# Specific Heat and Effects of Uniaxial Anisotropy of a $p$-wave Pairing Interaction in a Strongly Interacting Ultracold Fermi Gas

## TL;DR

This paper studies how uniaxial anisotropy in a $p$-wave interaction affects the specific heat of a strongly interacting ultracold Fermi gas, revealing anisotropy's significance in the strong-coupling regime and classifying different interaction regimes.

## Contribution

It provides the first detailed analysis of specific heat behavior in a $p$-wave Fermi gas with uniaxial anisotropy across interaction regimes using strong-coupling theory.

## Key findings

- Specific heat is sensitive to anisotropy in the strong-coupling regime.
- Population imbalance among $p_i$-wave molecules influences thermodynamics.
- Classification of strong-coupling regimes based on anisotropic effects.

## Abstract

We investigate the specific heat $C_V$ at constant volume and effects of uniaxial anisotropy of a $p$-wave attractive interaction in the normal state of an ultracold Fermi gas. Within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we evaluate this thermodynamic quantity as a function of temperature, in the whole interaction regime. While the uniaxial anisotropy is not crucial for $C_V$ in the weak-coupling regime, $C_V$ is found to be sensitive to the uniaxial anisotropy in the strong-coupling regime. This originates from the population imbalance among $p_i$-wave molecules ($i=x,y,z$), indicating that the specific heat is a useful observable to see which kinds of $p$-wave molecules dominantly exist in the strong-coupling regime when the $p$-wave interaction has uniaxial anisotropy. Using this strong point, we classify the strong-coupling regime into some characteristic regions. Since a $p$-wave pairing interaction with uniaxial anisotropy has been discovered in a $^{40}$K Fermi gas, our results would be useful in considering strong-coupling properties of a $p$-wave interacting Fermi gas, when the interaction is uniaxially anisotropic.