  We calculate the phase diagram of two-flavor quark matter in the
temperature-flavor asymmetry plane in the case where there are three competing
phases: the homogeneous Bardeen-Cooper-Schrieffer (BCS) phase, the unpaired
phase, and a phase with broken spatial symmetry, which is here taken to be the
counterpart of the Fulde-Ferrell (FF) phase in condensed matter physics. We
show that the system belongs to the universality class of
paramagnetic-ferromagnetic -helical systems. We vary the coupling constant of
the theory, which is obtained from integrating out the gluonic degrees of
freedom. In weak coupling, the FF phase is favored at arbitrary flavor
asymmetries for sufficiently low temperatures; at intermediate coupling its
occupancy domain is shifted towards larger asymmetries. Strong coupling
features a new regime of an inhomogeneous FF state, which we identify with a
current-carrying Bose-Einstein condensate of tightly bound up and down quarks.
We analyze the occupation numbers and the Cooper-pair wave function and show
that when the condensate momentum is orthogonal to the particle momentum the
minority component contains a blocking region (breach) around the Fermi sphere
in the weak-coupling limit, which engulfs more low-momentum modes as the
coupling is increased, and eventually leads to a topological change in strong
coupling, where the minority Fermi sphere contains either two occupied strips
or an empty sphere. For non-orthogonal momenta, the blocking region is either
reduced or extinct, i.e., no topological changes are observed.
