Theory of Scalable Spin Squeezing with Disordered Quantum Dipoles

TL;DR

This paper develops a theory for scalable spin squeezing in disordered quantum dipole systems, revealing how disorder and anisotropy affect entanglement generation and proposing strategies for experimental realization.

Contribution

It introduces a comprehensive theory for spin squeezing in disordered dipolar systems, including phase diagram mapping and disorder effects analysis, with practical strategies for NV centers.

Findings

Spin squeezing survives near the Heisenberg point despite disorder.

Rare tightly-coupled dimers heat the system and limit squeezing.

Decoupling dimers enables scalable spin squeezing in NV centers.

Abstract

Spin squeezed entanglement enables metrological precision beyond the classical limit. Understood through the lens of continuous symmetry breaking, dipolar spin systems exhibit the remarkable ability to generate spin squeezing via their intrinsic quench dynamics. To date, this understanding has primarily focused on lattice spin systems; in practice however, dipolar spin systems$\unicode{x2014}$ranging from ultracold molecules to nuclear spin ensembles and solid-state color centers$\unicode{x2014}$often exhibit significant amounts of positional disorder. Here, we develop a theory for scalable spin squeezing in a two-dimensional randomly diluted lattice of quantum dipoles, which naturally realize a dipolar XXZ model. Via extensive quantum Monte Carlo simulations, we map out the phase diagram for finite-temperature XY order, and by extension scalable spin squeezing, as a function of both disorder and Ising anisotropy. As the disorder increases, we find that scalable spin squeezing survives only near the Heisenberg point. We show that this behavior is due to the presence of rare tightly-coupled dimers, which effectively heat the system post-quench. In the case of strongly-interacting nitrogen-vacancy centers in diamond, we demonstrate that an experimentally feasible strategy to decouple the problematic dimers from the dynamics is sufficient to enable scalable spin squeezing.