Full counting statistics of interacting lattice gases after an expansion: The role of the condensate depletion in the many-body coherence

TL;DR

This study measures the full counting statistics of interacting bosons after expansion, revealing how condensate depletion affects many-body coherence and providing a model that matches experimental data across various interaction regimes.

Contribution

It introduces a heuristic model accounting for condensate depletion effects on FCS, validated by experiments, enhancing understanding of quantum gases' coherence properties.

Findings

Mott insulators show thermal FCS with $g^{(n)}(0)= n!$.

Superfluids exhibit deviations from ideal Poissonian statistics.

The model accurately predicts FCS across different interaction strengths.

Abstract

We study the full counting statistics (FCS) of quantum gases in samples of thousands of interacting bosons, detected atom-by-atom after a long free-fall expansion. In this far-field configuration, the FCS reveals the many-body coherence from which we characterize iconic states of interacting lattice bosons, by deducing the normalized correlations $g^{(n)}(0)$ up to the order $n=6$. In Mott insulators, we find a thermal FCS characterized by perfectly-contrasted correlations $g^{(n)}(0)= n!$. In interacting Bose superfluids, we observe small deviations to the Poisson FCS and to the ideal values $g^{(n)}(0)=1$ expected for a pure condensate. To describe these deviations, we introduce a heuristic model that includes an incoherent contribution attributed to the depletion of the condensate. The predictions of the model agree quantitatively with our measurements over a large range of interaction strengths, that includes the regime where the condensate is strongly depleted by interactions. These results suggest that the condensate component exhibits a full coherence $g^{(n)}(0) =1$ at any order $n$ up to $n=6$ and at arbitrary interaction strengths. The approach demonstrated here is readily extendable to characterize a large variety of interacting quantum states and phase transitions.