Optimal quantum parametric feedback cooling

TL;DR

This paper introduces an optimal feedback cooling protocol for quantum oscillators using phase-preserving measurements and phase-dependent modulations, achieving occupation numbers below one quantum and robust against dissipation and phase errors.

Contribution

It develops a theoretically optimal feedback protocol for quantum cooling that minimizes occupation number and is resilient to practical imperfections.

Findings

Achieves occupation number less than one quantum in steady state.

Derives optimal phase and duration for parametric modulations.

Demonstrates robustness against dissipation and phase errors.

Abstract

We propose an optimal protocol using phase-preserving quantum measurements and phase-dependent modulations of the trapping potential at parametric resonance to cool a quantum oscillator to an occupation number of less than one quantum. We derive the optimal phase relationship and duration for the parametric modulations, and compute the lowest-possible occupation number in the steady state. The protocol is robust against moderate amounts of dissipation and phase errors in the feedback loop. Our work has implications for the cooling of levitated mechanical resonators in the quantum regime.