Scalable spin squeezing in two-dimensional arrays of dipolar large-$S$ spins

TL;DR

This paper demonstrates that two-dimensional arrays of large-spin magnetic atoms can generate scalable spin squeezing through their dipolar interactions, with robustness against perturbations, opening avenues for quantum entanglement and metrology.

Contribution

The work shows that dipolar interactions in 2D large-spin atom arrays produce scalable spin squeezing similar to the OAT model, even with realistic perturbations.

Findings

Spin squeezing scales similarly to the OAT model.

Long-range ferromagnetic order protects squeezing against quadratic shifts.

Quantum Monte Carlo and mean-field theory confirm phase diagram robustness.

Abstract

Controlling the quantum many-body state of arrays of qudits, possessing a large local Hilbert space, opens the path to a broad range of possibilities for many-particle entanglement, interesting both for fundamental quantum science, as well as for potential metrological applications. In this work we theoretically show that the spin-spin interactions realized in two-dimensional Mott insulators of large-spin magnetic atoms (such as Cr, Er or Dy) lead to scalable spin squeezing along the non-equilibrium unitary evolution initialized in a coherent spin state. An experimentally relevant perturbation to the collective squeezing dynamics is offered by a quadratic Zeeman shift, which leads instead to squeezing of individual spins. Making use of a truncated cumulant expansion for the quantum fluctuations of the spin array, we show that, for sufficiently small quadratic shifts, the spin squeezing dynamics is akin to that produced by the paradigmatic one-axis-twisting (OAT) model -- as expected from an effective separation between collective spin and spin-wave variables. Spin squeezing with OAT-like scaling is shown to be protected by the robustness of long-range ferromagnetic order to quadratic shifts in the equilibrium phase diagram of the system, that we reconstruct via quantum Monte Carlo and mean-field theory.