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arXiv:cond-mat/0605085 · Physical Review Letters

Anomalous Specific-Heat Jump in a Two-Component Ultracold Fermi Gas

Armen Sedrakian, H. Müther, A. Polls

Published Oct 4, 2006• 14 citations
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Abstract

The thermodynamic functions of a Fermi gas with spin population imbalance are studied in the temperature-asymmetry plane in the BCS limit. The low-temperature domain is characterized by an anomalous enhancement of the entropy and the specific heat above their values in the unpaired state, decrease of the gap and eventual unpairing phase transition as the temperature is lowered. The unpairing phase transition induces a second jump in the specific heat, which can be measured in calorimetric experiments. While the superfluid is unstable against a supercurrent carrying state, it may sustain a metastable state if cooled adiabatically down from the stable high-temperature domain. In the latter domain the temperature dependence of the gap and related functions is analogous to the predictions of the BCS theory.

DOI
10.1103/physrevlett.97.140404

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The thermodynamic functions of a Fermi gas with spin population imbalance are studied in the temperature-asymmetry plane in the BCS limit. The low-temperature domain is characterized by an anomalous enhancement of the entropy and the specific heat above their values in the unpaired state, decrease of the gap and eventual unpairing phase transition as the temperature is lowered. The unpairing phase transition induces a second jump in the specific heat, which can be measured in calorimetric experiments. While the superfluid is unstable against a supercurrent carrying state, it may sustain a metastable state if cooled adiabatically down from the stable high-temperature domain. In the latter domain the temperature dependence of the gap and related functions is analogous to the predictions of the BCS theory.
The thermodynamic functions of a Fermi gas with spin population imbalance are studied in the temperature-asymmetry plane. The low temperature domain is characterized by anomalous enhancement of the entropy and the specific heat above their values in the unpaired state, decrease of the gap and eventual unpairing phase transition as the temperature is lowered. The unpairing phase transition induces a second jump in the specific heat, which can be measured in calorimetric experiments. While the superfluid is unstable against a supercurrent carrying state, it may sustain a metastable state if cooled adiabatically down from the stable high-temperature domain. In the latter domain the temperature dependence of the gap and related functions is analogous to the predictions of the BCS theory.
We investigate temperature effects in a Fermi gas with imbalanced spin populations. From the general expression of the thermal gap equation we find, in weak coupling limit , an analytical expression for the transition temperature T c as a function of various possibilities of chemical potential and mass asymmetries between the two particle species. For a range of asymmetry between certain specific values, this equation always has two solutions for T c , which has been interpreted as a reentrant phenomena or a pairing induced by a temperature effect. We show that the lower T c is never related to a stable solution. The same results are obtained in the strong coupling limit . The thermodynamical potential is carefully analyzed to avoid consideration of the unstable solutions. We also obtain the tricritical points for the chemical potential and mass imbalanced cases, and beyond these points we properly minimize the thermodynamic potential to find the stable and metastable first-order transition lines.
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.
We investigated possible superfluid phases at finite temperature in a two-component Fermi gas with density imbalance. In the frame of a general four-fermion interaction theory, we solved in the BCS region the gap equations for the pairing gap and pairing momentum under the restriction of fixed number densities and analyzed the stability of different phases by calculating the superfluid density and number susceptibilities. The homogeneous superfluid is stable only at high temperature and low number asymmetry, the inhomogeneous Larkin-Ovchinnikov-Fudde-Ferrell state survives at low temperature and high number asymmetry, and in between them there exists another possible inhomogeneous phase, that of phase separation. The critical temperatures and the orders of the phase transitions among the superfluid phases and normal phase are calculated analytically and numerically. The phase diagram we obtained in the temperature and number asymmetry plane is quite different from the one in the temperature and chemical potential difference plane for a system with fixed chemical potentials.
Mass imbalance changes not only pairing in a polarized Fermi gas but also the thermodynamic condition under which normal and superfluid components can remain phase separated. The low-temperature properties of mass imbalanced two component Fermi gases are investigated within the local density approximation on the BCS side of the BCS BEC crossover, with an unpolarized superfluid spatially separated from a partially polarized normal component. For each interaction strength and mass ratio, the pairing gap, average chemical potential, Hartree Fock potentials, and imbalance chemical potential are obtained self consistently, with the latter determined by the normal superfluid phase separation condition rather than varied independently. The results show that a larger mass ratio requires a larger imbalance chemical potential to maintain phase separation. For the 163Dy 40K mixture, an increase in the absolute value of the interaction strength raises the average and imbalance chemical potentials while reducing the pairing gap. The resulting changes modify the quasiparticle spectrum and the superfluid density of states and are reflected directly in the thermal response, with the quasiparticle specific heat decreasing at a fixed mass ratio. In contrast, increasing the mass ratio enhances the specific heat, which is associated with the larger density of available states near the Fermi surface of the heavier majority component. The results thus connect the normal superfluid phase separation condition with the quasiparticle spectrum and superfluid density of states, and show that the specific heat provides a clear thermal signature of mass imbalance in the phase separated regime.
We investigate magnetic properties of a strongly interacting ultracold Fermi gas. Within the framework of an extended T -matrix approximation, we calculate the spin susceptibility χ in the unitarity limit. We show that effects of pairing fluctuations on this magnetic quantity are quite different in between the normal state and the superfluid phase. In the normal state, pairing fluctuations cause spin-gap phenomenon near the superfluid phase transition temperature T c , where χ is anomalously suppressed. In the superfluid phase, on the other hand, the ordinary suppression of χ by the BCS energy gap is weakened by pairing fluctuations, because they induce finite density of states inside the gap. Our results indicate that the spin susceptibility is a useful quantity for the study of pairing fluctuations in the BCS-BEC crossover regime of an ultracold Fermi gas.