# Distant entanglement enhanced in $\mathcal{PT}$-symmetric optomechanics

## TL;DR

This paper demonstrates that in a $ ext{PT}$-symmetric optomechanical system, the entanglement between distant optical and mechanical modes can be significantly enhanced in the unbroken-$ ext{PT}$-symmetry regime, enabling advanced quantum state engineering.

## Contribution

It introduces a three-mode $ ext{PT}$-symmetric optomechanical system that enhances steady-state entanglement between distant modes, surpassing single-cavity setups.

## Key findings

- Enhanced optical-mechanical coupling in unbroken-$ ext{PT}$-symmetry regime.
- More stable steady-state solutions in gain-loss systems.
- Significant increase in distant entanglement compared to single cavity systems.

## Abstract

We study steady-state continuous variable entanglement in a three-mode optomechanical system consisting of an active optical cavity (gain) coupled to a passive optical cavity (loss) supporting a mechanical mode. For a driving laser which is blue-detuned, we show that coupling between optical and mechanical modes is enhanced in the unbroken-$\mathcal{PT}$-symmetry regime. We analyze the stability and this shows that steady-state solutions are more stable in the gain and loss systems. We use these stable solutions to generate distant entanglement between the mechanical mode and the optical field inside the gain cavity. It results in a giant enhancement of entanglement compared to what is generated in the single lossy cavity. This work offers the prospect of exploring quantum state engineering and quantum information in such systems. Furthermore, such entanglement opens up an interesting possibility to study spatially separated quantum objects.