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arXiv:1712.08318 · Physical Review A

Low-momentum dynamic structure factor of a strongly interacting Fermi gas at finite temperature: The Goldstone phonon and its Landau damping

Peng Zou, Hui Hu, Xia-Ji Liu

Published Jul 16, 2018• 20 citations
arXivHTMLPDF

Abstract

We develop a microscopic theory of the dynamic structure factor to describe the Bogoliubov-Anderson-Goldstone phonon mode and its damping rate in a strongly interacting Fermi gas at finite temperature. It is based on a density functional approach---the so-called superfluid local density approximation. The accuracy of the theory is quantitatively examined by comparing the theoretical predictions with recent experimental measurements for the local dynamic structure factor of a nearly homogeneous unitary Fermi gas at low transferred momentum [S. Hoinka et al., Nat. Phys. 13, 943 (2017)], without any free parameters. We calculate the dynamic structure factor as functions of temperature and transferred momentum, and determine the temperature evolution of the phonon damping rate, by considering the dominant decay process of the phonon mode via scatterings off fermionic quasiparticles. These predictions can be confronted with future Bragg scattering experiments on a unitary Fermi gas near the superfluid transition.

DOI
10.1103/physreva.98.011602

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•Jan 1, 2014•0 citations
We develop a microscopic theory of the dynamic structure factor to describe the Bogoliubov-Anderson-Goldstone phonon mode and its damping rate in a strongly interacting Fermi gas at finite temperature. It is based on a density functional approach---the so-called superfluid local density approximation. The accuracy of the theory is quantitatively examined by comparing the theoretical predictions with recent experimental measurements for the local dynamic structure factor of a nearly homogeneous unitary Fermi gas at low transferred momentum [S. Hoinka et al., Nat. Phys. 13, 943 (2017)], without any free parameters. We calculate the dynamic structure factor as functions of temperature and transferred momentum, and determine the temperature evolution of the phonon damping rate, by considering the dominant decay process of the phonon mode via scatterings off fermionic quasiparticles. These predictions can be confronted with future Bragg scattering experiments on a unitary Fermi gas near the superfluid transition.
We theoretically investigate the dynamic structure factor of a strongly interacting Fermi gas at the crossover from Bardeen–Cooper–Schrieffer superfluids to Bose–Einstein condensates, by developing an improved random phase approximation within the framework of a density functional theory (DFT)—the so-called superfluid local density approximation. Compared with the previous random-phase-approximation studies based on the standard Bogoliubov–de Gennes equations, the use of the DFT greatly improves the accuracy of the equation of state at the crossover, and leads to a better description of both collective Bogoliubov-Anderson-Goldstone phonon mode and single-particle fermionic excitations at small transferred momentum. Near unitarity, where the s -wave scattering length diverges, we show that the single-particle excitations start to significantly contribute to the spectrum of dynamic structure factor once the frequency is above a threshold of the energy gap at . The sharp rise in the spectrum at this threshold can be utilized to measure the pairing gap Δ. Together with the sound velocity determined from the phonon branch, the dynamic structure factor provides us some key information of the crossover Fermi superfluid. Our predictions could be examined in experiments with 6 Li or 40 K atoms using Bragg spectroscopy.
We provide a description of the dynamic structure factor of a homogeneous unitary Fermi gas at low momentum and low frequency, based on the dissipative two-fluid hydrodynamic theory. The viscous relaxation time is estimated and is used to determine the regime where the hydrodynamic theory is applicable and to understand the nature of sound waves in the density response near the superfluid phase transition. By collecting the best knowledge on the shear viscosity and thermal conductivity known so far, we calculate the various diffusion coefficients and obtain the damping width of the (first and second) sounds. We find that the damping width of the first sound is greatly enhanced across the superfluid transition and very close to the transition the second sound might be resolved in the density response for the transferred momentum up to half of Fermi momentum. Our work is motivated by the recent measurement of the local dynamic structure factor at low momentum at Swinburne University of Technology and the ongoing experiment on sound attenuation of a homogeneous unitary Fermi gas at Massachusetts Institute of Technology. We discuss how the measurement of the velocity and damping width of the sound modes in low-momentum dynamic structure factor may lead to an improved determination of the universal superfluid density, shear viscosity, and thermal conductivity of a unitary Fermi gas.
We present a theoretical investigation of the dynamic density structure factor of a strongly interacting Fermi gas near the Feshbach resonance at finite temperature, which can be exploited in two photon Bragg scattering experiments. This study is based on a fully gauge invariant linear response theory, which is consistent with a diagrammatic approach for the equilibrium state taking into account the pair fluctuation effects and respects important restrictions like the f -sum rule. At small incoming momentum, the dynamic density structure factor exhibits various features including the Nambu-Goldstone-mode peak and the quasiparticle-scattering, pairing-breaking continua. At large incoming momentum and at half recoil frequency, the structure factor has a qualitatively similar behavior as the order parameter, which can signify the appearance of the condensate. These results qualitatively agree with the recent Bragg spectroscopy experiments.
We present an experimental and theoretical study of the phonon mode in a unitary Fermi gas. Using two-photon Bragg spectroscopy, we measure excitation spectra at a momentum of approximately half the Fermi momentum, both above and below the superfluid critical temperature T_{c}. Below T_{c}, the dominant excitation is the Bogoliubov-Anderson (BA) phonon mode, driven by gradients in the phase of the superfluid order parameter. The temperature dependence of the BA phonon is consistent with a theoretical model based on the quasiparticle random phase approximation in which the dominant damping mechanism is via collisions with thermally excited quasiparticles. As the temperature is increased above T_{c}, the phonon evolves into a strongly damped collisional mode, accompanied by an abrupt increase in spectral width. Our study reveals strong similarities between sound propagation in the unitary Fermi gas and bosonic liquid helium.
Theoretical predictions for the dynamic structure factor of a harmonically trapped Fermi superfluid near the Bose-Einstein condensate--Bardeen-Cooper-Schrieffer (BEC-BCS) crossover are compared with recent Bragg spectroscopy measurements at large transferred momenta. The calculations are based on a random-phase (or time-dependent Hartree-Fock-Gorkov) approximation generalized to the strongly interacting regime. Excellent agreement with experimental spectra at low temperatures is obtained, with no free parameters. Theoretical predictions for zero-temperature static structure factor are also found to agree well with the experimental results and independent theoretical calculations based on the exact Tan relations. The temperature dependence of the structure factors at unitarity is predicted.
We use mean-field theory to investigate the dynamics of superfluid fermions. This thesis includes our two works. The first one is to study Josephson oscillations and self-trapping of superfluid fermions in a double-well potential with time-dependent Bogoliubov-de Gennes equations. We investigate the behaviour of a two-component Fermi superfluid. We numerically solve the time-dependent Bogoliubov-de Gennes equations and characterize the regimes of Josephson oscillations and self-trapping for different potential barriers and initial conditions. In the weak link limit the results agree with a two-mode model where the relative population and the phase difference between the two wells obey coupled nonlinear Josephson equations. A more complex dynamics is predicted for large amplitude oscillations and large tunneling. The second one is to calculate the dynamic structure factor of unitary fermions. We have studied the dynamic structure factor of unitary fermions both at zero and finite temperature using the Bogoliubov-de Gennes theory and also Superfluid Local Density Approximation. We have derived the expression of the linear response function and the dynamic structure factor in the random phase approximation. At zero temperature, the SLDA+RPA formalism indeed provides a better accuracy at low momentum transfer and also its static structure factor is closer to quantum Monte Carlo value than that in BdG+RPA; however SLDA seems to give worse results for the molecular excitations at large momentum transfer. We have discussed the role of temperature and the comparison between SLDA and BdG, as well as with experimental data. The analysis is still at a preliminary level, but it suggests that mean-field theories can indeed be used to extract quantitative information about the order parameter and the excitations of the system by two-photon Bragg scattering experiments.