Cooling of mechanical motion with a two level system: the high temperature regime

TL;DR

This paper investigates the limits of cooling a nano-mechanical resonator using a two-level system at high initial temperatures, deriving a comprehensive model that reveals the degradation and breakdown of cooling under certain conditions.

Contribution

The study introduces an effective Fokker-Planck equation that captures non-linear effects and saturation, providing new insights into high-temperature cooling dynamics of mechanical resonators.

Findings

Cooling rates degrade at high initial temperatures

Cooling breaks down at very high temperatures

Results applicable to various solid state quantum systems

Abstract

We analyze cooling of a nano-mechanical resonator coupled to a dissipative solid state two level system focusing on the regime of high initial temperatures. We derive an effective Fokker-Planck equation for the mechanical mode which accounts for saturation and other non-linear effects and allows us to study the cooling dynamics of the resonator mode for arbitrary occupation numbers. We find a degrading of the cooling rates and eventually a breakdown of cooling at very high initial temperatures and discuss the dependence of these effects on various system parameters. Our results apply to most solid state systems which have been proposed for cooling a mechanical resonator including quantum dots, superconducting qubits and electronic spin qubits.