Sharp Coherence Crossover and Multimode Phase Control in Coupled Exciton-Polariton Condensates

We investigate the formation of mutual coherence and deterministic phase control in a multimode exciton-polariton system realized in two optically induced traps with tunable intertrap coupling. As the coupling channel between the traps is progressively opened, the mutual first-order coherence rises sharply from nearly zero to values close to unity, revealing a threshold-like crossover from weakly correlated to highly coherent dynamics. We demonstrate deterministic multimode phase control with a short spatially localized nonresonant pulse, which allows the phase relations between selected polariton condensate modes to be set while keeping their amplitudes nearly unchanged. The induced phase transformation is read out directly from time-resolved interferograms and realized for different sets of modes in both intermediate- and high-coherence regimes. Within a reduced four-mode description, the control pulse implements an effective phase operator on the coherent multimode field with a fidelity exceeding 0.995. The same approach can be extended to larger networks of coupled traps, offering a route to optical control over phase relations in increasingly complex multimode polariton states.