Squeezed coherent state undergoing a continuous nondemolition observation

TL;DR

This paper analyzes how a squeezed coherent state evolves under continuous nondemolition observation, revealing deterministic quadrature uncertainties and providing explicit solutions for the state’s dynamics.

Contribution

It presents explicit solutions for the evolution of a squeezed coherent state under continuous measurement, highlighting the deterministic nature of quadrature uncertainties.

Findings

Quadrature uncertainties are deterministic during continuous measurement.

Explicit solutions for the state’s evolution are derived.

The squeeze parameter’s time development is characterized.

Abstract

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.