Finite-temperature phase-locking transition in three-dimensional arrays of Josephson coupled Bose–Einstein condensates

We consider theoretically a phase-locking transition in Bose–Einstein condensate in an optical lattice in the regime where system can realized as a three-dimensional Josephson junction array. The coherence between adjacent Bose condensates (trapped in the valleys of the periodic potential) caused by the Josephson tunneling can lead to a phase transition with a global phase coherence at certain critical temperature. Using a model Hamiltonian of Josephson weakly coupled Bose condensates we calculate the critical temperature for the three-dimensional system placed in a simple cubic lattice and discuss the result in the context of system parameters and possible experiments. -- Highlights: ► We consider a phase-locking transition in Bose–Einstein condensate in an optical lattice. ► System can realized as a three-dimensional Josephson junction array. ► System is placed in a simple cubic lattice. ► The critical temperature of the phase-locking transition is calculated.