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Register a new userFinite temperature phase diagram of a spin-polarized ultracold Fermi gas in a highly elongated harmonic trap
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We investigate the finite temperature properties of an ultracold atomic Fermi gas with spin population imbalance in a highly elongated harmonic trap. Previous studies at zero temperature showed that the gas stays in an exotic spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid state at the trap center; while moving to the edge, the system changes into either a non-polarized Bardeen-Cooper-Schriffer superfluid ($P<P_c$) or a fully polarized normal gas ($P>P_c$), depending on the smallness of the spin polarization $P$, relative to a critical value $P_c$. In this work, we show how these two phase-separation phases evolve with increasing temperature, and thereby construct a finite temperature phase diagram. For typical interactions, we find that the exotic FFLO phase survives below one-tenth of Fermi degeneracy temperature, which seems to be accessible in the current experiment. The density profile, equation of state, and specific heat of the polarized system have been calculated and discussed in detail. Our results are useful for the on-going experiment at Rice University on the search for FFLO states in quasi-one-dimensional polarized Fermi gases.
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We theoretically investigate excitation properties in the pseudogap regime of a trapped Fermi gas. Using a combined $T$-matrix theory with the local density approximation, we calculate strong-coupling corrections to single-particle local density of states (LDOS), as well as the single-particle local spectral weight (LSW). Starting from the superfluid phase transition temperature $T_{rm c}$, we clarify how the pseudogap structures in these quantities disappear with increasing the temperature. As in the case of a uniform Fermi gas, LDOS and LSW give different pseudogap temperatures $T^*$ and $T^{**}$ at which the pseudogap structures in these quantities completely disappear. Determining $T^*$ and $T^{**}$ over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensate) crossover region, we identify the pseudogap regime in the phase diagram with respect to the temperature and the interaction strength. We also show that the so-called back-bending peak recently observed in the photoemission spectra by JILA group may be explained as an effect of pseudogap phenomenon in the trap center. Since strong pairing fluctuations, spatial inhomogeneity, and finite temperatures, are important keys in considering real cold Fermi gases, our results would be useful for clarifying normal state properties of this strongly interacting Fermi system.
We study the out-of-equilibrium dynamics of a finite-temperature harmonically trapped Tonks-Girardeau gas induced by periodic modulation of the trap frequency. We give explicit exact solutions for the real-space density and momentum distributions of this interacting many-body system and characterize the stability diagram of the dynamics by mapping the many-body solution to the solution and stability diagram of Mathieus differential equation. The mapping allows one to deduce the exact structure of parametric resonances in the parameter space characterized by the driving amplitude and frequency of the modulation. Furthermore, we analyze the same problem within the finite-temperature hydrodynamic approach and show that the respective solutions to the hydrodynamic equations can be mapped to the same Mathieu equation. Accordingly, the stability diagram and the structure of resonances following from the hydrodynamic approach is exactly the same as those obtained from the exact many-body solution.
The mean-field properties of finite-temperature Bose-Einstein gases confined in spherically symmetric harmonic traps are surveyed numerically. The solutions of the Gross-Pitaevskii (GP) and Hartree-Fock-Bogoliubov (HFB) equations for the condensate and low-lying quasiparticle excitations are calculated self-consistently using the discrete variable representation, while the most high-lying states are obtained with a local density approximation. Consistency of the theory for temperatures through the Bose condensation point requires that the thermodynamic chemical potential differ from the eigenvalue of the GP equation; the appropriate modifications lead to results that are continuous as a function of the particle interactions. The HFB equations are made gapless either by invoking the Popov approximation or by renormalizing the particle interactions. The latter approach effectively reduces the strength of the effective scattering length, increases the number of condensate atoms at each temperature, and raises the value of the transition temperature relative to the Popov approximation. The renormalization effect increases approximately with the log of the atom number, and is most pronounced at temperatures near the transition. Comparisons with the results of quantum Monte Carlo calculations and various local density approximations are presented, and experimental consequences are discussed.
We investigate the strongly interacting hard-core anyon gases in a one dimensional harmonic potential at finite temperature by extending thermal Bose-Fermi mapping method to thermal anyon-ferimon mapping method. With thermal anyon-fermion mapping method we obtain the reduced one-body density matrix and therefore the momentum distribution for different statistical parameters and temperatures. At low temperature hard-core anyon gases exhibit the similar properties as those of ground state, which interpolate between Bose-like and Fermi-like continuously with the evolution of statistical properties. At high temperature hard-core anyon gases of different statistical properties display the same reduced one-body density matrix and momentum distribution as those of spin-polarized fermions. The Tans contact of hard-core anyon gas at finite temperature is also evaluated, which take the simple relation with that of Tonks-Girardeau gas $C_b$ as $C=frac12(1-coschipi)C_b$.
The superfluid phase diagrams of a two-dimensional cold polarized Fermi gas in the BCS-BEC crossover are systematically and analytically investigated. In the BCS-Leggett mean field theory, the transition from unpolarized superfluid phase to normal phase is always of first order. For a homogeneous system, the two critical Zeeman fields and the critical population imbalance are analytically determined in the whole coupling parameter region, and the superfluid-normal mixed phase is shown to be the ground state between the two critical fields. The density profile in the presence of a harmonic trap calculated in the local density approximation exhibits a shell structure, a superfluid core at the center and a normal shell outside. For weak interaction, the normal shell contains a partially polarized cloud with constant density difference surrounded by a fully polarized state. For strong interaction, the normal shell is totally in fully polarized state with a density profile depending only on the global population imbalance. The di-fermion bound states can survive in the whole highly imbalanced normal phase.
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