Finite-temperature Effect in Phase Transition to Superfluidity for Bose–Einstein Condensates in a 1-D Optical Lattice

Abstract

We experimentally study the phase transition of ⁸⁷Rb Bose–Einstein condensates adiabatically loaded to a combined trap of a 1D optical lattice and a magnetic trap. The phase coherence property of this system is probed by recording the interference pattern of the expanded atomic cloud suddenly released from the combined trap. We show that as the temperature is sufficiently low (below the critical temperature T _C ), an interference pattern has a “peak on a peak” feature which is a true signature of macroscopic superfluid states. The normal gas only contributes to the broad background and three wide peaks in an interference pattern. These observations qualitatively agree with the recent theoretical predictions (Diener et al. in Phys. Rev. Lett. 98:180404, 2007; Kato et al. in Nat. Phys. 4:617, 2008). We also computed both the critical temperature and the interference pattern for a practical combined trap as ours in the tight-binding limit, and the numerical results are consistent with our experimental observations.