# Phase transitions in electron spin resonance under continuous microwave driving

## TL;DR

This paper investigates phase transitions in electron spin resonance under continuous microwave driving, revealing collective phenomena and critical behavior in strongly coupled electron systems interacting with an environment, using mean-field and numerical methods.

## Contribution

It introduces a mean-field framework to analyze steady state phase transitions in driven, dissipative electron systems, supported by numerical simulations.

## Key findings

- Identification of phase transitions between high and low polarization states.
- Observation of metastable states and critical phenomena.
- Good agreement between mean-field predictions and exact simulations.

## Abstract

We study an ensemble of strongly coupled electrons under continuous microwave irradiation interacting with a dissipative environment, a problem of relevance to the creation of highly polarized non-equilibrium states in nuclear magnetic resonance. We analyse the stationary states of the dynamics, described within a Lindblad master equation framework, at the mean-field approximation level. This approach allows us to identify steady state phase transitions between phases of high and low polarization controlled by the distribution of electronic interactions. We compare the mean-field predictions to numerically exact simulations of small systems and find good agreement. Our study highlights the possibility of observing collective phenomena, such as metastable states, phase transitions and critical behaviour in appropriately designed paramagnetic systems. These phenomena occur in a low-temperature regime which is not theoretically tractable by conventional methods, e.g., the spin-temperature approach.