Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0506187 · Physical Review A

Quantum feedback cooling of a single trapped ion in front of a mirror

Viktor Steixner, Peter Rabl, P. Zoller

Published Oct 31, 2005• 37 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.72.043826

Related papers

Quantum feedback cooling of two trapped ions

Shuo Zhang, Wei Wu, Chun-Wang Wu +4 more

We present a sub-Doppler cooling scheme of a two-trapped-ion crystal by quantum feedback control method. In the scheme, we obtain the motional information by continuously measuring the spontaneous emission photons from one single ion of the crystal, and then apply a feedback force to cool the whole chain down.We derive the cooling dynamics of the cooling scheme using quantum feedback theory and quantum regression theorem. The result shows that with experimentally achievable parameters, our scheme can achieve lower temperature and faster cooling rate than Doppler cooling.

Chinese Physics B•Jun 1, 2017•2 citations

Doppler cooling of a trapped ion with feedback

Zhi Liang Jiang, Ping‐Xing Chen

Basing on the theory of quantum feedback by Steixner and his coworkers, we develop the master equation of Doppler cooling with feedback in an ion trap. The result of simulation shows the property of speedup the cooling,besides the influences of those arguments and whether we could realize it in experiment.

Acta Physica Sinica•Jan 1, 2012•2 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.

quant-pharXiv:2512.16368•Physical Review A•Dec 19, 2025•0 citations

Feedback Cooling of a Single Trapped Ion

Pavel A. Bushev, D. Rotter, Alex Wilson +7 more

Based on a real-time measurement of the motion of a single ion in a Paul trap, we demonstrate its electromechanical cooling below the Doppler limit by homodyne feedback control (cold damping). The feedback cooling results are well described by a model based on a quantum mechanical master equation.

arXiv:quant-ph/0509125•Physical Review Letters•Feb 3, 2006•200 citations

Semi-classical theory of coherent atom cooling with a single mirror

André Xuereb, Péter Horák, Tim Freegarde

We investigate theoretically a novel optical technique to cool atomic or molecular species without a closed transition: a particle in front of a mirror illuminated by an off-resonant light beam. The interaction between the particle, the pump and the time-delayed reflected pump results in a net loss of energy from the particle to the field and therefore cooling. Cooling rates depending on particle position and coupling parameters are obtained by an analytical perturbative approach. Finally, we present a semiclassical computational model incorporating momentum diffusion, which will eventually allow us to predict steady-state temperatures.

•Jan 1, 2008•0 citations

Quantum-limited velocity readout and quantum feedback cooling of a trapped ion via electromagnetically induced transparency

Peter Rabl, Viktor Steixner, P. Zoller

We discuss continuous observation of the momentum of a single atom by employing the high velocity sensitivity of the index of refraction in a driven $\ensuremath{\Lambda}$-system based on electromagnetically induced transparency. In the ideal limit of unit collection efficiency this provides a quantum-limited measurement with minimal backaction on the atomic motion. A feedback loop, which drives the atom with a force proportional to measured signal, provides a cooling mechanism for the atomic motion. We derive the master equation which describes the feedback cooling and show that in the Lamb-Dicke limit the steady state energies are close to the ground state, limited only by the photon collection efficiency. Outside of the Lamb-Dicke regime the predicted temperatures are well below the Doppler limit.

arXiv:quant-ph/0506185•Physical Review A•Oct 27, 2005•18 citations
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 present a sub-Doppler cooling scheme of a two-trapped-ion crystal by quantum feedback control method. In the scheme, we obtain the motional information by continuously measuring the spontaneous emission photons from one single ion of the crystal, and then apply a feedback force to cool the whole chain down.We derive the cooling dynamics of the cooling scheme using quantum feedback theory and quantum regression theorem. The result shows that with experimentally achievable parameters, our scheme can achieve lower temperature and faster cooling rate than Doppler cooling.
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 ℏΓ/2kB\hbarΓ/2 k_\mathrm{B}ℏΓ/2kB​. 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 investigate theoretically a novel optical technique to cool atomic or molecular species without a closed transition: a particle in front of a mirror illuminated by an off-resonant light beam. The interaction between the particle, the pump and the time-delayed reflected pump results in a net loss of energy from the particle to the field and therefore cooling. Cooling rates depending on particle position and coupling parameters are obtained by an analytical perturbative approach. Finally, we present a semiclassical computational model incorporating momentum diffusion, which will eventually allow us to predict steady-state temperatures.
We discuss continuous observation of the momentum of a single atom by employing the high velocity sensitivity of the index of refraction in a driven $\ensuremath{\Lambda}$-system based on electromagnetically induced transparency. In the ideal limit of unit collection efficiency this provides a quantum-limited measurement with minimal backaction on the atomic motion. A feedback loop, which drives the atom with a force proportional to measured signal, provides a cooling mechanism for the atomic motion. We derive the master equation which describes the feedback cooling and show that in the Lamb-Dicke limit the steady state energies are close to the ground state, limited only by the photon collection efficiency. Outside of the Lamb-Dicke regime the predicted temperatures are well below the Doppler limit.