Quantum Fokker-Planck Master Equation for Continuous Feedback Control

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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• Probe thermometry with continuous measurements
• Maxwell's demon across the quantum-to-classical transition
• Steady-state entanglement production in a quantum thermal machine with continuous feedback control
• Quantum feedback control in quantum photosynthesis
• Continuous feedback protocols for cooling and trapping a quantum harmonic oscillator
• Artificially intelligent Maxwell's demon for optimal control of open quantum systems
• Asymmetric Transmission Through a Classical Analogue of the Aharonov-Bohm Ring
• Quantum-classical hybrid dynamics: coupling mechanisms and diffusive approximation
• Deterministic Equations for Feedback Control of Open Quantum Systems II: Properties of the memory function
• Revisiting Kinetic Monte Carlo Algorithms for Time-dependent Processes: from open-loop control to feedback control
• Markovian description of a wide class of feedback-controlled systems: Application to the feedback flashing ratchet
• Restoring the second law to classical-quantum dynamics
• Extracting filtered signal statistics of continuously measured quantum systems
• Time-cost-error trade-off relation in thermodynamics: The third law and beyond