A mean-field model for condensates in the BEC-BCS crossover regime

Zhang Deng

Cheng Chin

We present a mean-field model to describe condensates in the BEC-BCS crossover regime based on pairs of fermionic atoms. By introducing an effective potential, the mean-field equation allows us to calculate the chemical potential, the equation of states, and the atomic correlation function. The results agree surprisingly well with recent many-body calculations. We show that the smooth crossover from the bosonic mean-field repulsion between molecules to the Fermi pressure among atoms is associated with the evolution of the atomic correlation function.

Wei Zhang, Guin-Dar Lin, L.-M. Duan

We study the crossover of a quasi-two-dimensional Fermi gas trapped in the radial plane from the Bardeen-Cooper-Schrieffer (BCS) regime to the Bose-Einstein condensation (BEC) regime by crossing a wide Feshbach resonance. We consider two effective two-dimensional Hamiltonians within the mean-field level, and calculate the zero-temperature cloud size and number density distribution. For a model 1 Hamiltonian with renormalized atom-atom interaction, we observe a constant cloud size for arbitrary detunings. For a model 2 Hamiltonian with renormalized interactions between atoms and dressed molecules, the cloud size deceases from the BCS to BEC side, which is consistent with the picture of BCS-BEC crossover. This qualitative discrepancy between the two models indicates that the inclusion of dressed molecules is essential for a mean-field description of quasi-two-dimensional Fermi systems, especially on the BEC side of the Feshbach resonance.

Alfred Hammond, L. Lavoine, Alessio Recati +2 more

Filippo Pascucci, Luca Salasnich

We investigate the macroscopic quantum tunneling of fermionic superfluids in the two-dimensional BCS-BEC crossover by using an effective tunneling energy which explicitly depends on the condensate fraction and the chemical potential of the system. We compare the mean-field effective tunneling energy with the beyond-mean-field one, finding that the mean-field tunneling energy is not reliable in the BEC regime of the crossover. Then we solve the Josephson equations of the population imbalance and the relative phase, calculating the frequency of tunneling oscillation both in the linear regime and in the nonlinear one. Our results show that the Josephson frequency is higher in the intermediate regime of the BCS-BEC crossover due to the peculiar behavior of the effective tunneling energy in the crossover.

William Hoston