Criteria for 2D kinematics in an interacting Fermi gas

TL;DR

This paper establishes the conditions under which an interacting ultracold Fermi gas behaves as a two-dimensional system, highlighting how interactions influence the transition from 2D to 3D kinematics.

Contribution

It provides criteria for 2D behavior in interacting Fermi gases, including the effects of interactions on the critical atom number for transverse excitations.

Findings

Transverse excitations occur at a critical atom number $N_{2D}$.

Weak interactions set $N_{2D}$ by trap aspect ratio.

Strong interactions lower $N_{2D}$, causing excitations at lower densities.

Abstract

Ultracold Fermi gases subject to tight transverse confinement offer a highly controllable setting to study the two-dimensional (2D) BCS to Berezinskii-Kosterlitz-Thouless superfluid crossover. Achieving the 2D regime requires confining particles to their transverse ground state which presents challenges in interacting systems. Here, we establish the conditions for an interacting Fermi gas to behave kinematically 2D. Transverse excitations are detected by measuring the transverse expansion rate which displays a sudden increase when the atom number exceeds a critical value $N_{2D}$ signifying a density driven departure from 2D kinematics. For weak interactions $N_{2D}$ is set by the aspect ratio of the trap. Close to a Feshbach resonance, however, the stronger interactions reduce $N_{2D}$ and excitations appear at lower density.