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arXiv:0801.1743 · Journal of Statistical Mechanics Theory and Experiment

Temperature effects in a Fermi gas with population imbalance

Heron Caldas, A L Mota

Published Aug 27, 2008• 11 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1742-5468/2008/08/p08013

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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.
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 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.
In this article we present a Monte Carlo calculation of the critical temperature and other thermodynamic quantities for the unitary Fermi gas with a population imbalance (unequal number of fermions in the two spin components). We describe an improved worm-type algorithm that is less prone to autocorrelations than the previously available methods and show how this algorithm can be applied to simulate the unitary Fermi gas in presence of a small imbalance. Our data indicate that the critical temperature remains almost constant for small imbalances $h=\ensuremath{\Delta}\ensuremath{\mu}/{\ensuremath{\varepsilon}}_{F}\ensuremath{\lesssim}0.2$. We obtain the continuum result ${T}_{c}=0.171(5){\ensuremath{\varepsilon}}_{F}$ in units of Fermi energy and derive a lower bound on the deviation of the critical temperature from the balanced limit, ${T}_{c}(h)\ensuremath{-}{T}_{c}(0)>\ensuremath{-}0.5{\ensuremath{\varepsilon}}_{F}{h}^{2}$. Using an additional assumption a tighter lower bound can be obtained. We also calculate the energy per particle and the chemical potential in the balanced and imbalanced cases.
In this chapter the recent theoretical work on phase transition in imbalanced fermion superfluids is reviewed. The imbalanced systems are those in which the two fermionic species candidate to form pairing have different Fermi surfaces or densities. We consider systems subjected to weak interactions. In this scenario two distinct phase transitions are predicted to occur. A thermodynamical phase transition, induced by the temperature (T), and a quantum phase transition as a function of the increasing chemical potentials asymmetry, that takes place at zero temperature. We also briefly discuss some recent experimental work at non-zero T with imbalanced Fermi gases in cold atomic traps.
We investigate single-particle properties of a strongly interacting ultracold Fermi gas with mass imbalance. Using an extended TTT-matrix theory, we calculate the density of states, as well as the single-particle spectral weight, in the unitarity limit above the superfluid phase transition temperature TcT_{\rm c}Tc​. We show that the momentum regions where pairing fluctuations strongly affect single-particle excitations are different between light fermions and heavy fermions, reflecting the difference of the Pauli blocking effects between them. In addition, we obtain different pseudogap phenomena associated with pairing fluctuations in between the two components. Since the realization of a mass-imbalanced superfluid Fermi gas is an important challenge in this field, our results would contribute to the understanding of physical properties of the hetero-pairing state.
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.