Specific heat and effects of pairing fluctuations in the BCS-BEC crossover regime of an ultracold Fermi gas

TL;DR

This paper studies the specific heat in an ultracold Fermi gas across the BCS-BEC crossover, revealing how pairing fluctuations influence thermodynamics and identifying regimes of stable and metastable pairs.

Contribution

It provides a theoretical analysis of specific heat behavior related to pairing fluctuations, connecting experimental observations with the stability of preformed Cooper pairs in the crossover.

Findings

Enhanced specific heat due to metastable pairs near $T_c$ in the unitary regime

Agreement of theoretical results with recent $^6$Li Fermi gas experiments

Identification of regimes with stable molecules versus preformed pairs

Abstract

We investigate the specific heat at constant volume $C_V$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas above the superfluid phase transition temperature $T_{\rm c}$. Within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that this thermodynamic quantity is sensitive to the stability of preformed Cooper pairs. That is, while $C_V(T\gesim T_{\rm c})$ in the unitary regime is remarkably enhanced by {\it metastable} preformed Cooper pairs or pairing fluctuations, it is well described by that of an ideal Bose gas of long-lived {\it stable} molecules in the strong-coupling BEC regime. Using these results, we identify the region where the system may be viewed as an almost ideal Bose gas of stable pairs, as well as the pseudogap regime where the system is dominated by metastable preformed Cooper pairs, in the phase diagram of an ultracold Fermi gas with respect to the strength of a pairing interaction and the temperature. We also show that the calculated specific heat agrees with the recent experiment on a $^6$Li unitary Fermi gas. Since the formation of preformed Cooper pairs is a crucial key in the BCS-BEC crossover phenomenon, our results would be helpful in considering how fluctuating preformed Cooper pairs appear in a Fermi gas, to eventually become stable, as one passes through the BCS-BEC crossover region.