Cross-over to quasi-condensation: mean-field theories and beyond

Abstract

We analyze the cross-over of a homogeneous one-dimensional Bose gas from the ideal gas into the dense quasi-condensate phase. We review a number of mean-field theories, perturbative or self-consistent, and provide accurate evaluations of equation of state, density fluctuations, and correlation functions. A smooth crossover is reproduced by classical-field simulations based on the stochastic Gross-Pitaevskii equation, and the Yang-Yang solution to the one-dimensional Bose gas.

21 pages, 16 figures

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• Complex wave fields in the interacting one-dimensional Bose gas
• Mesoscopic density grains in the 1d interacting Bose gas from the exact Yang-Yang solution
• Quantum Borderlines -- Fluctuation Energies in Ultracold Bose Gases
• Effects of classical stochastic webs on the quantum dynamics of cold atomic gases in a moving optical lattice
• Exact $\mathcal{N}$-point function mapping between pairs of experiments with Markovian open quantum systems