Berezinskii-Kosterlitz-Thouless transition in two-dimensional arrays of Josephson coupled Bose-Einstein condensates

We study the phase transition occurring in Bose-Einstein condensates placed in an optical lattice where the system is arranged in a form of a two-dimensional bosonic Josephson junction array. It is shown that the Josephson interaction between adjacent condensates (trapped in the valleys of the periodic lattice potential) can trigger Berezinskii-Kosterlitz-Thouless transition at a finite temperature TKT to the ordered state composed of bound vortex-antivortex phase-field configurations of individual condensates. Using a lattice model of the bosonic Josephson junction array, we derive the effective phase-only Hamiltonian and calculate the critical temperature TKT. Finally, we discuss the results in the context of system parameters and possible experiments.