Phase locking of ring-shaped exciton-polariton condensates to coherent optical drive

The effect of an additional quasiresonant drive on the dynamics of the ring-shaped incoherently pumped polariton condensates carrying angular momentum (vorticity) is studied theoretically. Numerical simulations of the 2D and 1D Gross-Pitaevskii equations show that the difference of the topological charges (vorticities) Δn of the condensate and the quasiresonant coherent drive plays a crucial role in the synchronization dynamics. It is shown that in an axially symmetric system, synchronization can only occur if |Δn|=0, whereas in the other cases the phase of the condensate cannot be locked to the phase of the coherent drive. To explain this effect observed in the numerical simulations a perturbation theory is developed. The theory shows that the phase slip between the condensate and the coherent drive can be understood in terms of the motion of 2π kinks. It is shown that the breaking of the axial symmetry can stop the motion of the kinks, allowing the phase locking of the condensate to the coherent drive.