Temperature effects in a Fermi gas with population imbalance

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 Tc 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 Tc which has been interpreted as a reentrant phenomena or a pairing induced by temperature effect. We show that the lower Tc is never related to a stable solution. The same results are obtained in strong coupling limit. The thermodynamical potential is carefully analyzed to avoid the 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 recent advances in experiments with ultracold fermionic atoms have provided the possibility for the understanding of superfluidity in several physical situations, from high temperature superconductivity to the pairing of quarks in the cores of neutron stars.When a two fermion species system have the same number of spin-up and spin-down particles, its ground state is described by the well known Bardeen-CooperSchrieffer (BCS) theory of superconductivity [1]. In this case, if the temperature is below a certain critical temperature (T c ), fermions with opposite spins interact near their common Fermi surface resulting in pair formation, even at arbitrarily weak coupling. For temperatures above T c the system is found to be in the normal state i.e., the fermions are unpaired. [6,7], and also the possibility of new coexisting phases in the BEC regime [8]. Other pairing mechanisms beyond BCS, such as P-wave superfluidity, have also been investigated [9]. Observation of phase separation between a fully paired superfluid core surrounded by the unpaired excess atoms, have been reported independently by the Rice [10,11] and MIT [12,13] groups. This phase separation can be viewed in terms of three phase transitions of different nature. Differently from the standard BCS thermodynamical phase transition we mentioned above, in an imbalanced system the phase * hcaldas@ufsj.edu.br † motaal@ufsj.edu.br transitions that may happen are: I. At zero temperature (T ), increasing the chemical potential or number asymmetry the system undergoes a (first-order) quantum phase transition to the normal state [6]; II. Still at T = 0, first order phase transitions occur from the normal to a phase separation (PS) phase, and from PS to a spatially homogeneous (magnetized) superfluid as the interaction parameter 1/k F a is varied [8,14], with a tricritical point sitting in the fully polarized line [14], and III. Lowering the temperature, a system with different and fixed number particles phase separates into a unpolarized superfluid core surrounded by a pol...

Superfluidity in two-dimensional imbalanced Fermi gases

“…which is the same 3D result known as the Chandrasekhar-Clogston limit of superfluidity [56,57]. We have seen above that, as happens in 3D [8][9][10], the BCS phase turns from stable, while h < h c , to metastable, when h > h c , in which case the normal phase is stable. Besides these two phases, there is an unstable phase, known as Sarma state, corresponding to a local maximum of Ω versus ∆, that is located between the BCS minimum at ∆ 0 and the normal phase with ∆ = 0.…”

Finite-temperature phase diagram of quasi-two-dimensional imbalanced Fermi gases beyond mean field

“…A graphical inspection shows that at the (tri)critical chemical potential imbalance h tc , both f (T, h) and its derivative with respect to T , g(T, h) ≡ df (T, h)/dT , are zero [34]. The vanishing of these two functions corresponds to α = β = 0. α and β are the first and second coefficients of the expansion of the free energy in terms of the gap parameter, according to the Landau theory of phase transitions.…”

The gap equation for spin-polarized fermions

“…Numerical calculations in [5] (see, in particular, Fig. 2 there) predict that between the curves T i δµ and T g δµ the gap equation has at least two solutions.…”

“…In the region between T i δµ and T o δµ , there can exist non-trivial solutions to the gap equation even if α vanishes identically for the minimizer of F T . In fact it was shown in [5] by numerical calculations, using a contact interaction potential, that there is a parameter regime where the gap equation has a solution but the corresponding energy is higher than that of the normal state.…”