# Dynamics of an ultra-strongly-coupled system interacting with a driven nonlinear resonator

## TL;DR

This paper explores how a driven nonlinear resonator can be used to measure and control the ground state of an ultra-strongly-coupled light-matter system, revealing strong correlations and entanglement effects despite weak coupling.

## Contribution

It demonstrates that a driven nonlinear resonator can induce significant correlations and enable measurement-based control of an ultra-strongly-coupled system's ground state.

## Key findings

- Strong correlation between nonlinear resonator and light-matter system.
- Measurement on the nonlinear resonator influences the light-matter system's phase.
- Conditions identified for entanglement and projection of the ground state.

## Abstract

In the ultra-strong coupling regime of a light-matter system, the ground state exhibits non-trivial entanglement between the atom and photons. For the purposes of exploring the measurement and control of this ground state, here we analyze the dynamics of such an ultra-strongly-coupled system interacting with a driven nonlinear resonator acting as a measurement apparatus. Interestingly, although the coupling between the atom and the nonlinear resonator is much smaller than the typical energy scales of the ultra-strongly-coupled system, we show that we can generate a strong correlation between the nonlinear resonator and the light-matter system. A subsequent coarse- grained measurement on the nonlinear resonator significantly affects the light-matter system, and the phase of the light changes depending on the measurement results. Also, we investigate the conditions for when the nonlinear resonator can be entangled with the ultra-strongly coupled system, which is the mechanism that allows us to project the ground state of the ultra-strongly coupled system into a non-energy eigenstate.