Stabilizing preparation of quantum Gaussian states via continuous measurement

This paper provides a stabilizing method for preparation of quantum Gaussian states by utilizing continuous measurement. We first present a necessary and sufficient condition for the Riccati equation of the covariance matrix of the Gaussian states to have a unique stabilizing steady solution. Then general parametric conditions of how to prepare a Gaussian state with desired covariance matrix are provided. These conditions are much weaker than those required when preparing Gaussian states via dissipation-induced approach. Thus, our method provides more degrees of freedom to choose the system Hamiltonian and the system–environment coupling operators. These results may benefit practical experimental implementations in preparing quantum Gaussian states.