Free Expansion of a Weakly-interacting Dipolar Fermi Gas

TL;DR

This paper provides a theoretical analysis of the free expansion dynamics of a polarized dipolar Fermi gas, revealing deformation behaviors and scaling laws relevant for experimental time-of-flight measurements.

Contribution

It introduces an exact prediction of quadrupole deformation during expansion and proposes a method to analyze weakly-interacting dipolar Fermi gases.

Findings

Minimal quadrupole deformation predicted for high-temperature and zero-temperature gases.

Scaling law related to Liouville's theorem identified in long-time expansion behavior.

A proper approach for time-of-flight analysis of dipolar Fermi gases developed.

Abstract

We theoretically investigate a polarized dipolar Fermi gas in free expansion. The inter-particle dipolar interaction deforms phase-space distribution in trap and also in the expansion. We exactly predict the minimal quadrupole deformation in the expansion for the high-temperature Maxwell-Boltzmann and zero-temperature Thomas-Fermi gases in the Hartree-Fock and Landau-Vlasov approaches. In conclusion, we provide a proper approach to develop the time-of-flight method for the weakly-interacting dipolar Fermi gas and also reveal a scaling law associated with the Liouville's theorem in the long-time behaviors of the both gases.