Expansion velocity of a one-dimensional, two-component Fermi gas during the sudden expansion in the ballistic regime

TL;DR

This paper investigates how a two-component Fermi gas expands in a one-dimensional optical lattice, showing that the expansion velocity depends on initial conditions and reveals signatures of Mott-insulating regions, with implications for cold atom experiments.

Contribution

It provides a detailed analysis of the expansion velocity dependence on initial conditions and Mott-insulating regions using time-dependent DMRG simulations.

Findings

Expansion radius grows linearly with time in the ballistic regime.

Presence of Mott-insulating regions affects the expansion velocity.

Results are applicable to cold atom experimental setups.

Abstract

We show that in the sudden expansion of a spin-balanced two-component Fermi gas into an empty optical lattice induced by releasing particles from a trap, over a wide parameter regime, the radius $R_n$ of the particle cloud grows linearly in time. This allow us to define the expansion velocity $V_{ex}$ from $R_n=V_{ex}t$. The goal of this work is to clarify the dependence of the expansion velocity on the initial conditions which we establish from time-dependent density matrix renormalization group simulations, both for a box trap and a harmonic trap. As a prominent result, the presence of a Mott-insulating region leaves clear fingerprints in the expansion velocity. Our predictions can be verified in experiments with ultra-cold atoms.