Dynamical Phase Transitions and Quantum Metrology in an Optical Parametric Oscillator

Optical parametric oscillators (OPOs) are increasingly explored as sources of nonclassical light, making their parameter-dependent sensitivity directly relevant for quantum metrology. We study a two-parameter OPO using a combination of mean-field analysis and full quantum simulations. In the mean-field limit, varying the parameters reorganizes the classical equilibrium points and produces distinct regions and new dynamical phase diagrams in parameter space associated with the disappearance of stable solutions and saddle points. Treating each oscillator mode as quantized, we compute the quantum Fisher information (QFI) for various initial states and find pronounced features that trace the same boundaries. Heisenberg scaling of the QFI is observed in various regimes, and the preservation of these structural signatures is assessed under dissipative dynamics.