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

• Published in: Physical review research Vol. 5; no. 1; p. L012037
• Main Authors: Hercé, Gaétan, Bureik, Jan-Philipp, Ténart, Antoine, Aspect, Alain, Dareau, Alexandre, Clément, David
• Format: Journal Article
• Language: English
• Published: American Physical Society 01.03.2023
• Subjects: Physics
• ISSN: 2643-1564; 2643-1564
• DOI: 10.1103/PhysRevResearch.5.L012037

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)g(n)(0)g^{(n)}(0) up to the order n=6n=6n=6. In Mott insulators, we find a thermal FCS characterized by perfectly-contrasted correlations g(n)(0)=n!g(n)(0)=n!g^{(n)}(0)= n!. In interacting Bose superfluids, we observe small deviations to the Poisson FCS and to the ideal values g(n)(0)=1g(n)(0)=1g^{(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, suggesting that the condensate component exhibits a full coherence g(n)(0)=1g(n)(0)=1g^{(n)}(0) =1 at any order nnn up to n=6n=6n=6. The approach demonstrated here is readily extendable to characterize a large variety of interacting quantum states and phase transitions.