Abstract
We calculate the sound velocity and the damping rate of the collective excitations of a 2D fermionic superfluid in a non-perturbative manner. Specifically, we focus on the Anderson–Bogoliubov excitations in the BEC-BCS crossover regime, as these modes have a sound-like dispersion at low momenta. The calculation is performed within the path-integral formalism and the Gaussian pair fluctuation approximation. From the action functional, we obtain the propagator of the collective excitations and determine their dispersion relation by locating the poles of this propagator. We find that there is only one kind of collective excitation, which is stable at T = 0 and has a sound velocity of v F / 2 for all binding energies, i.e., throughout the BEC-BCS crossover. As the temperature is raised, the sound velocity decreases and the damping rate shows a non-monotonous behavior: after an initial increase, close to the critical temperature T C the damping rate decreases again. In general, higher binding energies provide higher damping rates. Finally, we calculate the response functions and propose that they can be used as another way to determine the sound velocity.
Highlights
Collective excitations in ultra-cold atomic Fermi gases are a subject of intense experimental [1,2,3,4,5,6,7,8] and theoretical [9,10,11,12,13,14] research, because their spectra provide valuable information on the internal states of the atomic system
The microscopic Gaussian pair fluctuation (GPF) method is complementary to the frequently used two-fluid hydrodynamic approximation, which is capable of obtaining the sound velocity in both uniform and trapped quantum gases, see, e.g., References [18,19,20], and is effectively used to study collective properties, such as density distribution, discrete collective modes of a trapped gas, and the sound velocity in the BCS-BEC crossover
The fluctuation propagator is in turn obtained via an expansion of the matrix elements of the GPF action up to the second order in powers of q
Summary
Collective excitations in ultra-cold atomic Fermi gases are a subject of intense experimental [1,2,3,4,5,6,7,8] and theoretical [9,10,11,12,13,14] research, because their spectra provide valuable information on the internal states of the atomic system. In recent works [12,13,14], the eigenfrequencies and damping rates of different collective excitations (phonons, pair-breaking “Higgs”modes, Leggett modes) have been calculated in a non-perturbative way within the Gaussian pair fluctuation (GPF) approach based on the GPF effective bosonic action [15,16,17] These studies are related to fermionic systems in three dimensions. The microscopic GPF method is complementary to the frequently used two-fluid hydrodynamic approximation, which is capable of obtaining the sound velocity in both uniform and trapped quantum gases, see, e.g., References [18,19,20], and is effectively used to study collective properties, such as density distribution, discrete collective modes of a trapped gas, and the sound velocity in the BCS-BEC crossover These two approaches can be applied in parallel which is significant for a comparison and verification of results. Both methods have their own advantages: the hydrodynamic approach can lead to good results for many observables at a low cost, while the microscopic approach allows us to derive both the eigenfrequencies and damping factors of collective modes mutually consistently
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