Thermal blurring of a coherent Fermi gas

It is generally assumed that a condensate of paired fermions at equilibrium is characterized by a macroscopic wavefunction with a well-defined, immutable phase. In reality, all systems have a finite size and are prepared at non-zero temperature; the condensate then has a finite coherence time, even when the system is isolated in its evolution and the particle number N is fixed. The loss of phase memory is due to interactions of the condensate with the excited modes that constitute a dephasing environment. This fundamental effect, crucial for applications using the condensate of pairs macroscopic coherence, was scarcely studied. In my presentation, I will link the coherence time to the condensate phase dynamics, and show with a microscopic theory that the time derivative of the condensate phase operator is proportional to a chemical potential operator that I will construct including both the pair-breaking and pair-motion excitation branches. In a single realization of energy E, the phase operator evolves at long times as -2\mu_mc(E) t where mu_mc(E) is the microcanonical chemical potential; energy fluctuations from one realization to the other then lead to a ballistic spreading of the phase and to a Gaussian decay of the temporal coherence function with a characteristic time proportional to sqrt(N).
In the absence of energy fluctuations, the coherence time scales as N due to the diffusive motion of the phase. I will also propose a method to measure the coherence time with ultracold atoms, which we predict to be tens of milliseconds for the canonical ensemble unitary Fermi gas.
Preprint: H. Kurkjian, Y. Castin, A. Sinatra, arXiv:1502.05644