Dissipative transverse-field Ising model: steady-state correlations and spin squeezing

TL;DR

This paper investigates a dissipative transverse-field Ising model with infinite-range interactions, revealing steady-state spin squeezing and entanglement despite decoherence, using analytical phase-space methods relevant to trapped ion experiments.

Contribution

It introduces an analytical phase-space approach to study steady-state correlations and spin squeezing in a dissipative Ising model with infinite-range coupling.

Findings

Spin squeezing occurs in steady state due to the transverse field.

Entanglement persists despite spontaneous emission.

Analytical calculations match experimental conditions for trapped ions.

Abstract

We study the transverse-field Ising model with infinite-range coupling and spontaneous emission on every site. We find that there is spin squeezing in steady state due to the presence of the transverse field. This means that there is still entanglement, despite the decoherence from spontaneous emission. We analytically calculate fluctuations beyond mean-field theory using a phase-space approach, which involves converting the master equation into a Fokker-Planck equation for the Wigner function. Our calculations are relevant to current experiments with trapped ions.