Strong Coupling Effects on the Specific Heat of an Ultracold Fermi Gas in the Unitarity Limit

TL;DR

This paper explains the anomalous peak in the specific heat of a unitary Fermi gas near the superfluid transition as a result of strong pairing fluctuations, without stable preformed pairs contributing.

Contribution

It demonstrates that strong pairing fluctuations alone can account for the specific heat anomaly in a unitary Fermi gas, contrasting with liquid helium where stable pairs cause the effect.

Findings

Pairing fluctuations explain the specific heat peak near T_c.

Stable preformed Cooper pairs do not contribute to the specific heat at unitarity.

The specific heat anomaly is due to entropy suppression from metastable pairs.

Abstract

We investigate strong-coupling corrections to the specific heat $C_V$ in the normal state of an ultracold Fermi gas in the BCS-BEC crossover region. A recent experiment on a $^6$Li unitary Fermi gas [M. J. H. Ku, {\it et. al.}, Science {\bf 335}, 563 (2012)] shows that $C_V$ is remarkably amplified near the superfluid phase transition temperature $T_{\rm c}$, being similar to the well-known $\lambda$-structure observed in liquid $^4$He. Including pairing fluctuations within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that strong pairing fluctuations are sufficient to explain the anomalous behavior of $C_V$ observed in a $^6$Li unitary Fermi gas near $T_{\rm c}$. We also show that there is no contribution from {\it stable} preformed Cooper pairs to $C_V$ at the unitarity. This indicates that the origin of the observed anomaly is fundamentally different from the case of liquid $^{4}$He, where {\it stable} $^4$He Bose atoms induce the $\lambda$-structure in $C_V$ near the superfluid instability. Instead, the origin is the suppression of the entropy $S$, near $T_{\rm c}$, due to the increase of {\it metastable} preformed Cooper pairs. Our results indicate that the specific heat is a useful quantity to study the effects of pairing fluctuations on the thermodynamic properties of an ultracold Fermi gas in the BCS-BEC crossover region.