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

TitleDynamical quantum correlations of Ising models on an arbitrary lattice and their resilience to decoherence
Publication TypeJournal Article
Year of Publication2013
AuthorsFoss-Feig, M, Hazzard, KRA, Bollinger, JJ, Rey, AMaria, Clark, CW
JournalNew Journal of Physics
Date Published2013/11/07

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.

Short TitleNew J. Phys.