On a scale-invariant Fermi gas in a time-dependent harmonic potential

TL;DR

This paper derives exact solutions for the dynamics of a scale-invariant Fermi gas in a time-varying harmonic trap, revealing novel breathing modes and methods to measure Tan contact, with implications for ultracold gas experiments.

Contribution

It provides exact time evolution solutions for a scale-invariant Fermi gas under dynamic trapping potentials, including perturbative analysis of deviations from ideal conditions.

Findings

Exact density evolution in any dimension

Identification of undamped breathing modes

Proposed method to measure Tan contact

Abstract

We investigate a scale-invariant two-component Fermi gas in a time-dependent isotropic harmonic potential. The exact time evolution of the density distribution in position space in any spatial dimension is obtained. Two experimentally relevant examples, an abrupt change and a periodic modulation of the trapping frequency are solved. Small deviations from scale invariance and isotropy of the confinement are addressed within first order perturbation theory. We discuss the consequences for experiments with ultracold quantum gases such as the excitation of a tower of undamped breathing modes and a new alternative for measuring the Tan contact.