Condensate fraction of a Fermi gas in the BCS-BEC crossover, Phys

Consider the problem of the T = 0 state of a gas of interacting spin-12 fermions. As the interaction is turned on and gradually increased, the system evolves continuously from the ideal Fermi gas, to the BCS (Bardeen-Cooper-Schrieffer) state of extremely wide weakly-bound Cooper pairs, to a gas of in-creasingly tightly bound “molecular ” bosonic dimers, to finally reach the limit of an ideal Bose gas in its Bose-Einstein condensate state. As the interaction strength is varied we eval-uate the “condensate ” density of the fermion pairs, namely those particles contributing to the long-range order of the collective coher-ent state. In particular, we derive an explicit formula for the condensed fraction as a func-tion of the chemical potential and the super-conducting gap [1]. We use this relation to compute the condensate fraction in the crossover from the BCS state to the Bose-Einstein condensate of molecular dimers. By using a local density approximation we study ultracold clouds of several million alkali fermionic atoms in vapor phase, confined in magnetic traps. We compare the observed fraction of condensed atoms [2] with the outcome of our theory, and find good accord. General Theory for dilute interacting Fermi gas Consider the Hamiltonian density: H ̂ = − h̄