Dynamical quantum correlations of Ising models on an arbitrary lattice and their resilience to decoherence

TL;DR

This paper develops a comprehensive theoretical framework for analyzing the dynamics of long-range Ising models on arbitrary lattices, including effects of decoherence, revealing non-local dephasing phenomena and potential mitigation strategies.

Contribution

It introduces exact expressions for correlation functions in driven Ising systems and incorporates decoherence effects, extending previous models to include arbitrary initial states and local dissipation.

Findings

Derived exact correlation functions for non-equilibrium Ising dynamics.

Revealed non-local dephasing amplification due to local decoherence.

Suggested measurement-based feedback to counteract decoherence effects.

Abstract

Ising models, and the physical systems described by them, play a central role in generating entangled states for use in quantum metrology and quantum information. In particular, ultracold atomic gases, trapped ion systems, and Rydberg atoms realize long-ranged Ising models, which even in the absence of a transverse field can give rise to highly non-classical dynamics and long-range quantum correlations. In the first part of this paper, we present a detailed theoretical framework for studying the dynamics of such systems driven (at time t=0) into arbitrary unentangled non-equilibrium states, thus greatly extending and unifying the work of Ref. [1]. Specifically, we derive exact expressions for closed-time-path ordered correlation functions, and use these to study experimentally relevant observables, e.g. Bloch vector and spin-squeezing dynamics. In the second part, these correlation functions are then used to derive closed-form expressions for the dynamics of arbitrary spin-spin correlation functions in the presence of both T_1 (spontaneous spin relaxation/excitation) and T_2 (dephasing) type decoherence processes. Even though the decoherence is local, our solution reveals that the competition between Ising dynamics and T_1 decoherence gives rise to an emergent non-local dephasing effect, thereby drastically amplifying the degradation of quantum correlations. In addition to identifying the mechanism of this deleterious effect, our solution points toward a scheme to eliminate it via measurement-based coherent feedback.