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arXiv:0711.4615 · Physical Review A

Equation of state and phases of a polarized unitary Fermi gas

S. Y. Chang

Published May 23, 2008• 4 citations
arXivHTMLPDF

Abstract

The equation of state of the partially polarized two component Fermi gas at zero temperature in the unitary limit is computed by the ab initio auxiliary field Monte Carlo method. From this, we obtain the critical ratio of the chemical potentials ${\ensuremath{\mu}}_{\ensuremath{\downarrow}}∕{\ensuremath{\mu}}_{\ensuremath{\uparrow}}$ at the phase transitions. The value of ${\ensuremath{\mu}}_{\ensuremath{\downarrow}}∕{\ensuremath{\mu}}_{\ensuremath{\uparrow}}$ at the transition between the fully paired superfluid and the partially polarized phases is 0.11, while the critical value at the phase transition between the partially polarized phase and the fully polarized normal fluid is $\ensuremath{-}0.59$. We also determine the radial boundaries of the phase transitions of the Fermi gas in the harmonic trap as a function of the total polarization. We find that beyond the critical polarization 0.65, the fully paired superfluid core disappears in the trapped Fermi gas.

DOI
10.1103/physreva.77.051602

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The equation of state of the partially polarized two component Fermi gas at zero temperature in the unitary limit is computed by the ab initio auxiliary field Monte Carlo method. From this, we obtain the critical ratio of the chemical potentials \ensuremathμ\ensuremath↓∕\ensuremathμ\ensuremath↑{\ensuremath{\mu}}_{\ensuremath{\downarrow}}∕{\ensuremath{\mu}}_{\ensuremath{\uparrow}}\ensuremathμ\ensuremath↓​∕\ensuremathμ\ensuremath↑​ at the phase transitions. The value of \ensuremathμ\ensuremath↓∕\ensuremathμ\ensuremath↑{\ensuremath{\mu}}_{\ensuremath{\downarrow}}∕{\ensuremath{\mu}}_{\ensuremath{\uparrow}}\ensuremathμ\ensuremath↓​∕\ensuremathμ\ensuremath↑​ at the transition between the fully paired superfluid and the partially polarized phases is 0.11, while the critical value at the phase transition between the partially polarized phase and the fully polarized normal fluid is \ensuremath−0.59\ensuremath{-}0.59\ensuremath−0.59. We also determine the radial boundaries of the phase transitions of the Fermi gas in the harmonic trap as a function of the total polarization. We find that beyond the critical polarization 0.65, the fully paired superfluid core disappears in the trapped Fermi gas.
Using many-body results available from diagrammatic and ab initio Monte Carlo calculations we analyze the phase diagram $\ensuremath{\mu}=({\ensuremath{\mu}}_{\ensuremath{\uparrow}}+{\ensuremath{\mu}}_{\ensuremath{\downarrow}})/2$ versus $h=({\ensuremath{\mu}}_{\ensuremath{\uparrow}}\ensuremath{-}{\ensuremath{\mu}}_{\ensuremath{\downarrow}})/2$ of a unitary Fermi gas at zero temperature with population imbalance and unequal masses. We identify different regions where the gas is superfluid, partially polarized or fully polarized, and determine the corresponding coexistence conditions. The asymmetry in the phase diagram, caused by the mass imbalance, and its effect on the Chandrasekhar-Clogston limit for the critical polarization are explicitly discussed. The equation of state of the superfluid and normal phases is employed, within the local density approximation, to predict phase separated configurations in the presence of harmonic trapping potentials.
We investigate the phase diagram of asymmetric two-component Fermi gases at zero temperature as a function of polarization and interaction strength. The equations of state of the uniform superfluid and normal phase are determined using quantum Monte Carlo simulations. We find three different mixed states, where the superfluid and the normal phase coexist in equilibrium, corresponding to phase separation between (a) the polarized superfluid and the fully polarized normal gas, (b) the polarized superfluid and the partially polarized normal gas, and (c) the unpolarized superfluid and the partially polarized normal gas.
In this thesis we first review the theory of the normal state of the unitary Fermi gas at T = 0 and the main properties of the normal-to-superfluid transition. Then we study the trapped gas under adiabatic rotation, i.e., avoiding the formation of vortices. We show that for polarized systems the rotation enhances the Chandrasekhar-Clogston limit due to pair breaking at the border between the superfluid and the normal phase, while it leaves the global critical polarization Pc of the trapped system unaffected. In the case of an unpolarized unitary superfluid the rotation causes a phase separation between a superfluid core and an unpolarized normal shell, in which the densities of the spin-up and spin-down atom numbers is equal. For both the polarized and the unpolarized systems we calculate experimental observables such as the density profiles and the angular momenta. From the study of Bose-Einstein condensates it is well known that an adiabatic rotation induces a quadrupole deformation of the trapped atomic cloud when the rotation exceeds a certain angular velocity. In Fermi gases the situation is different due to the phase separation discussed above, and the quadrupole instabilities are found to set on at smaller angular velocity than in the BEC case. This phenomenon together with a more general discussion concerning not only the energetic but also the dynamic instabilities of the phase separated system is presented. We use the present knowledge of the equation of state of Fermi mixtures with unequal masses to give quantitative predictions for the phase separation between the normal and superfluid components. The analysis is based on the study of the zero temperature μ-h phase diagram of the uniform two component gas. The phase diagram at unitarity is determined thanks to the knowledge of the equation of state available from diagrammatic techniques applied to highly polarized configurations and from Monte Carlo simulations. The phase diagram is then used, in the local density approximation, to calculate the density profiles of the two Fermi components in the presence of harmonic trapping. Eventually we investigate the polarization produced by the relative displacement of the potentials trapping two spin species of a unitary Fermi gas with population imbalance. We investigate the dipole polarizability of a polarized system both in the two-fluid and the three-fluid model at zero temperature and point out the major differences between the two treatments.
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 in a fully polarized state with a density profile depending only on the global population imbalance. The difermion bound states can survive in the whole highly imbalanced normal phase.
Abstract We investigate the superfluid-to-normal zero temperature quantum phase transitions of asymmetric two-component Fermi gases as a function of the chemical potential imbalance h . The calculations are performed for homogeneous and trapped imbalanced systems. We concentrate at unitarity, characterized by a divergent interaction parameter k F a , where most of the current experiments are realized. For homogeneous systems, we determine the critical chemical potential imbalance h c at which possible phase transitions occur. In the case of trapped gases, we show how h c can be consistently determined from experimental observations.
We study the zero temperature properties of a trapped polarized Fermi gas at unitarity by assuming phase separation between an unpolarized superfluid and a polarized normal phase. The effects of the interaction are accounted for using the formalism of quasiparticles to build up the equation of state of the normal phase with the Monte Carlo results for the relevant parameters. Our predictions for the Chandrasekhar-Clogston limit of critical polarization and for the density profiles, including the density jump at the interface, are confirmed with excellent accuracy by the recent experimental results at MIT. The role of interaction on the radial width of the minority component, on the gap of spectral functions, and on the spin oscillations in the normal phase is also discussed. Our analysis points out the Fermi liquid nature of these strongly interacting spin-polarized configurations.