  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 that a spatially random
photo-associative-dissociative symmetry breaking coupling of the systems. Such
coupling allows to control the relative phase between a superfluid order
parameter of the Fermi system and the condensate wavefunction of molecules for
temperatures below the BCS critical temperature. The presented mechanism of
phase control belongs to the general class of disorder-induced order phenomena
that rely on breaking of continuous symmetry.
