  This paper provides a stabilizing preparation method for quantum Gaussian
states by utilizing continuous measurement. The stochastic evolution of the
open quantum system is described in terms of the quantum stochastic master
equation. We present necessary and sufficient conditions for the system to have
a unique stabilizing steady Gaussian state. The conditions are much weaker than
those existing results presented in the approach of preparing Gaussian states
through environment engineering. Parametric conditions of how to prepare an
arbitrary pure Gaussian state are provided. This approach provides more degrees
of freedom to choose the system Hamiltonian and the system-environment coupling
operators, as compared with the case where dissipation-induced approach is
employed. The stabilizing conditions for the case of imperfect measurement
efficiency are also presented. These results may benefit practical experimental
implementation in preparing quantum Gaussian states.
