Full counting statistics of time of flight images

TL;DR

This paper introduces a new method called time of flight full counting statistics to analyze quantum states in cold atomic systems, revealing universal regimes and fluctuations, and capturing thermalization and exotic states.

Contribution

The paper presents a novel characterization scheme for cold atomic systems using time of flight full counting statistics, applicable to various quantum regimes and states.

Findings

Universal regimes in time of flight images of Bose gases

Distribution crossover from exponential to Gamma with momentum resolution

Gumbel distribution for zero momentum particles in weak interactions

Abstract

Inspired by recent advances in cold atomic systems and non-equilibrium physics, we introduce a novel characterization scheme, the time of flight full counting statistics. We benchmark this method on an interacting one dimensional Bose gas, and show that there the time of flight image displays several universal regimes. Finite momentum fluctuations are observed at larger distances, where a crossover from exponential to Gamma distribution occurs upon decreasing momentum resolution. Zero momentum particles, on the other hand, obey a Gumbel distribution in the weakly interacting limit, characterizing the quantum fluctuations of the former quasi-condensate. Time of flight full counting statistics is demonstrated to capture thermalization processes after a quantum quench, and can be useful for characterizing exotic quantum states such as many-body localized systems or models of holography.