# Dynamical Generation of Synthetic Electric Fields for Photons in the Quantum Regime

## TL;DR

This paper explores how synthetic electric fields for photons can be generated dynamically in optomechanical systems, demonstrating robustness against quantum noise and enabling unidirectional photon transport in the quantum regime.

## Contribution

It introduces a quantum model using a van-der-Pol oscillator to study the quantum-to-classical crossover of synthetic gauge fields in optomechanics.

## Key findings

- Synthetic electric fields are robust against quantum noise.
- Unidirectional photon transport persists in the quantum regime.
- Reduced isolation ratio observed due to quantum fluctuations.

## Abstract

Optomechanics offers a natural way to implement synthetic dynamical gauge fields, leading to synthetic electric fields for phonons and, as a consequence, to unidirectional light transport. Here we investigate the quantum dynamics of synthetic gauge fields in the minimal setup of two optical modes coupled by phonon-assisted tunneling where the phonon mode is undergoing self-oscillations. We use the quantum van-der-Pol oscillator as the simplest dynamical model for a mechanical self-oscillator that allows us to perform quantum master equation simulations. We identify a single parameter, which controls the strength of quantum fluctuations, enabling us to investigate the classical-to-quantum crossover. We show that the generation of synthetic electric fields is robust against noise and that it leads to unidirectional transport of photons also in the quantum regime, albeit with a reduced isolation ratio. Our study opens the path for studying dynamical gauge fields in the quantum regime based on optomechanical arrays.