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All-to-all connected networks by multi-frequency excitation of polaritons

We analyze theoretically a network of all-to-all coupled polariton modes, realized by a trapped polariton condensate excited by a comb of different frequencies. In the low-density regime the system dynamically finds a state with maximal gain defined by the average intensities (weights) of the excitation beams, analogous to active mode locking in lasers, and thus solves a maximum eigenvalue problem set by the matrix of weights. The method opens the possibility to tailor a superposition of populated bosonic modes in the trapped condensate by appropriate choice of drive.