Time-of-flight expansion of trapped dipolar Fermi gases: From the collisionless to the hydrodynamic regime

TL;DR

This paper provides a comprehensive analytical and numerical study of the ground-state properties and time-of-flight dynamics of trapped dipolar Fermi gases across different regimes, aiding experimental understanding and future design.

Contribution

It introduces a systematic approach to model TOF expansion in dipolar Fermi gases using the Boltzmann-Vlasov equation with relaxation-time approximation, covering various collisional regimes.

Findings

Dipolar interactions significantly affect aspect ratios during expansion.

The model accurately describes experimental observations of Fermi surface deformation.

Extension to self-consistent relaxation times improves the description of collisional dynamics.

Abstract

A recent time-of-flight (TOF) expansion experiment with polarized fermionic erbium atoms measured a Fermi surface deformation from a sphere to an ellipsoid due to dipole-dipole interaction, thus confirming previous theoretical predictions. Here we perform a systematic study of the ground-state properties and TOF dynamics for trapped dipolar Fermi gases from the collisionless to the hydrodynamic regime at zero temperature. To this end we solve analytically the underlying Boltzmann-Vlasov equation within the relaxation-time approximation in the vicinity of equilibrium by using a suitable rescaling of the equilibrium distribution. The resulting ordinary differential equations for the respective scaling parameters are then solved numerically for experimentally realistic parameters and relaxation times that correspond to the collisionless, collisional, and hydrodynamic regime. The equations for the collisional regime are first solved in the approximation of a fixed relaxation time, and then this approach is extended to include a self-consistent determination of the relaxation time. The presented analytical and numerical results are relevant for a detailed quantitative understanding of ongoing experiments and the design of future experiments with ultracold fermionic dipolar atoms and molecules. In particular, the obtained results are relevant for systems with strong dipole-dipole interaction, which turn out to affect significantly the aspect ratios during the TOF expansion.