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arXiv:1507.02818 · Physical Review A

Critical region of the superfluid transition in the BCS-BEC crossover

Thibault Debelhoir, N. Dupuis

Published Feb 24, 2016• 17 citations
arXivHTMLPDF

Abstract

We determine the size of the critical region of the superfluid transition in the Bardeen-Cooper-Schrieffer--Bose-Einstein condensation (BCS-BEC) crossover of a three-dimensional fermion gas, using a renormalization-group approach to a bosonic theory of pairing fluctuations. For the unitary Fermi gas, we find a sizable critical region $[{T}_{G}^{\ensuremath{-}},{T}_{G}^{+}]$, of order ${T}_{c}$, around the transition temperature ${T}_{c}$ with a pronounced asymmetry: $|{T}_{G}^{+}\ensuremath{-}{T}_{c}|/|{T}_{G}^{\ensuremath{-}}\ensuremath{-}{T}_{c}|\ensuremath{\sim}8$. The critical region is strongly suppressed on the BCS side of the crossover but remains important on the BEC side.

DOI
10.1103/physreva.93.023642

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We investigate the specific heat at constant volume CV{C}_{V}CV​ in the Bardeen-Cooper-Schrieffer--Bose-Einstein-condensate (BCS-BEC)-crossover regime of an ultracold Fermi gas above the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​. 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 ${C}_{V}(T\ensuremath{\gtrsim}{T}_{\mathrm{c}})$ in the unitary regime is remarkably enhanced by metastable preformed Cooper pairs or pairing fluctuations, it is well described by that of an ideal Bose gas of long-lived 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 6Li^{6}\text{Li}6Li 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.