Berezinskii-Kosterlitz-Thouless crossover in a photonic lattice

We show that a periodic two-dimensional (2D) photonic lattice with Kerr nonlinearity exhibits a Berezinskii-Kosterlitz-Thouless (BKT) crossover associated with a vortex-unbinding transition. We find that averaging over random initial conditions is equivalent to Boltzmann thermal averaging with the discrete nonlinear Schro••dinger Hamiltonian. By controlling the initial randomness we can continuously vary the effective temperature. Since this Hamiltonian is in the 2D XY universality class, a BKT transition ensues. We verify this prediction using experimentally accessible observables and find good agreement between theory and simulations. This opens the possibility of experimental access to interesting phase transitions known in condensed matter using nonlinear optics.