Modified Research Of Thermodynamic Properties For Bose Einstein Condensing Gas

Bose-Einstein condensation (BEC) is science masters Einstein predicted a new state of matter in80years ago. Here the condensed is different from the usual condensed, it expressed that the atoms of different state suddenly condensed to the same state (usually the ground state). That is atoms in a different states together to the same kind of states.BEC has become one of the hot spot in the research of contemporary physics, this paper research content for:First of all, we recalled about the history of Bose-Einstein and simply described the current results in the experiment and theory in recent years.Secondly, The research and influences of the finite size and interaction effects for the thermodynamic properties of BEC is very importantly. In the framework of the semiclassical approximation (KBT>>hΩ), an accurate ansatz formula for the density of states is suggested.This formula is able to include the finite size and interatomic interaction effects simultaneously,in anisotropic confining potential trap.The condensed fraction of BEC、critical temperature and the average energy of atoms is calculated, the theoretical calculated value is in a good agreement with the experimental measured value and also the same to the other theoretical calculation results.Finally,after research of these thermodynamic properties of BEC, the method of density of state is generalized to optical lattice potential,The condensed fraction and critical temperature in an optical lattice are calculated by using an accurate formula for the density of states, at the same time considering the influence of the finite size effects and interaction effects. Discussing about when some conditions is changed,how to change for these thermodynamic properties.Interestingly, we found when the recoil frequency in optical lattice are less than the geometrical average of the harmonic frequency, the condensed fraction is vanishing;increasing optical lattice depths or relative frequency (the ratio of the recoil frequency of the optical lattice and the geometrical average of the harmonic frequency) leads to the critical temperature Tc decreasing. The reduced value can be calculated by controlling the harmonic frequency. Our research methods provides certain theoretical foundation for the experiments of the optical lattice today.