Optimal control for feedback cooling in cavityless levitated optomechanics

Abstract

We consider feedback cooling in a cavityless levitated optomechanics setup, and we investigate the possibility to improve the feedback implementation. We apply optimal control theory to derive the optimal feedback signal both for quadratic (parametric) and linear (electric) feedback. We numerically compare optimal feedback against the typical feedback implementation used for experiments. In order to do so, we implement a state estimation scheme that takes into account the modulation of the laser intensity. We show that such an implementation allows us to increase the feedback strength, leading to faster cooling rates and lower center-of-mass temperatures.

Performance and limits of feedback cooling methods for levitated oscillators: A direct comparison

“…These simulations show the modulation depth is not limited to 1.5% as previously reported for optical traps [46]. We found the modulation depths were also not limited by this value in the experiment where modulation depths of up to 5% were used.…”

“…Kalman filtering could be used for both parametric feedback and velocity damping to more accurately predict the state of the particle. However, previous studies have shown this is unlikely to make a large improvement on the minimum achievable temperature of the particle [24,46]. Last, unlike standard parametric cooling which leads to nonthermal energy distributions, both schemes studied here produce cold thermal distributions.…”

Performance and limits of feedback cooling methods for levitated oscillators: a direct comparison

“…These simulations show the modulation depth is not limited to 1.5% as previously reported for optical traps [34].…”

“…Kalman filtering could be used for both parametric feedback and velocity damping to more accurately predict the state of the particle. However, previous studies have shown this is unlikely to make a large improvement on the minimum achievable temperature of the particle [2,34]. Lastly, unlike standard parametric cooling which leads to non-thermal energy distributions, both schemes studied here produce cold thermal distributions.…”

Classical Tracking for Quantum Trajectories

“…The ability to use classical state estimation methods across a wide range of temperatures to control the cooling mechanism, for example, would be beneficial. Some preliminary results using real-time Kalman filter based methods have already been demonstrated [14], and more sophisticated approaches have been proposed [40]. The bootstrap filter used for this work demonstrates the utility of the approach, and the relative simplicity of the filter should mean that the results presented in this paper could be improved using more sophisticated state estimation methods.…”