Easy-plane ferromagnetism in a disordered two-dimensional NV ensemble

Spontaneous symmetry breaking provides a fundamental organizing principle for understanding distinct phases of quantum matter. In this work, we combine experimental and theoretical investigations to study the physics of dilute quantum dipoles in 2D. Via extensive quantum Monte Carlo simulations, we map out the phase diagram for finite-temperature XY order as a function of positional disorder. In order to probe this phase diagram experimentally, we work with a 2D ensemble of strongly-interacting Nitrogen-Vacancy centers in diamond. We combine a variety of techniques, including adiabatic state preparation, Floquet Hamiltonian driving, and lattice engineering to control the underlying spatial disorder. Together, these techniques enable us to directly utilize NV quench dynamics to identify the formation of XY ferromagnetic order. Looking forward, this work opens the door for using such XY ordering dynamics to generate scalable spin squeezing.