%0 Generic %1 FossFeig2013Dynamical %A Foss-Feig, Michael %A Hazzard, Kaden R. A. %A Bollinger, John J. %A Rey, Ana M. %A Clark, Charles W. %D 2013 %K ising %T Dynamical quantum correlations of Ising models on an arbitrary lattice and their resilience to decoherence %U http://arxiv.org/abs/1306.0172 %X 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.

@misc{FossFeig2013Dynamical, 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.}, added-at = {2014-01-09T15:14:33.000+0100}, archiveprefix = {arXiv}, author = {Foss-Feig, Michael and Hazzard, Kaden R. A. and Bollinger, John J. and Rey, Ana M. and Clark, Charles W.}, biburl = {https://www.bibsonomy.org/bibtex/2f24127f9977e1a6416ce76f9798479b7/jaspervh}, citeulike-article-id = {12802628}, citeulike-linkout-0 = {http://arxiv.org/abs/1306.0172}, citeulike-linkout-1 = {http://arxiv.org/pdf/1306.0172}, day = 2, eprint = {1306.0172}, interhash = {c1c0ac06247619204fbb6c3002674aec}, intrahash = {f24127f9977e1a6416ce76f9798479b7}, keywords = {ising}, month = jun, posted-at = {2013-11-26 12:41:31}, priority = {2}, timestamp = {2014-01-09T15:14:33.000+0100}, title = {Dynamical quantum correlations of Ising models on an arbitrary lattice and their resilience to decoherence}, url = {http://arxiv.org/abs/1306.0172}, year = 2013 }