# Optical signatures of Mott-superfluid transition in nitrogen-vacancy centers coupled to photonic crystal cavities

## TL;DR

This paper investigates a controllable quantum phase transition in a system of nitrogen-vacancy centers coupled to photonic crystal cavities, highlighting optical signatures and the effects of dissipation for potential quantum simulation applications.

## Contribution

It introduces a method to observe and characterize the Mott-superfluid transition in a spin-cavity system using optical measurements, accounting for dissipation effects.

## Key findings

- Dissipation influences the phase boundary of the transition.
- Distinct optical signatures differentiate quantum phases.
- Experimental observables can detect the quantum phase transition.

## Abstract

We study the phenomenon of controllable localization-delocalization transition in a quantum many-body system composed of nitrogen-vacancy centers coupled to photonic crystal cavities, through tuning the different detunings and the relative amplitudes of two optical fields that drive two nondegenerate transitions of the $\Lambda $-type configuration. We not only characterize how dissipation affects the phase boundary using the mean-field quantum master equation, but also provide the possibility of observing this photonic quantum phase transition (QPT) by employing several experimentally observable quantities, such as mean intracavity photon number, density correlation function and emitted spectrum, exhibiting distinct optical signatures in different quantum phases. Such a spin-cavity system opens new perspectives in quantum simulation of condensed-matter and many-body physics in a well-controllable way.