Abstract
Phase correlations, density fluctuations and three-body loss rates are relevant for many experiments in quasi one-dimensional geometries. Extended mean-field theory is used to evaluate correlation functions up to third order for a quasi one-dimensional trapped Bose gas at zero and finite temperature. At zero temperature and in the homogeneous limit, we also study the transition from the weakly correlated Gross–Pitaevskii regime to the strongly correlated Tonks–Girardeau regime analytically. We compare our results with the exact Lieb–Liniger solution for the homogeneous case and find good agreement up to the cross-over regime.
Highlights
Much attention has been directed toward second-order correlation functions [33]–[40], while less is known about the third-order correlation function
We compare results for the trapped case with analytic calculations for the second-order correlation function obtained with local density approximation (LDA)-LL theory
We have presented a detailed study of quantum correlations beyond mean-field in a trapped quasi one-dimensional Bose gas at zero and finite temperatures
Summary
LL theory based on the Bethe ansatz [10] describes a 1D homogeneous gas of N bosons on a ring of length L It is one of the very few exactly solvable problems in many-body physics and provides a solution for every value of the correlation parameter γ. Lieb and Liniger [12] that the ground state energy only depends on the dimensionless correlation parameter γ It is basically the ratio of the repulsive mean-field energy gn to the kinetic energy h 2/2md at an average distance d = 1/n. We call bosons weakly correlated for γ 1 (GP regime) and strongly correlated for γ 1 In terms of this parameter, the ground state energy and second-order correlation function. A comparison of the exact result for the third-order correlation function with the approximations in the GP and the TG regime [36] is presented in figure 1
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