Quantum Fokker-Planck master equation with general signal filtering

In this paper, we derive a general master equation for continuous feedback based on arbitrary linear signals. This result is an extension of the Quantum Fokker-Planck Master Equation derived by Annby-Andersson et al (Phys. Rev. Lett. 129, 050401) to the case where the experiment has a general filtering structure. The filtering operation can include delayed information, memory effects, and non-Markovian signal processing. Using this general master equation, we derive analytical results for the ground state cooling of a quantum harmonic oscillator. We compared our results with those derived by De Sousa et al (Phys. Rev. E 111, 014152). Our framework aims to capture more realistic situations, to allow experiments to be better modeled, and to study non-Markovian effects in the spectral properties of the measurement signal.