Critical temperature of a Bose–Einstein condensate in a 3D non-cubic optical lattice

In this paper, The condensation fraction and the critical temperature of the harmonically trapped Bose gas in a 3D non-cubic optical lattice, Tc, are investigated. Corrections due to the finite-size and interatomic interaction are given simultaneously. More interestingly, we have found that the condensate fraction is vanishes (experimentally the Mott-insulating phase is identified by vanishing the condensed fraction) when the recoil frequency at lattice sites are less than the geometrical average of the harmonic frequencies. The critical temperature Tc is shifted to downward due to increasing the lattice depth or the relative frequency (the ratio between recoil frequency and geometrical average of the harmonic frequencies). This shift for Tc can be controlled by adjusting the harmonic frequency. Our approach provides a solid theoretical foundation for current experiments.