Three-phonon and four-phonon interaction processes in a pair-condensed Fermi gas

Abstract

We study the interactions among phonons and the phonon lifetime in a pair-condensed Fermi gas in the BEC-BCS crossover in the collisionless regime. To compute the phonon-phonon coupling amplitudes we use a microscopic model based on a generalized BCS Ansatz including moving pairs, which allows for a systematic expansion around the mean field BCS approximation of the ground state. We show that the quantum hydrodynamic expression of the amplitudes obtained by Landau and Khalatnikov apply only on the energy shell, that is for resonant processes that conserve energy. The microscopic model yields the same excitation spectrum as the Random Phase Approximation, with a linear (phononic) start and a concavity at low wave number that changes from upwards to downwards in the BEC-BCS crossover. When the concavity of the dispersion relation is upwards at low wave number, the leading damping mechanism at low temperature is the Beliaev-Landau process 2 phonons $\leftrightarrow$ 1 phonon while, when the concavity is downwards, it is the Landau-Khalatnikov process 2 phonons $\leftrightarrow$ 2 phonons. In both cases, by rescaling the wave vectors to absorb the dependence on the interaction strength, we obtain a universal formula for the damping rate. This universal formula corrects and extends the original analytic results of Landau and Khalatnikov [ZhETF {\bf 19}, 637 (1949)] for the $2\leftrightarrow 2$ processes in the downward concavity case. In the upward concavity case, for the Beliaev 1$\leftrightarrow$ 2 process for the unitary gas at zero temperature, we calculate the damping rate of an excitation with wave number $q$ including the first correction proportional to $q^7$ to the $q^5$ hydrodynamic prediction, which was never done before in a systematic way.

in english (published version except for single column presentation, 44 pages) and in french (35 pages, double column)

References in corpus (14)

• Vortices and Superfluidity in a Strongly Interacting Fermi Gas
• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• Collective excitations of a degenerate gas at the BEC-BCS crossover
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Extension of Bogoliubov theory to quasi-condensates
• Viscosity and scale invariance in the unitary Fermi gas
• Shear viscosity of a superfluid Fermi gas in the unitarity limit
• Density Functional Theory for non-relativistic Fermions in the Unitarity Limit
• Concavity of the collective excitation branch of a Fermi gas in the BEC-BCS crossover
• Non-diffusive phase spreading of a Bose-Einstein condensate at finite temperature
• Thermal blurring of a coherent Fermi gas
• Beliaev damping of the Goldstone mode in atomic Fermi superfluids
• Effective theory for the Goldstone field in the BCS-BEC crossover at T=0
• Landau-Khalatnikov phonon damping in strongly interacting Fermi gases

Cited by in corpus (15)

• Universal Sound Diffusion in a Strongly Interacting Fermi Gas
• Pair-Breaking Collective Branch in BCS Superconductors and Superfluid Fermi Gases
• Prethermalization to thermalization crossover in a dilute Bose gas following an interaction ramp
• Phononic collective excitations in superfluid Fermi gases at nonzero temperatures
• Low-momentum dynamic structure factor of a strongly interacting Fermi gas at finite temperature: The Goldstone phonon and its Landau damping
• Absorption and emission of a collective excitation by a fermionic quasiparticle in a Fermi superfluid
• Collective excitation branch in the continuum of pair-condensed Fermi gases : analytical study and scaling laws
• Superfluid Optomechanics with Phononic Nanostructures
• Beyond mean-field corrections to the quasiparticle spectrum of superfluid Fermi gases
• Phonon damping in a 2D superfluid: insufficiency of Fermi's golden rule at low temperature
• Anderson-Bogoliubov collective excitations in superfluid Fermi gases at nonzero temperatures
• Damping of elementary excitations in one-dimensional dipolar Bose gases
• Dispersion of first sound in a weakly interacting ultracold Fermi liquid
• Comment on "Excitation Spectrum and Superfluid Gap of an Ultracold Fermi Gas"
• Low-Lying Collective Excitations of Superconductors and Charged Superfluids