Momentum distribution of a freely expanding Lieb-Liniger gas

Abstract

We numerically study free expansion of a few Lieb-Liniger bosons, which are initially in the ground state of an infinitely deep hard-wall trap. Numerical calculation is carried out by employing a standard Fourier transform, as follows from the Fermi-Bose transformation for a time-dependent Lieb-Liniger gas. We study the evolution of the momentum distribution, the real-space single-particle density, and the occupancies of natural orbitals. Our numerical calculation allows us to explore the behavior of these observables in the transient regime of the expansion, where they are non-trivially affected by the particle interactions. We derive analytically (by using the stationary phase approximation) the formula which connects the asymptotic shape of the momentum distribution and the initial state. For sufficiently large times the momentum distribution coincides (up to a simple scaling transformation) with the shape of the real-space single-particle density (the expansion is asymptotically ballistic). Our analytical and numerical results are in good agreement.

small changes; references corrected

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Cited by in corpus (5)

• Quantum distillation: dynamical generation of low-entropy states of strongly correlated fermions in an optical lattice
• Geometric quenches in quantum integrable systems
• Modulated trapping of interacting bosons in one dimension
• Lieb-Liniger gas in a constant force potential
• Density ripples in expanding low-dimensional gases as a probe of correlations