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Chinese Physics B

Dispersion relation of excitation mode in spin-polarized Fermi gas

Ke Liu, Jisheng Chen

Published Mar 1, 2012• 0 citations
Publisher

Abstract

We study the dispersion relation of the excitation mode in a spin-polarized Fermi gas. In the frame of the imaginary-time finite temperature field theory, the polarization tensor is calculated by taking the random phase approximation. The population imbalance effects on the dispersion relation of the excitation mode and the spin-spin correlation susceptibility are investigated. The numerical results in terms of the imbalance ratio indicate the polarization effects on the dispersion relation and susceptibility χ.

DOI
10.1088/1674-1056/21/3/030309

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We study the dispersion relation of the excitation mode in a spin-polarized Fermi gas. In the frame of the imaginary-time finite temperature field theory, the polarization tensor is calculated by taking the random phase approximation. The population imbalance effects on the dispersion relation of the excitation mode and the spin-spin correlation susceptibility are investigated. The numerical results in terms of the imbalance ratio indicate the polarization effects on the dispersion relation and susceptibility χ.
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The shear viscosity has been an important topic in ultracold Fermi gases, and it has served as a diagnostic of various theories. Due to the complicated phase structures of population-imbalanced (polarized) Fermi gases with tunable attraction, past works on the shear viscosity mainly focused on unpolarized Fermi gases. Here we investigate the shear viscosity of homogeneous, population-imbalanced Fermi superfluid at finite temperatures by a pairing fluctuation theory for thermodynamical quantities and a gauge-invariant linear response theory for transport coefficients. The Cooper pairs lead to the anomalous shear viscosity analogous to the shear viscosity. We derive an exact relation connecting certain thermodynamic quantities and transport coefficients at the mean-field level for polarized unitary Fermi superfluids. An approximate relation beyond mean-field is proposed and only exhibits mild deviations from our numerical results. In the unitary and Bose-Einstein condensation (BEC) regimes, the total shear viscosity increases with the polarization because the excess majority fermions cause gapless excitations acting like a normal fluid. Moreover, competition among the excess fermions, noncondensed pairs, and fermionic quasiparticles may lead to non-monotonic behavior of the ratio between the shear viscosity and relaxation time as the polarization increases.
We develop a non-Hermitian effective theory for a repulsively interacting Fermi gas in the excited branch. The on-shell TTT-matrix is employed as a complex-valued interaction term, which describes a repulsive interaction between atoms in the excited branch and a two-body inelastic decay to the attractive branch. To see the feature of this model, we have addressed, in the weak coupling regime, the excitation properties of a repulsive Fermi polaron as well as the time-dependent number density. The analytic expressions obtained for these quantities qualitatively show a good agreement with recent experiments. By calculating the dynamical transverse spin susceptibility in the random phase approximation, we show that a ferromagnetic system with nonzero polarization undergoes a dynamical instability and tends towards a heterogeneous phase.
This thesis presents a theoretical study of strongly-interacting Fermi systems with population imbalance, which is motivated by some differences in cold atoms experiments. We calculate the energy of a single fermion interacting resonantly with a Fermi sea of different species fermions in anisotropic traps, and show that finite particle numbers and the trap geometry impact the phase structure and the critical polarization, the limit of resonance superfluidity in traps. Our findings contribute to understanding some experimental discrepancies as finite-size and confinement effects. For an imbalanced gas in the uniform system, we calculate the energy of adding an impurity, and construct the equation of state of the partially-polarized normal Fermi liquid. Finally, we study the properties of a spin-down polaron in a trapped gas containing arbitrary numbers of spin-up and spin-down fermions, and derive a self-consistent equation for the polaron energy.