Temporal fluctuations in the bosonic Josephson junction as a probe for phase space tomography

TL;DR

This paper demonstrates that analyzing long-time coherence fluctuations in a two-mode Bose-Hubbard model can effectively probe the phase space structure of quantum many-body states, enabling phase space tomography.

Contribution

It introduces a method to use temporal fluctuations of coherence as a probe for phase space tomography in quantum many-body systems.

Findings

Variance of fluctuations factorizes into a preparation-dependent term and a phase space function.

Temporal fluctuations serve as a sensitive probe for phase space characterization.

The approach links long-time dynamics to phase space properties.

Abstract

We study the long time coherence dynamics of a two-mode Bose-Hubbard model in the Josephson interaction regime, as a function of the relative phase and occupation imbalance of an arbitrary coherent preparation. We find that the variance of the long time fluctuations of the one-body coherence can be factorized as a product of the inverse participation number 1/M that depends only on the preparation, and a semi-classical function C(E) that reflects the phase space characteristics of the pertinent observable. Temporal fluctuations can thus be used as a sensitive probe for phase space tomography of quantum many-body states.