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arXiv:2207.14070

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

Gaétan Hercé, Jan‐Philipp Bureik, Antoine Ténart, Alain Aspect, Alexandre Dareau, David Clément

Published Jul 28, 2022• 0 citations
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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.

DOI
10.48550/arxiv.2207.14070

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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 their 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.These deviations become larger as we increase the interaction strength and reveal the role of the quantum depletion of the condensate on many-body coherence.The approach to many-body correlations demonstrated here is readily extendable to characterize a large variety of interacting quantum states and phase transitions.
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We show that the visibility in interference experiments with Bose-Einstein condensates is directly related to the condensate fraction. The probability distribution of the contrast over many runs of an interference experiment thus gives the full counting statistics of the condensed atom number. For two-dimensional Bose gases, we discuss the universal behavior of the probability distribution in the superfluid regime and provide analytical expressions for the distributions for both homogeneous and harmonically trapped samples. They are non-Gaussian and unimodal with a variance that is directly related to the superfluid density. In general, the visibility is a self-averaging observable only in the presence of long-range phase coherence. Close to the transition temperature, the visibility distribution reflects the universal order-parameter distribution in the vicinity of the critical point.