Critical temperature for Bose-Einstein condensation in quartic potentials

Abstract

The quartic confining potential has emerged as a key ingredient to obtain fast rotating vortices in BEC as well as observation of quantum phase transitions in optical lattices. We calculate the critical temperature Tc of bosons at which normal to BEC transition occurs for the quartic confining potential. Further more, we evaluate the effect of finite particle number on Tc and find that ΔTc/Tc is larger in quartic potential as compared to quadratic potential for number of particles <105. Interestingly, the situation is reversed if the number of particles is $\gtrsim$ 105.