General behavior for the condensation of an interacting Bose gas in an 1D optical lattice

The general behavior of the condensation of an interacting Bose gas in a combined 3D magnetic potential with 1D optical potential is theoretically investigated. A simple analytical procedure based on a piecewise density of states is used to calculate the condensate fraction and the critical temperature for this system. The calculated results showed that the condensation in this system can be founded in three different quantum phases. Transition between them are identified by the condensate fraction behavior as a function of lattice depth and the reduced temperature. I have presented results over a wide parameter regime appropriate to current experiments at NIST and ENS. The calculated results are in a good agreement with the experimental measured data of Spielman et al. (2008) [5].