Natural Sciences, Physical Sciences, Other Physics Topics, Naturvetenskap, Fysik, Annan fysik, Condensed Matter Physics (including Material Physics, Nano Physics), Den kondenserade materiens fysik (Här ingår: Materialfysik, nanofysik), Atom and Molecular Physics and Optics, Atom- och molekylfysik och optik (Här ingår: Kemisk fysik, kvantoptik)

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)0031-900710.1103/PhysRevLett.129.050401]. 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.