Full Counting Statistics of the momentum occupation numbers of the Tonks-Girardeau gas

Abstract

We compute the fluctuations of the number of bosons with a given momentum for the Tonks-Girardeau gas at zero temperature. We show that correlations between opposite momenta, which is an important fingerprint of long range order in weakly interacting Bose systems, are suppressed and that the full distribution of the number of bosons with non zero momentum is exponential. The distribution of the quasi-condensate is however quasi Gaussian. Experimental relevance of our findings for recent cold atoms experiments are discussed.

arXiv comment10 pages, 4 figures

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• Strongly interacting trapped one-dimensional quantum gases: an exact solution
• Full counting statistics of interacting lattice gases after an expansion: The role of the condensate depletion in the many-body coherence
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• Exact spectral function of the Tonks-Girardeau gas at finite temperature
• Statistical properties of the momentum occupation numbers of the Tonks-Girardeau gas in a harmonic trap
• Full-counting statistics of particle distribution on a digital quantum computer
• $n$-body Correlation of Tonks-Girardeau Gas