Abstract
We consider a mixture of a superfluid Fermi gas of ultracold atoms and a Bose-Einstein condensate of molecules possessing a continuous U(1) (relative phase) symmetry. We study the effects of a spatially random photo-associative–dissociative symmetry-breaking coupling of the systems. Such coupling allows one to control the relative phase between a superfluid order parameter of the Fermi system and the condensate wave function of molecules for temperatures below the Bardeen-Cooper-Schriefer critical temperature. The presented mechanism of phase control belongs to the general class of phenomena in which disorder interacts with continuous symmetry. Our results show the robustness and wide range of applicability of disorder-induced order and are valid for both disordered and regular couplings. Here, the effect is studied in the case of interacting fermionic and bosonic gases in the superfluid phase.