Spin squeezing from bilinear spin-spin interactions: two simple theorems

TL;DR

This paper presents two theorems demonstrating how bilinear spin-spin interactions induce spin squeezing, revealing quantum correlations at equilibrium and during unitary evolution, applicable to many quantum spin models.

Contribution

The paper introduces two simple theorems linking bilinear spin-spin interactions to spin squeezing, applicable to a wide range of quantum spin models.

Findings

Squeezing captures initial quantum correlations at equilibrium.

Squeezing occurs during unitary evolution away from equilibrium.

Applicable to most quantum spin models in current quantum simulators.

Abstract

We demonstrate two simple theorems about squeezing induced by bilinear spin-spin interactions that conserve spin parity -- including a vast majority of quantum spin models implemented by state-of-the-art quantum simulators. In particular we show that squeezing captures the first form of quantum correlations which are produced: 1) at equilibrium, by adiabatically turning on the spin-spin interactions starting from a factorized state aligned with an external, arbitrary field; 2) away from equilibrium, by evolving unitarily the same state with the interacting Hamiltonian.