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Estimating the state of a One-sided quantum Cavity Driven by Vacuum field in Schrödinger Picture

A major component of establishing quantum technologies in the quantum optic platform is the cavity. This paper concerns state estimation (filtering) of a quantum one-sided cavity driven by a vacuum field while the output field is monitored by either Homodyne or photodetector. The stochastic master equation in the schrödinger picture is presented for Homodyne and photon measurements. Then, the infinite state space of the cavity is truncated by considering some reasonable simplifying assumptions. Finally, the number of photons in the cavity is estimated using the derived equations. Simulation results are validated by demonstrating that the average of several paths of the derived filter matches the corresponding master equation.