Deterministic Equations for Feedback Control of Open Quantum Systems

TL;DR

This paper introduces a comprehensive framework for feedback control in open quantum systems, unifying previous models and enabling realistic, time-dependent feedback protocols with experimental relevance.

Contribution

It presents a single general equation for all feedback schemes in measured quantum systems and introduces new feedback based on jump channels and elapsed time.

Findings

Unified feedback master equation covering all schemes

New feedback protocol based on last detected jump channel

Demonstrated protocols achieving population inversion and quantum transition reversal

Abstract

Feedback control in open quantum dynamics is crucial for the advancement of various coherent platforms. However, currently only a handful of feedback master equations exist in the literature, which are restricted to specific types of feedback. In this letter we first introduce a unifying framework, based on a single general equation, that describes all possible feedback schemes in sequentially (and continuously) measured systems, and from which all previous results follow. Next, we specialize it to the case of quantum jumps and introduce a new type of feedback based on the channel of the last detected jump, as well as the time elapsed since it occurred. Our description is experimentally grounded, and naturally allows for the introduction of realistic effects, such as time-delays in the feedback loop. We illustrate our results with two time-dependent feedback protocols conditioned on quantum-jump detections: one achieving population inversion of a two-level system against a thermal bath, and another enabling real-time reversal of quantum transitions, both admitting steady-state solutions.