# Entangling light field with mechanical resonator at high temperature

## TL;DR

This paper demonstrates that using blue-detuned continuous-wave pumping in cavity optomechanical systems can generate and stabilize quantum entanglement at high temperatures, even under thermal decoherence, simplifying the creation of macroscopic quantum states.

## Contribution

It introduces a novel approach using blue-detuned continuous-wave drive to achieve stable optomechanical entanglement at high temperatures, with an analytical boundary condition for entanglement existence.

## Key findings

- Entanglement can be achieved at high temperatures with blue-detuned CW pump.
- A simple analytical relation defines the parameter boundary for entanglement.
- Stable entanglement persists despite thermal decoherence in the studied regime.

## Abstract

We present a study on how to realize the widely interested optomechanical entanglement at high temperature. Unlike the majority of the previous experimental and theoretical researches that consider the entanglement of a mechanical resonator with a cavity field created by red-detuned continuous-wave or blue-detuned pulsed driving field, we find that applying blue-detuned continuous-wave pump field to cavity optomechanical systems can achieve considerable degrees of quantum entanglement, which is generally challenging to obtain at high temperature for the known physical systems. The competition between the induced squeezing-type interaction and the existing decoherence leads to stable entanglement in dynamically unstable regime. There is a much more relaxed condition for the existence of entanglement, as compared with the well-known criterion for neglecting the thermal decoherence on optomechanically coupled systems. A simple relation about a boundary in the parameter space, across which the entanglement can exist or not, is found with an analytical expression for the degree of the achieved entanglement at any temperature, which is derived for the systems of highly resolved sideband. The studied scenario with blue-detuned continuous-wave driving field can greatly simplify the generation of the widely interested optomechanical entanglement of macroscopic quantum states. Our study also provides the answers to two fundamentally meaningful open problems: (1) what is the condition for a system to avoid its loss of quantum entanglement under thermal decoherence? (2) is it possible to preserve the entanglement in a thermal environment by increasing the interaction that entangles the subsystems?