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arXiv:cond-mat/0605335 · Physical Review A

Ultracold polarized Fermi gas at intermediate temperatures

J.-P. Martikainen

Published Jul 11, 2006• 21 citations
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Abstract

We consider nonzero temperature properties of the polarized two-component Fermi gas. We point out that stable polarized paired states which are more stable than their phase-separated counterparts with unpolarized superfluid region can exist below the critical temperature. We also solve the system behavior in a trap using the local density approximation and find gradually increasing polarization in the center of the system as the temperature is increased. However, in the strongly interacting region the central polarization increases most rapidly close to the mean-field critical temperature, which is known to be substantially higher than the critical temperature for superfluidity. This indicates that most of the phase separation occurs in the fluctuation region prior to superfluidity and that the polarization in the actual superfluid is modest.

DOI
10.1103/physreva.74.013602

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We consider nonzero temperature properties of the polarized two-component Fermi gas. We point out that stable polarized paired states which are more stable than their phase-separated counterparts with unpolarized superfluid region can exist below the critical temperature. We also solve the system behavior in a trap using the local density approximation and find gradually increasing polarization in the center of the system as the temperature is increased. However, in the strongly interacting region the central polarization increases most rapidly close to the mean-field critical temperature, which is known to be substantially higher than the critical temperature for superfluidity. This indicates that most of the phase separation occurs in the fluctuation region prior to superfluidity and that the polarization in the actual superfluid is modest.
After an introduction into 100 years of research on superfluidity and the concept of the BCS-BEC crossover, we describe recent experimental studies of a spin-polarized Fermi gas with strong interactions. Tomographically resolving the spatial structure of an inhomogeneous trapped sample, we have mapped out the superfluid phases in the parameter space of temperature, spin polarization, and interaction strength. Phase separation between the superfluid and the normal component occurs at low temperatures, showing spatial discontinuities in the spin polarization. The critical polarization of the normal gas increases with stronger coupling. Beyond a critical interaction strength all minority atoms pair with majority atoms, and the system can be effectively described as a boson-fermion mixture. Pairing correlations have been studied by rf spectroscopy, determining the fermion pair size and the pairing gap energy in a resonantly interacting superfluid.
The density distributions of the two components of a trapped, ultracold Fermi gas with population imbalance reveal the effect of imbalance on superfluid pairing. We develop a path-integral derivation of the density, that takes into account both fluctuations beyond mean-field and effects of nonzero temperature. The calculated density profiles compare favorably to the measured density profiles, and illustrate the necessity to incorporate both quantum fluctuations and finite temperature effects. The temperature dependence of the density profiles, especially near the superfluid-normal interface, allows for determining the temperature of the superfluid core in current experiments.
The real-space densities of a polarized strongly interacting two-component Fermi gas of 6Li atoms reveal two low-temperature regimes, both with a fully paired core. At the lowest temperatures, the unpolarized core deforms with increasing polarization. Sharp boundaries between the core and the excess unpaired atoms are consistent with a phase separation driven by a first-order phase transition. In contrast, at higher temperatures the core does not deform but remains unpolarized up to a critical polarization. The boundaries are not sharp in this case, indicating a partially polarized shell between the core and the unpaired atoms. The temperature dependence is consistent with a tricritical point in the phase diagram.
After an introduction into 100 years of research on superfluidity and the concept of the BCS-BEC crossover, we describe recent experimental studies of a spin-polarized Fermi gas with strong interactions. Tomographically resolving the spatial structure of an inhomogeneous trapped sample, we have mapped out the superfluid phases in the parameter space of temperature, spin polarization, and interaction strength. Phase separation between the superfluid and the normal component occurs at low temperatures, showing spatial discontinuities in the spin polarization. The critical polarization of the normal gas increases with stronger coupling. Beyond a critical interaction strength, all minority atoms pair with majority atoms, and the system can be effectively described as a boson-fermion mixture. Pairing correlations have been studied by RF spectroscopy, determining the fermion pair size and the pairing gap energy in a resonantly interacting superfluid.
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.
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.