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arXiv:2311.18395 · Journal of the Optical Society of America B

Effective algorithms for calculation of quasi-probability distributions of bright “banana” states

Boulat N. Nougmanov

Published May 29, 2024• 0 citations
arXivHTMLPDF

Abstract

Non-Gaussian quantum states, described by negative-valued Wigner functions, are important for both fundamental tests of quantum physics and for emerging quantum information technologies. One of the promising ways of generating a non-Gaussian state from a coherent one is the use of cubic (Kerr) optical nonlinearity, which produces the characteristic banana-like shape of the resulting quantum states. However, the Kerr effect is weak in highly transparent optical materials (dimensionless nonlinearity parameter Γ≲10 −6 ). Therefore, a big number of the photons in the optical mode ( n ≳10 6 ) is necessary to generate an observable non-Gaussianity. In this case, the direct approach to calculation of the Wigner function becomes extremely computationally expensive. In this work, we develop quick algorithms for computing the Husimi and Wigner quasi-probability functions of these non-Gaussian states by means of the Kerr nonlinearity. This algorithm can be used for any realistic values of the photon numbers and the nonlinearity.

DOI
10.1364/josab.524387

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