# Stability of quantum degenerate Fermi gases of tilted polar molecules

## TL;DR

This paper develops a mean-field variational approach to analyze the stability and Fermi surface deformation of quantum degenerate dipolar Fermi gases of polar molecules, revealing universal stability conditions and geometry-dependent effects.

## Contribution

It introduces a new theoretical framework based on the Wigner function to study ground-state properties of dipolar Fermi gases, highlighting the role of trap geometry and dipole orientation.

## Key findings

- Stability depends only on trap aspect ratios and dipole orientation.
- The Fermi surface deforms significantly in molecular systems compared to atomic species.
- The stability diagram is species-independent and universal.

## Abstract

A recent experimental realization of quantum degenerate gas of $^{40}$K$^{87}$Rb molecules opens up prospects of exploring strong dipolar Fermi gases and many-body phenomena arising in that regime. Here we derive a mean-field variational approach based on the Wigner function for the description of ground-state properties of such systems. We show that the stability of dipolar fermions in a general harmonic trap is universal as it only depends on the trap aspect ratios and the dipoles' orientation. We calculate the species-independent stability diagram and the deformation of the Fermi surface (FS) for polarized molecules, whose electric dipoles are oriented along a preferential direction. Compared to atomic magnetic species, the stability of a molecular electric system turns out to strongly depend on its geometry and the FS deformation significantly increases.