Dynamical Superfluid and Bose-Insulator Phases in Quantized Polariton Lattices

We demonstrate that Hilbert-space quantization in polariton lattices-manifested as multiple quantized energy levels in strongly confined sites-provides an unconventional route to realizing and manipulating different quantum phases. We show that nonlinear interactions transfer population into excited on-site quantum levels, which acts as an intrinsic dynamical channel controlling quantum coherence across the lattice. While weak nonlinearity confines polaritons to the lowest mode, yielding a robust superfluid phase with broken U(1) symmetry, strong nonlinearity induces phase diffusion through inter-level mixing. This dynamically generated fluctuations suppress global phase coherence and drives the system into a dynamical Bose-insulating phase. The changes between these phases occurs either as a nonequilibrium phase transition or a sharp crossover.