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arXiv:0804.2280 · Physical Review A

Mean-field analysis of pairing in asymmetric Fermi systems at finite temperature

Rishi Sharma, Sanjay K. Reddy

Published Dec 16, 2008• 8 citations
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Abstract

We study the phase diagram of a two component Fermi system with a weak attractive interaction. Our analysis includes the leading order Hartree energy shifts and pairing correlations at finite temperature and chemical potential difference between the two fermion species. We show that in an asymmetric system, the Hartree shift to the single particle energies is important for the phase competition between normal and superfluid phase and can change the phase transition curve qualitatively. At large chemical potential asymmetry we find that a somewhat fragile superfluid state can be favored due to finite-temperature effects. We also investigate the transition between the normal phase and an inhomogeneous superfluid phase to study how gradient instabilities evolve with temperature and asymmetry. Finally, we adopt our analysis to study the density profiles of similar asymmetric Fermi systems that are being observed in cold-atom experiments.

DOI
10.1103/physreva.78.063609

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We study the phase diagram of a two component Fermi system with a weak attractive interaction. Our analysis includes the leading order Hartree energy shifts and pairing correlations at finite temperature and chemical potential difference between the two fermion species. We show that in an asymmetric system, the Hartree shift to the single particle energies is important for the phase competition between normal and superfluid phase and can change the phase transition curve qualitatively. At large chemical potential asymmetry we find that a somewhat fragile superfluid state can be favored due to finite-temperature effects. We also investigate the transition between the normal phase and an inhomogeneous superfluid phase to study how gradient instabilities evolve with temperature and asymmetry. Finally, we adopt our analysis to study the density profiles of similar asymmetric Fermi systems that are being observed in cold-atom experiments.
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We study the phase structure of a dilute two-component Fermi system with attractive interactions as a function of the coupling and a finite number asymmetry or polarization. In weak coupling, a number asymmetry results in phase separation. A mixed phase containing symmetric superfluid matter and an asymmetric normal phase is favored. For strong coupling we show that the stress on the superfluid phase to accommodate a number asymmetry increases. Near the infinite-scattering length, we calculate the single-particle excitation spectrum and the ground-state energy. A picture of weakly interacting quasiparticles emerges for modest polarizations. In this regime a homogeneous phase with a finite population of quasiparticle states characterized by a gapless spectrum is favored over the phase separated state. These states may be realized in cold atom experiments.
Abstract We study phase separation in a dilute two-component Fermi system with attractive interactions as a function of the coupling strength and the polarization or number density asymmetry between the two components. In weak and strong couplings with a finite number density asymmetry, phase separation is energetically more favorable. A heterogeneous phase containing a symmetric superfluid component and an asymmetric normal phase has lower energy than a homogeneous normal phase. We show that for a small number density asymmetry, taking into consideration the leading order corrections at order of the interaction parameter, phase separation is stable against the normal phase in the whole BCS range. We investigate the consequences of the consideration of the leading order corrections to the thermodynamic potentials of the normal and BCS phase on the Chandrasekhar–Clogston limit. We have also investigated the stability of a Bose–Fermi mixture in the far-BEC limit. We find that the molecular BEC is locally stable against an external magnetic field h , provided is smaller than the pairing gap .
We present the analytical results at the mean-field level for the asymmetrical fermion system with attractive contact interaction at zero temperature. The results can be expressed in terms of linear combinations of the elliptic integrals of the first and second kinds. In the limit of small gap parameter, we discuss how the asymmetry in fermion species affects the phases of the ground state of the system. In the limit of large gap parameter, we show that two candidate phases are competing for the system's ground state. The Sarma phase containing a pure Fermi fluid and a mixed condensate is favored at a large degree of asymmetry. The separated phase consisting of a pure Fermi fluid and a boson condensate supports the system at a small degree of asymmetry. The two phases are degenerate in the limit of infinite pairing gap.
We discuss the superfluid phase transition of a strongly interacting Fermi gas with unequal (asymmetric) chemical potentials in two pairing hyperfine states, and map out its phase diagram near the BCS-BEC crossover. Our approach includes the fluctuation contributions of "preformed Cooper pairs" to the thermodynamic potential at finite temperature. We show that, below a critical difference in chemical potentials between species, a normal gas is unstable towards the formation of either a finite-momentum paired Fulde-Ferrell-Larkin-Ovchinnikov superconducting phase or a uniform superfluid, depending on the asymmetry and interaction strengths. We determine the value of critical chemical potential mismatch, and find that it is consistent with a recent measurement by Zwierlein et al. ( Science , 311 (2006) 492).