Polariton XY-simulators revisited

Introduction: Arrays of bosonic condensates of exciton–polaritons have emerged as a promising platform for simulating classical XY-models, capable of rapidly reaching phase-locked states that may be mapped to arrays of two-dimensional classical spins. The relation between the collective spatial modes and minimization of the corresponding XY-Hamiltonian requires clarification. Materials and methods: Here, we develop an analytical model based on the overlap matrix of individual condensate wavefunctions, its nearest-neighbor approximation, and reservoir-fed rate equations. Results: The model gives collective spatial configurations for chains, triangular lattices, and perturbed graphs. The triangular-lattice minimum changes between ferromagnetic (FM) and frustrated antiferromagnetic (AFM) order with the outflow wavevector. Near threshold, the normalized growth rates depend on pump overlap and mode losses. The small-array simulations illustrate the development of intensity patterns over 100 ps. Conclusions: The model relates spatial interference in polariton lattices to XY-type phase configurations and identifies how the pump geometry enters the condensation threshold. It provides a basis for studying the dynamics of mode selection.