Semiclassical Hartree-Fock theory of a rotating Bose-Einstein condensation

In this paper, we investigate the thermodynamic behavior of a rotating Bose-Einstein condensation with non-zero interatomic interactions theoretically. The analysis relies on a semiclassical Hartree-Fock approximation where an integral is performed over the phase space and function of the grand canonical ensemble is derived. Subsequently, we use this result to derive several thermodynamic quantities including the condensate fraction, critical temperature, entropy and heat capacity. Thereby, we investigate the effect of the rotation rate and interactions parameter on the thermodynamic behavior. The role of finite size is discussed. Our approach can be extended to consider the rotating condensate in optical potential

Temperature dependence of the entropy and the in situ size of a rotating condensate cloud in an optical lattice

In this paper, the temperature dependence of the entropy and the in situ size (effective widths and effective area) and the expansion energy, of a rotating condensate cloud in an optical lattice are investigated. A simple semiclassical approximation, in comparison to the quantum-mechanical calculations, is suggested. The calculated results showed that the temperature dependence of the above mentioned parameters is changed in an optical lattice and depends crucially on the rotation rate. The obtained results provide useful qualitative theoretical results for future Bose Einstein condensation experiments in such traps