  The phase and the frequency of an exciton polariton condensate excited by a
nonresonant pump can be efficiently manipulated by an external coherent light.
Being tuned close to the resonance with the condensate eigenfrequency, the
external laser light imposes its frequency to the condensate and locks its
phase, thereby manifesting a synchronization effect. The conditions of
formation of the phase synchronized regime are determined. The synchronization
of a couple of closely spaced polariton condensates by a spatially uniform
coherent light is examined. At the moderate strength of the coherent driving
the synchronization is accompanied by the appearance of symmetry-breaking
states of the polariton dyad, while these states are superseded by the
symmetric state at the high-intensity driving. By employing a zero-dimensional
model of coupled dissipative oscillators with both dissipative and conservative
coupling, we study the bifurcation scenario of the symmetry-breaking state
formation.
