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arXiv:1307.1294 · Physical Review A

Collective excitations of a trapped Fermi gas at finite temperature

Anna Korolyuk, J. J. Kinnunen, Päivi Törmä

Published Jan 6, 2014• 19 citations
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Abstract

We study collective excitations of a trapped Fermi gas at finite temperature using the Bogoliubov--de Gennes mean-field theory in conjunction with the generalized random-phase approximation. The collective excitations are analyzed through the density response of a monopole excitation. We show the appearance of several modes at the normal-fluid--superfluid phase-transition temperature: Higgs mode--like pairing amplitude modulations, analogues of the second sound in the trapped gas, and an edge mode that is also the strongest mode in the response.

DOI
10.1103/physreva.89.013602

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We study collective excitations of a trapped Fermi gas at finite temperature using the Bogoliubov--de Gennes mean-field theory in conjunction with the generalized random-phase approximation. The collective excitations are analyzed through the density response of a monopole excitation. We show the appearance of several modes at the normal-fluid--superfluid phase-transition temperature: Higgs mode--like pairing amplitude modulations, analogues of the second sound in the trapped gas, and an edge mode that is also the strongest mode in the response.
We discuss collective monopole and quadrupole excitations of a collisionless gas of trapped Fermionic atoms in the superfluid BCS phase, comparing the fully microscopic Bogoliubov--de Gennes and quasiparticle random-phase approximation method with widely used semiclassical methods. In particular, the microscopic treatment allows us to address the questions of temperature dependence and nontrivial dependence on the trap parameters, which cannot be answered within the semiclassical approach. The main result concerning the temperature dependence is a strong Landau damping at intermediate temperature, which disappears in the limits of zero and critical temperature. However, even at zero temperature, considerable deviations from superfluid hydrodynamics are found if the trap frequency is of the same order of magnitude as the pairing gap.
We present a detailed study of the low-lying collective excitations of a spherically trapped Bose-Fermi mixture at finite temperature in the collisionless regime. The excitation frequencies of the condensate are calculated self-consistently using the static Hartree-Fock-Bogoliubov theory within the Popov approximation. The frequency shifts and damping rates due to the coupled dynamics of the condensate, noncondensate, and degenerate Fermi gas are also taken into account by means of the random-phase approximation and linear-response theory. In our treatment, the dipole excitation remains close to the bare trapping frequency for all temperatures considered, and thus is consistent with the generalized Kohn theorem. We discuss in some detail the behavior of monopole and quadrupole excitations as a function of the Bose-Fermi coupling. At nonzero temperatures we find that, as the mixture moves towards spatial separation with increasing Bose-Fermi coupling, the damping rate of the monopole (quadrupole) excitation increases (decreases). This provides us a useful signature to identify the phase transition of spatial separation.
We investigate the collective oscillations in the BCS-BEC crossover region of a trapped Fermi superfluid at T=0. We explicitly include the effect of a Feshbach resonance, which leads to a tunable pairing interaction adjusted by the threshold energy of the resonance, as well as the associated mol ecules. In a previous paper,we obtained solutions of the Bogoliubov-de Gennes coupled equations, describing a trapped Fermi superfluid ga s. Using these Bogoliubov quasi-particle excitations, we calculate the density correlation function in the Hartree-Fock-Bogoliubov generalized random phase approximation (HFB-GRPA). Previous discussions of collective modes were based on solving the T=0 equation of motion for the superfluid in a trap, ignoring the effect of single-particle excitations. We determine the frequencies of the quadrupole and the monopole modes. In the crossover region, the frequencies of these two modes are shown to be stro ngly depressed by the threshold energy of the two-particle continuum, originating from Andreev single-particle bound states (or in-gap states) localized at the edge of the trap. This effect becomes less important as one enters the BEC regime, due to the absence of these low energy fermion bound states. This suppression of collective mode frequencies by the two-particle continuum may be a useful experimental signature of the single-particle energy gap in the crossover region of trapped Fermi superfluids.
We study low-energy collective excitations in a trapped superfluid Fermi gas. These excitations originate from slow variations of the phase of the superfluid order parameter and, in this sense, are similar to the Bogolyubov sound in a homogeneous superfluid Fermi gas. Well below the critical temperature the eigenfrequencies of the lowest collective excitations are of the order of the trap frequency, and these modes manifest themselves in the density oscillations under periodic modulations of the trap frequencies. This gives a clear signature of the presence of a superfluid phase.
Abstract We study the signatures of the collective modes of a superfluid Fermi gas in its linear response functions for the order-parameter and density fluctuations in the Random Phase Approximation (RPA). We show that a resonance associated to the Popov-Andrianov (or sometimes “Higgs”) mode is visible inside the pair-breaking continuum at all values of the wavevector q, not only in the (order-parameter) modulus-modulus response function but also in the modulus-density and density-density responses. At nonzero temperature, the resonance survives in the presence of thermally broken pairs even until the vicinity of the critical temperature Tc, and coexists with both the Anderson-Bogoliubov modes at temperatures comparable to the gap Δ and with the low-velocity phononic mode predicted by RPA near Tc. The existence of a Popov-Andrianov-“Higgs” resonance is thus a robust, generic feature of the high-energy phenomenology of pair-condensed Fermi gases, and should be accessible to state-of-the-art cold atom experiments.
Phase diagrams and collective excitations are investigated for a trapped imbalanced Fermi gas in two dimensions with sss-wave pairing at finite temperatures. The treatment of collective modes is performed within the hydrodynamic approach using the Euler and continuity equations. The equations of state for different phases are simulated by a polytropic law with parameters obtained using a fit to the microscopic equilibrium distributions of the pressure and density. These are determined within the whole range of the BCS-BEC crossover using a path-integral description and taking into account fluctuations about the saddle point. We focus on the case of imbalanced gases, when the number of ``spin-up'' and ``spin-down'' fermions that form the pair is not equal. The superfluid-to-normal transition in the trapped Fermi gas is governed by the Berezinskii-Kosterlitz-Thouless mechanism. The eigenfrequencies of collective modes behave differently from those in the zero-temperature case. They can be used to study a realistic equation of state of a trapped Fermi gas at finite temperatures.