Sudden Expansion of a One-Dimensional Bose Gas from Power-Law Traps

Abstract

We analyze free expansion of a trapped one-dimensional Bose gas after a sudden release from the confining trap potential. By using the stationary phase and local density approximations, we show that the long-time asymptotic density profile and the momentum distribution of the gas are determined by the initial distribution of Bethe rapidities (quasimomenta) and hence can be obtained from the solutions to the Lieb-Liniger equations in the thermodynamic limit. For expansion from a harmonic trap, and in the limits of very weak and very strong interactions, we recover the self-similar scaling solutions known from the hydrodynamic approach. For all other power-law traps and arbitrary interaction strengths, the expansion is not self-similar and shows strong dependence of the density profile evolution on the trap anharmonicity. We also characterize dynamical fermionization of the expanding cloud in terms of correlation functions describing phase and density fluctuations.

Final published version with modified title and a couple of other minor changes. 5 pages, 2 figures, and Supplemental Material

References in corpus (10)

• Many-Body Physics with Ultracold Gases
• Thermalization and its mechanism for generic isolated quantum systems
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Exact coherent states of a harmonically confined Tonks-Girardeau gas
• Fermionization in an expanding 1D gas of hard-core bosons
• Correlations in an expanding gas of hard-core bosons
• Fermi-Bose transformation for the time-dependent Lieb-Liniger gas
• Long-time behavior of the momentum distribution during the sudden expansion of a spin-imbalanced Fermi gas in one dimension
• Spatial nonlocal pair correlations in a repulsive 1D Bose gas
• Free expansion of a Lieb-Liniger gas: Asymptotic form of the wave functions

Cited by in corpus (23)

• Observation of Dynamical Fermionization
• Generalized Hydrodynamics in the 1D Bose gas: theory and experiments
• The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas
• Conformal field theory on top of a breathing one-dimensional gas of hard core bosons
• Breakdown of Tan's relation in lossy one-dimensional Bose gases
• Generalized hydrodynamics: a perspective
• Emergent Pauli blocking in a weakly interacting Bose gas
• The one-dimensional Bose gas with strong two-body losses: the effect of the harmonic confinement
• Probing the local rapidity distribution of a 1D Bose gas
• Analytic thermodynamic properties of the Lieb-Liniger gas
• Dynamical fermionization in a one-dimensional Bose-Fermi mixture
• One-particle density matrix and momentum distribution of the out-of-equilibrium 1D Tonks-Girardeau gas: Analytical results at large $N$
• Efficiency of fermionic quantum distillation
• Tailoring Dynamical Fermionization: Delta kick cooling of a Tonks-Girardeau gas
• Exact spectral function of the Tonks-Girardeau gas at finite temperature
• Dynamical fermionization in one-dimensional spinor gases at finite temperature
• Experimental Investigation of a Bipartite Quench in a 1D Bose gas
• The Theory of Generalised Hydrodynamics for the One-dimensional Bose Gas
• One-dimensional Fermi polaron after a kick: two-sided singularity of the momentum distribution, Bragg reflection and other exact results
• Nonequilibrium dynamics in one-dimensional strongly interacting two-component gases
• Quasicondensation and off-diagonal long-range order of hard-core bosons during a free expansion
• Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons
• Expansion of one-dimensional spinor gases from power-law traps