Comparing resolved-sideband cooling and measurement-based feedback cooling on an equal footing: analytical results in the regime of ground-state cooling

TL;DR

This paper analytically compares resolved-sideband cooling and measurement-based feedback cooling for harmonic oscillators in the ground-state regime, revealing that coherent feedback outperforms measurement-based methods due to differences in noise utilization.

Contribution

It provides simple analytical expressions for both cooling methods' performance in the ground-state regime and clarifies why coherent feedback surpasses measurement-based feedback.

Findings

Coherent feedback achieves better cooling performance than measurement-based feedback.

The performance gap is due to projection noise, not measurement back-action.

Optimal interaction strength maximizes cooling in both methods.

Abstract

We show that in the regime of ground-state cooling, simple expressions can be derived for the performance of resolved-sideband cooling --- an example of coherent feedback control --- and optimal linear measurement-based feedback cooling for a harmonic oscillator. These results are valid to leading order in the small parameters that define this regime. They provide insight into the origins of the limitations of coherent and measurement-based feedback for linear systems, and the relationship between them. These limitations are not fundamental bounds imposed by quantum mechanics, but are due to the fact that both cooling methods are restricted to use only a linear interaction with the resonator. We compare the performance of the two methods on an equal footing --- that is, for the same interaction strength --- and confirm that coherent feedback is able to make much better use of the linear interaction than measurement-based feedback. We find that this performance gap is caused not by the back-action noise of the measurement but by the projection noise. We also obtain simple expressions for the maximal cooling that can be obtained by both methods in this regime, optimized over the interaction strength.