Belavkin Filtering with Squeezed Light Sources

Abstract

We derive the filtering equation for Markovian systems undergoing homodyne measurement in the situation where the output processes being monitored are squeezed. The filtering theory applies to case where the system is driven by Fock noise (that, quantum input processes in a coherent state) and where the output is mixed with a squeezed signal. It also applies to the case of a system driven by squeezed noise, but here there is a physical restriction to emission/absorption coupling only. For the special case of a cavity mode where the dynamics is linear, we are able to derive explicitly the filtered estimate ${\pi }_t(a)$ for the mode annihilator $a$ based on the homodyne quadrature observations up to time $t$.

20 pages, 4 figures (Dedicated to Slava Belavkin)

References in corpus (2)

• Feedback control of quantum state reduction
• Hamilton-Jacobi-Bellman equations for Quantum Filtering and Control

Cited by in corpus (6)

• A Quantum Extended Kalman Filter
• Quantum trajectories for a system interacting with environment in a single photon state: counting and diffusive processes
• Master equations and quantum trajectories for squeezed wave packets
• Quantum trajectories for environment in superposition of coherent states
• Quantum filtering equations for system driven by non-classical fields
• Stochastic approach to evolution of a quantum system interacting with a wave packet in squeezed number state