Continuous feedback protocols for cooling and trapping a quantum harmonic oscillator

TL;DR

This paper explores feedback-based cooling protocols for quantum harmonic oscillators using a recently derived quantum Fokker-Planck master equation, demonstrating effective ground state cooling through continuous measurements and feedback.

Contribution

It provides an analytically solvable framework applying the QFPME to design and analyze feedback protocols for cooling quantum oscillators.

Findings

Protocols can cool oscillators close to the ground state

Effective feedback protocols depend on measurement choices

The study offers a case example of quantum measurement and feedback

Abstract

Quantum technologies and experiments often require preparing systems in low-temperature states. Here, we investigate cooling schemes using feedback protocols modeled with a Quantum Fokker-Planck Master Equation (QFPME) recently derived by Annby-Andersson et. al. (Phys. Rev. Lett. 129, 050401, 2022). This equation describes systems under continuous weak measurements, with feedback based on the outcome of these measurements. We apply this formalism to study the cooling and trapping of a harmonic oscillator for several protocols based on position and/or momentum measurements. We find that the protocols can cool the oscillator down to, or close to, the ground state for suitable choices of parameters. Our analysis provides an analytically solvable case study of quantum measurement and feedback and illustrates the application of the QFPME to continuous quantum systems.