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

Published

November 7, 2013

Author(s)

Michael S. Foss-Feig, Kaden R. Hazzard, John J. Bollinger, Ana Maria Rey, Charles W. Clark

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 Foss-Feig et al (2013 Phys. Rev. A 87 042101). 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 T1 (spontaneous spin relaxation/excitation) and T2 (dephasing) type decoherence processes. Even though the decoherence is local, our solution reveals that the competition between Ising dynamics and T1 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.

Citation

New Journal of Physics

Volume

15

Pub Type

Journals

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DOI Link

Keywords

Ising model, non-equilibrium dynamics, entanglement, decoherence

Citation

Foss-Feig, M. , Hazzard, K. , Bollinger, J. , Rey, A. and Clark, C. (2013), Dynamical quantum correlations of Ising models on an arbitrary lattice and their resilience to decoherence, New Journal of Physics, [online], https://doi.org/10.1088/1367-2630/15/11/113008 (Accessed December 26, 2024)