Squeezed coherent state undergoing a continuous nondemolition observation

The time evolution of a squeezed coherent state conditioned by the results of a single and double heterodyne measurement is discussed. The mean values of quadratures as well as the dynamics of quadrature uncertainties have been obtained within the framework of the theory of continuous measurements based on filtration equations. It has been found that while the mean values depend on the measured noise, the uncertainties in the optical quadratures are deterministic. Explicit solutions for the latter have been provided. Finally, a time development of the squeeze parameter for the posterior squeezed coherent state has been found. -- Highlights: → The theory of continuous quantum measurement is applied. → The Belavkin linear filtering equation for the heterodyne observation is used. → The posterior evolution of a squeezed coherent state is discussed. → The posterior mean values of quadratures and their uncertainties are obtained. → A time development of the posterior squeeze parameter is found.