Phase spreading and temporal coherence of a pair-condensed Fermi gas at low temperature

Abstract

A condensate of pairs in an isolated, homogeneous, unpolarised, finite-size spin 1/2 Fermi gas at low nonzero temperature T, undergoes with time a phase change with a random component, due to coupling to the gas thermal phonons. With the quantum second Josephson relation relating the derivative of the condensate phase operator to the phonon occupation numbers, and linearised kinetic equations giving the evolution of occupation number fluctuations, we access the behaviour of the phase change variance at times much longer than the phonon collision time. The case of a convex phonon branch is similar to the Bose gas case: the leading collisional processes are the Beliaev-Landau 3-phonons processes, and the variance is the sum of a ballistic term and of a delayed diffusive term, whose analytical expressions are given in the thermodynamic limit. The concave case is more exotic. It is analysed at time scales $T^{-9}$, allowing one to restrict to 2 phonons $\to$ 2 phonons small-angle Landau-Khalatnikov processes. The total number of phonons is conserved and the phonon mean occupation numbers at equilibrium can exhibit a negative chemical potential, assumed isotropic. The phase change variance is then the sum of a ballistic term, of a diffusive term, of exotic subsubleading terms and of a constant term. The analytic expression of some of the corresponding coefficients is obtained, as well as the diverging leading behavior of the other ones when the phonon chemical potential tends to 0. When this chemical potential is 0, the variance sub-ballistic part becomes superdiffusive, with an exponent 5/3 and an exactly-known coefficient. For a nonzero infinitesimal phonon chemical potential, a law is found, interpolating between superdiffusive and diffusive phase spreading. Also new results are obtained on the phonon Landau-Khalatnikov damping rate, in particular at negative phonon chemical potential.

final version, in English (30 pages) and in French (31 pages)

References in corpus (10)

• Thermalization and its mechanism for generic isolated quantum systems
• Vortices and Superfluidity in a Strongly Interacting Fermi Gas
• Weakly bound dimers of fermionic atoms
• 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
• Genuine phase diffusion of a Bose-Einstein condensate in the microcanonical ensemble: A classical field study
• Momentum distribution of a dilute unitary Bose gas with three-body losses
• Finite temperature damping of collective modes of a BCS-BEC crossover superfluid
• Thermal blurring of a coherent Fermi gas
• Coherence time of a Bose-Einstein condensate in an isolated harmonically trapped gas