Temperature dependence for the synthetic magnetization of a rotating Bose gas in harmonic trap

In this paper, the temperature dependence for synthetic magnetization ¯M of a rotating Bose gas in harmonic trap and the magnetic field dependence of the critical temperature are investigated. A simple semiclassical approximation for the density of state approach is used in this study. The suggested approach simultaneously gives corrections to quantities which arise from the finite size and interatomic interaction effects. The calculated results show that the critical temperature decreases due to the increase of the synthetic magnetic field. The synthetic magnetization also exhibits a characteristic temperature dependence. It is proportional to T^3 if ¯T ¯ Tc , while it is proportional to T if ¯T ¯ Tc . The calculated results provide a solid theoretical foundation of the current experiments.