Theoretical framework for enhancing or enabling cooling of a mechanical resonator via the anti-Stokes or Stokes interaction and zero-photon detection

TL;DR

This paper presents a comprehensive theoretical framework for laser cooling of mechanical resonators using zero-photon detection, enabling enhanced cooling via anti-Stokes and Stokes interactions, with implications for quantum control and thermodynamics.

Contribution

It introduces a novel theoretical approach that includes pulsed and continuous measurements, analyzing their effects on cooling efficiency and system dynamics, especially in the context of Stokes and anti-Stokes interactions.

Findings

Zero-photon detection can enhance anti-Stokes cooling.

Cooling via Stokes interaction is possible with zero-photon detection.

Efficiency thresholds for cooling are identified.

Abstract

We develop a theoretical framework to describe how zero-photon detection may be utilized to enhance laser cooling via the anti-Stokes interaction and, somewhat surprisingly, enable cooling via the Stokes interaction commonly associated with heating. Our description includes both pulsed and continuous measurements as well as optical detection efficiency and open-system dynamics. For both cases, we discuss how the cooling depends on the system parameters such as detection efficiency and optomechanical cooperativity, and we study the continuous-measurement-induced dynamics, contrasting to single-photon detection events. For the Stokes case, we explore the interplay between cooling and heating via optomechanical parametric amplification, and we find the efficiency required to cool a mechanical oscillator via zero-photon detection. This work serves as a companion article to the recent experiment [E. A. Cryer-Jenkins, K. D. Major, et al., arXiv:2408.01734 (2024)], which demonstrated enhanced laser cooling of a mechanical oscillator via zero-photon detection on the anti-Stokes signal. The framework developed here provides new approaches for cooling mechanical resonators that can be applied to a wide range of areas including nonclassical state preparation, quantum thermodynamics, and avoiding the often unwanted heating effects of parametric amplification.