We develop a theory of quantum feedback cooling of a single ion trapped in front of a mirror. By monitoring the motional sidebands of the light emitted into the mirror mode we infer the position of the ion, and act back with an appropriate force to cool the ion. We derive a feedback master equation along the lines of the quantum feedback theory developed by Wiseman and Milburn, which provides us with cooling times and final temperatures as a function of feedback gain and various system parameters.We develop a theory of quantum feedback cooling of a single ion trapped in front of a mirror. By monitoring the motional sidebands of the light emitted into the mirror mode we infer the position of the ion, and act back with an appropriate force to cool the ion. We derive a feedback master equation along the lines of the quantum feedback theory developed by Wiseman and Milburn, which provides us with cooling times and final temperatures as a function of feedback gain and various system parameters.

arXiv:quant-ph/0506187Physical Review AOct 31, 200537 citations

Feedback Cooling and Thermometry of a Single Trapped Ion Using a Knife Edge

Hans Dang, Sebastian Luff, Martin Fischer +2 more

We report on a simple and easy to implement method of feedback cooling trapped ions to temperatures below those achievable using only Doppler cooling. Additionally, the feedback cooling results in significantly shorter cooling times. For selected parameters, we demonstrate cooling to temperatures below $\hbarΓ/2 k_\mathrm{B}$ . The motion of a single ion is monitored in real-time, allowing for the generation of a feedback signal that is applied to an auxiliary trap electrode. Motion detection is implemented by imaging the fluorescence photons emitted by the ion onto a knife edge and detecting the transmitted light, a method used so far to cool trapped nanoparticles. The intensity modulation of the fluorescence resulting from the ion motion is used to generate and apply the feedback signal and also to determine the ion temperature. While the method benefits from a high rate of detected scattered photons, which can be a challenge, and which we address by using a parabolic mirror for collecting the fluorescence, we expect the method to also be applicable when using lenses with moderate numerical apertures.We report on a simple and easy to implement method of feedback cooling trapped ions to temperatures below those achievable using only Doppler cooling. Additionally, the feedback cooling results in significantly shorter cooling times. For selected parameters, we demonstrate cooling to temperatures below $\hbarΓ/2 k_\mathrm{B}$. The motion of a single ion is monitored in real-time, allowing for the generation of a feedback signal that is applied to an auxiliary trap electrode. Motion detection is implemented by imaging the fluorescence photons emitted by the ion onto a knife edge and detecting the transmitted light, a method used so far to cool trapped nanoparticles. The intensity modulation of the fluorescence resulting from the ion motion is used to generate and apply the feedback signal and also to determine the ion temperature. While the method benefits from a high rate of detected scattered photons, which can be a challenge, and which we address by using a parabolic mirror for collecting the fluorescence, we expect the method to also be applicable when using lenses with moderate numerical apertures.

quant-pharXiv:2512.16368Physical Review ADec 19, 20250 citations

\hbarΓ/2 k_\mathrm{B}

. The motion of a single ion is monitored in real-time, allowing for the generation of a feedback signal that is applied to an auxiliary trap electrode. Motion detection is implemented by imaging the fluorescence photons emitted by the ion onto a knife edge and detecting the transmitted light, a method used so far to cool trapped nanoparticles. The intensity modulation of the fluorescence resulting from the ion motion is used to generate and apply the feedback signal and also to determine the ion temperature. While the method benefits from a high rate of detected scattered photons, which can be a challenge, and which we address by using a parabolic mirror for collecting the fluorescence, we expect the method to also be applicable when using lenses with moderate numerical apertures.