministically and most schemes for their probabilistic generation can only attain amplitudes too small for practical use. This is for example the case for photon-subtracted squeezed vacuum (PSSV), which can be used to approximate cat states of amplitude no larger than y = 1.5 if the fidelity is to be maintained above 95%. One way to reach larger amplitudes is to start with pairs of small cats and then to interfere them on a balanced beam splitter. The projective measurement of one of the outputs is used to herald a larger cat resulting from the constructive interference of the initial states. The scheme proposed here uses the projection |x = 0〉〈x = 0| as the heralding condition. Homodyning is proposed, as opposed to photon counting, because homodyne detection has high a quantum efficiency, and - as demonstrated in the paper - can be tuned to increase the success probability of the amplification without heavily compromising the output's fidelity.
Superpositions of macroscopically distinct quantum states, introduced in Schrödinger’s famous Gedankenexperiment, are an epitome of quantum “strangeness” and a natural tool for determining the validity limits of quantum physics. The optical incarnation of Schrödinger’s cat — the superposition of two opposite-amplitude coherent states — is also the backbone of quantum information processing in the continuous-variable domain. Here we implement two protocols for producing and amplifying optical Schrödinger’s cats. In the first protocol we remotely prepare a high-efficiency Schrödinger cat state by applying the remote state preparation to a N00N state prepared between two parties that are separated by a lossy medium. The second protocol consists in bringing the initial states into interference on a beamsplitter and a subsequent heralding quadrature measurement in one of the output channels. The latter technique enables implementation in an iterative manner, in principle allowing creation of Schrödinger’s cat states of arbitrarily high amplitude.
We proposed and analyzed a scheme to generate large-size Schr\"odinger cat states based on linear operations of Fock states, squeezed vacuum states, and conditional measurements. By conducting conditional measurements via photon number detectors, two unbalanced small-amplitude Schr\"odinger kitten states combined by a beam splitter can be amplified to a large-size cat state with the same parity. According to simulation results, two Schr\"odinger odd kitten states with amplitudes of $|\ensuremath{\beta}|=1.06$ and $|\ensuremath{\beta}|=1.11$ generated from one-photon-subtracted 3 dB squeezed vacuum states, are amplified to an odd cat state of $|\ensuremath{\beta}|=1.73$ with a fidelity of F=99F=99%F=99. A large-size Schr\"odinger odd cat state with $|\ensuremath{\beta}|=2.51$ and F=97.30F=97.30%F=97.30 is predicted when 5.91 dB squeezed vacuum states are employed. According to the analysis on the impacts of experimental imperfections in practice, Schr\"odinger odd cat states of $|\ensuremath{\beta}|>2$ are available. A feasible configuration based on a quantum frequency comb is developed to realize the large-size cat state generation scheme we proposed.