Elongated Fermi superfluid: absence of critical imbalance enhancement at equilibrium

TL;DR

This study investigates how trap aspect ratio affects the maximum population imbalance in a Fermi superfluid near unitarity, finding no increase in critical imbalance with higher aspect ratios through two different theoretical methods.

Contribution

It demonstrates that the trap aspect ratio does not enhance the critical population imbalance in elongated Fermi superfluids, clarifying discrepancies between experimental observations.

Findings

Maximum population imbalance ratio $P_\mathrm{CC}$ remains unchanged with increasing trap aspect ratio.

Cloud shape deviations from trap shape are minor even at high aspect ratios.

Equilibrium states are consistent across different experimental setups despite previous discrepancies.

Abstract

We show that the maximum population imbalance ratio $P_\mathrm{CC}$ for a two-component Fermi gas near the unitarity limit to condense does not increase with the trap aspect ratio $\lambda$, by two methods of 1) solving the Bogoliubov-de Gennes equations with coupling-constant renormalization, and 2) studying the pairing susceptibility by the real-space self-consistent $T$-matrix approximation. The deviation of the cloud shape from what is expected from the trap shape increases but stays minor with increasing $\lambda$ up to 50. This finding indicates that despite the apparent discrepancy between the MIT and Rice experiments over the value of $P_\mathrm{CC}$ and the validity of local density approximation, the equilibrium state of the system for the aspect ratio in the Rice experiment should be consistent with that of MIT.