Non-Gaussian pure states and positive Wigner functions

Abstract

Non-Gaussian correlations in a pure state are inextricably linked with non-classical features, such as a non positive-definite Wigner function. In a commonly used simulation technique in ultracold atoms and quantum optics, known as the truncated Wigner method, the quantum dynamics is mapped to stochastic trajectories in phase space, governed by a positive approximation to the true Wigner distribution. The question thus arises: how accurate is this approach in predicting truly non-classical behaviour? In this article, we benchmark the ability of the truncated Wigner phase-space method to reproduce the non-Gaussian statistics of the single mode anharmonic oscillator. We find that the this method can reliably predict departures from Gaussian statistics over a wide range of particle numbers, whereas the positive-P representation method, which is in principle exact, can suffer from divergent instabilities. The truncated Wigner function, furthermore, is able to reproduce the non-Gaussian correlations while satisfying the condition for purity.

arXiv commentCorrected the rather obvious typos in Eqs (9)-(10). Expanded discussion on +P, sampling error and related issues. To appear in Phys. Rev. A

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• Pseudo steady-state non-Gaussian EPR-steering of massive particles in pumped and damped Bose-Hubbard dimers
• Collisions of solitary waves in condensates beyond mean-field theory
• Quantum behaviour of open pumped and damped Bose-Hubbard trimers
• Quantum corrections of the truncated Wigner approximation applied to an exciton transport model
• Quantum signatures and semiclassical limitations in the transmission of Fock states
• Gaussian approximation and its corrections for driven dissipative Kerr model
• Benchmarking quantum phase-space methods for near-resonant light propagation