Quantum Fokker-Planck Master Equation for Continuous Feedback Control

• URL: http://arxiv.org/abs/2110.09159v2
• Date: Wed, 10 Aug 2022 09:46:33 GMT
• Title: Quantum Fokker-Planck Master Equation for Continuous Feedback Control
• Authors: Bj\"orn Annby-Andersson, Faraj Bakhshinezhad, Debankur Bhattacharyya, Guilherme De Sousa, Christopher Jarzynski, Peter Samuelsson, Patrick P. Potts
• Abstract summary: Measurement and feedback control are essential features of quantum science, with applications ranging from quantum technology protocols to information-to-work conversion in quantum thermodynamics. Here we present a formalism for continuous quantum measurement and feedback, both linear and nonlinear. Our main result is a quantum Fokker-Planck master equation describing the joint dynamics of a quantum system and a detector with finite bandwidth. For fast measurements, we derive a Markovian master equation for the system alone, amenable to analytical treatment.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Measurement and feedback control are essential features of quantum science, with applications ranging from quantum technology protocols to information-to-work conversion in quantum thermodynamics. Theoretical descriptions of feedback control are typically given in terms of stochastic equations requiring numerical solutions, or are limited to linear feedback protocols. Here we present a formalism for continuous quantum measurement and feedback, both linear and nonlinear. Our main result is a quantum Fokker-Planck master equation describing the joint dynamics of a quantum system and a detector with finite bandwidth. For fast measurements, we derive a Markovian master equation for the system alone, amenable to analytical treatment. We illustrate our formalism by investigating two basic information engines, one quantum and one classical.

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