BCS-BEC crossovers and unconventional phases in dilute nuclear matter

We study the phase diagram of isospin-asymmetrical nuclear matter in the density-temperature plane, allowing for four competing phases of nuclear matter: (i) the unpaired phase, (ii) the translationally and rotationally symmetric, but isospin-asymmetrical BCS condensate, (iii) the current-carrying Larkin-Ovchinnikov-Fulde-Ferrell phase, and (iv) the heterogeneous phase-separated phase. The phase diagram of nuclear matter composed of these phases features two tri-critical points in general, as well as crossovers from the asymmetrical BCS phase to a BEC of deuterons plus a neutron gas, both for the homogeneous superfluid phase (at high temperatures) and for the heterogeneous phase (at low temperatures). The BCS-BEC type crossover in the condensate occurs as the density is reduced. We analyze in detail some intrinsic properties of these phases, including the Cooper-pair wave function, the coherence length, the occupation numbers of majority and minority nucleonic components, and the dispersion relations of quasiparticle excitations about the ground state. We show by explicit examples that the physics of the individual phases and the transition from weak to strong coupling can be well understood by tracing the behavior of these quantities.