Amplification of realistic Schrödinger-cat-state-like states by homodyne heralding

Abstract

We present a scheme for the amplification of Schrödinger cats that collapses two smaller states onto their constructive interference via a homodyne projection. We analyze the performance of the amplification in terms of fidelity and success rate when the input consists of either exact coherent state superpositions or of photon-subtracted squeezed vacua. The impact of imprecise homodyne detection and of impure squeezing is quantified. We also assess the scalability of iterated amplifications.Coherent state superpositions, or optical Schrödinger cat states, are widely recognized as promising resources in quantum information [1][2][3][4][5], quantum metrology [6][7][8], and fundamental tests [9][10][11][12]. In the near-orthogonal basis of coherent states γ|−γ = e −2γ 2 , two particular instances for these states arewhere the sign (±) of the superposition refers to the even and odd cat state, respectively. These states exhibit quasi-probability distributions in phase space which are distinctly non-classical. This makes them all the more challenging to generate deterministically as that would require strong Kerr-type non-linearities [13][14][15].One has then to resort to heralding techniques which, though probabilistic, need only linear optics and projective measurements [16]. These state-engineering schemes are nonetheless approximative and present a limitation in the fidelity they produce with ideal cat states. Photon-subtraction of squeezed vacuum, for example, is a well-established method to generate approximations of small amplitude cat states, colloquially referred to as Schrödinger kittens [17][18][19][20][21]. Even in the best experimental conditions, the fidelity between the photon-subtracted squeezed vacuum (PSSV) and an actual odd cat state |κ − (γ) degrades markedly for γ ≥ 1.2 [22]. Yet, for these states to be reliable resources in quantum computation, their fidelity with cat states at least as large as γ = 1.2 need to be maintained at near-unit fidelity [3,23]. Single-photon subtraction is only one example of several measurement-induced schemes which have been proposed to generate kitten states [20,[24][25][26][27][28][29]. However, none of these schemes can produce arbitrarily large cats in a single run. Ways to get around this issue have been devised using the recursive amplification of small, approximate cats [30,31]. For example, it was suggested in [32] to interfere a supply of delocalized single photons followed by homodyne heralding to generate large entangled cat states. These proposals have in common that they rely on the coherent mixing of two small cats, whereupon a projective measurement collapses one of the two outputs onto a constructive interference of the inputshence the amplification. Here, we shall pursue the same idea but make use solely of homodyne heralding for its relative simplicity and high quantum efficiency. We also demonstrate that the acceptance window of homodyne heralding can be widened to increase the success rate of the amplification while at the same time maintaining a s...

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

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A quantum optomechanical interface beyond the resolved sideband limit

“…A more intriguing application of this squeezed transfer is generation of small-amplitude mechanical Schrödinger cat states (coherent state superpositions), termed 'kitten' states. As has been demonstrated in optical systems, these may be 'bred' into large-amplitude cat states by a number of schemes [60][61][62]; this could result in a macroscopic superposition of a massive object. Creating such a state is a research goal of foundational interest [12], and is also sufficient to allow universal quantum computation [63,64] with phonons.…”

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