BEC–BCS Crossover in Strongly Interacting Matter

Abstract

A quantum field theoretical approach to the thermodynamics of dense Fermi systems is developed for the description of the formation and the dissolution of quantum condensates and bound states in dependence of temperature and density. As a model system, we study the chiral and superconducting phase transitions in two-flavor quark matter within the NJL model and their interrelation with the formation of quark–antiquark and diquark bound states. The phase diagram of quark matter is evaluated as a function of the diquark coupling strength, and a coexistence region of chiral symmetry breaking and color superconductivity is obtained at very strong coupling. The crossover between Bose–Einstein condensation of diquark bound states and condensation of diquark resonances (Cooper pairs) in the continuum is discussed as a Mott effect. This effect consists in the transition of bound states into the continuum of scattering states under the influence of compression and heating. We explain the physics of the Mott transition, with special emphasis on the role of the Pauli principle for the case of the pion in quark matter.