Vortex pair annihilation in arrays of photon cavities

Abstract

We investigate theoretically the evolution of the vortex number in an array of photon condensates that is brought from an incoherent low density state to a coherent high density state by a sudden change in the pumping laser intensity. We analyze how the recombination of vortices and antivortices depends on the system parameters such as the coefficients for emission and absorption of photons by the dye molecules, the rate of tunneling between the cavities, the photon loss rate and the number of photons in the condensate. I. INTRODUCTIONVortex excitations of superfluids [1] play a crucial role in a variety of phenomena such as the Berezinskii-Kosterlitz-Thouless (BKT) transition, the Kibble-Zurek (KZ) mechanism, the formation of Abrikosov vortex lattices and the the drag force on objects moving through a superfluid. These phenomena have been experimentally studied on a number of physical platforms such as superconductors, liquid helium and ultracold atoms [2]. What all these systems have in common is that they are up to a very good approximation in (local) thermal equilibrium, a condition that is typically broken in experimental platforms that are based on optical systems [3,4]. Optical Bose-Einstein condensates (BECs) have been experimentally achieved in optical cavities filled with a dye molecule solution and in microcavities where a photon is strongly coupled to an exciton resulting in excitonpolariton [5]. While in the latter system, interactions between exciton-polaritons can lead to stimulated scattering into the ground state, in the photon-dye system it is repeated absorption and reemission of photons [6] that enables a macroscopic occupation of the ground state [7][8][9].Due to photon losses, optical BECs need constant pumping by an excitation laser in order to reach a steady state where pumping balances the losses. Experimentally realized photon condensates are therefore drivendissipative systems. The availability of several other experimental platforms, such as exciton-polaritons [4], superconducting circuits [10] and Rydberg atoms [11], for the study of driven-dissipative systems and their interest for quantum simulation and quantum computation has spurred substantial theoretical activity [4,10,12,13].A typical photon condensation experiment starts from an empty cavity and optical excitations are created by turning on the pumping laser where the phase transition is crossed when the photon density exceeds threshold. Upon crossing the threshold, the system goes from the disordered to the ordered state, which according to the KZ mechanism may lead to the formation of vortex pairs. Vortices in nonequilibrium BECs have been the subject of both experimental [14][15][16][17][18] and theoretical [19][20][21][22] study in exciton-polariton systems, whereas in nonequilibrium photon condensates, vortices have only been studied the-