Tan's contact in a cigar-shaped dilute Bose gas
Jean Decamp, Mathias Albert, Patrizia Vignolo
TL;DR
This paper derives an analytical formula for Tan's contact in a weakly interacting Bose gas confined in a cigar-shaped trap, bridging 3D and 1D regimes, aiding experimental exploration of dimensional crossover effects.
Contribution
It presents the first analytical interpolation formula for Tan's contact across dimensional regimes in a Bose gas using Gross-Pitaevskii and Bogoliubov theories.
Findings
Derived an analytical formula for Tan's contact in a cigar-shaped Bose gas.
Validated the 1D limit with Lieb-Liniger theory.
Provides a theoretical guide for experiments on dimensional crossover.
Abstract
We compute the Tan's contact of a weakly interacting Bose gas at zero temperature in a cigar-shaped configuration. Using an effective one-dimensional Gross-Pitaeskii equation and Bogoliubov theory, we derive an analytical formula that interpolates between the three-dimensional and the one-dimensional mean-field regimes. In the strictly one-dimensional limit, we compare our results with Lieb-Liniger theory. Our study can be a guide for actual experiments interested in the study of Tan's contact in the dimensional crossover.
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