Characterization and moment stability analysis of quasilinear quantum stochastic systems with quadratic coupling to external fields

The paper is concerned with open quantum systems whose Heisenberg dynamics are described by quantum stochastic differential equations driven by external boson fields. The system-field coupling operators are assumed to be quadratic polynomials of the system variables, with the latter satisfying canonical commutation relations. In combination with a cubic system Hamiltonian, this leads to quasilinear quantum stochastic systems which extend the class of linear quantum systems and yet retain algebraic closedness in the evolution of mixed moments of system variables up to any order. Although such a system is nonlinear and its quantum state is no longer Gaussian, the dynamics of the moments are amenable to exact analysis, including the computation of their steady-state values. A generalized criterion is outlined for quadratic stability of the quasilinear systems.