Residual Quantum Effects beyond Mean‐Field Treatment in Quantum Optics Systems

Abstract

AbstractMean‐field treatment (MFT) is frequently applied to approximately predict the dynamics of quantum optics systems. It simplifies the system Hamiltonian by neglecting the quantum statistics of certain modes that are driven strongly by lasers or couple weakly with other modes. However, the neglected quantum correlations between different modes result in unanticipated quantum effects and might lead to significantly distinct system dynamics. Here, a general and systematic theoretical framework based on perturbation theory in company with MFT is provided to capture these quantum effects. The form of nonlinear dissipation and parasitic Hamiltonian as well as their relationship to the nonlinear coupling rate are predicted. Furthermore, the indicator is also proposed as a measure of the accuracy of mean‐field treatment. As an example, this theory is applied to quantum frequency conversion, in which mean‐field treatment is commonly applied, to test its limitation under strong pump and large coupling strength. The analytical results show excellent agreement with the numerical simulations. This work clearly reveals the residual quantum effects neglected by MFT and provides a more precise theoretical framework for nonlinear optics and quantum optics.