Expansion of one-dimensional spinor gases from power-law traps

TL;DR

This paper analytically and numerically investigates the free expansion dynamics of one-dimensional spinor gases with contact interactions, revealing how initial trap geometry influences asymptotic density profiles and extending results to mixtures and finite temperatures.

Contribution

It provides analytical solutions for the asymptotic behavior of spinor gases after expansion, highlighting differences between bosonic and fermionic gases across interaction regimes.

Findings

Asymptotic density and momentum distributions are determined by initial quasimomentum distributions.

Fermionic gases exhibit similar profiles in weak and strong interactions.

Self-similar expansion occurs only from harmonic traps, not general power-law traps.

Abstract

Free expansion following the removal of axial confinement represents a fundamental nonequilibrium scenario in the study of many-body ultracold gases. Using the stationary phase approximation, we analytically demonstrate that for all one-dimensional spinor gases with repulsive contact interactions, whether bosonic or fermionic, the asymptotic density and momentum distribution can be directly determined from the quasimomentum distribution (Bethe rapidities) of the trapped gas. We efficiently obtain the quasimomentum distribution numerically by solving the integral equations that characterize the ground state of the integrable system within the local density approximation. Additionally, we derive analytical solutions for both weakly and strongly interacting regimes. Unlike in bosonic gases, where rapidity distributions and density profiles vary significantly across interaction regimes, fermionic gases maintain similar profiles in both weakly and strongly interacting limits. Notably, the gas expands self-similarly only when released from a harmonic trap. For other power-law trapping potentials, the asymptotic density profile is strongly influenced by the initial confinement geometry. Our results extend readily to Bose-Fermi mixtures and finite temperatures.