Phase operators and blurring time of a pair-condensed Fermi gas

TL;DR

This paper derives the collapse time of the order parameter in a pair-condensed Fermi gas, linking it to atom number fluctuations and chemical potential derivatives, using multiple theoretical frameworks.

Contribution

It introduces two distinct phase operators for the fermionic field and compares their roles in the dynamics of the condensate, extending beyond mean field theory.

Findings

Derived microscopic expression for blurring time.

Compared two phase operators and explained their differences.

Extended analysis beyond mean field approximation.

Abstract

Due to atomic interactions and dispersion in the total atom number, the order parameter of a pair-condensed Fermi gas experiences a collapse in a time that we derive microscopically. As in the bosonic case, this blurring time depends on the derivative of the gas chemical potential with respect to the atom number and on the variance of that atom number. The result is obtained first using linearized time-dependent Bogoliubov-de Gennes equations, then in the Random Phase Approximation, and then it is generalized to beyond mean field. In this framework, we construct and compare two phase operators for the paired fermionic field: The first one, issued from our study of the dynamics, is the infinitesimal generator of adiabatic translations in the total number of pairs. The second one is the phase operator of the amplitude of the field of pairs on the condensate mode. We explain that these two operators differ due to the dependence of the condensate wave function on the atom number.