CMT Theory seminar: Far-from equilibrium dynamics of open Ising spin models
Wednesday, April 17, 2013 – 1:30pm – 3:00pm
Joint Quantum Institute of UMD and NIST
Ising models, and the physical systems in which they are realized, play a central role in the generation of entangled states for use in quantum metrology and quantum information. In recent years, trapped ion systems have emerged as a promising platform for implementing long-ranged Ising models, which even in the absence of a transverse field can give rise to non-classical dynamics and long-range quantum correlations. However, existing large-scale implementations of these spin models operate in a regime where decoherence is appreciable. Though decoherence is usually regarded as a nuisance to be avoided, in this talk I will take the perspective that these systems offer a controlled platform from which to study the effects of decoherence on the generation of quantum correlations. In a typical (closed) Ising model, a crucial question is how a coherent drive that does not commute with the Ising interaction (i.e. a transverse field) affects the ground state properties. I will address a natural generalization of this question to an open system: How does a non-commuting incoherent drive (spontaneous spin relaxation or incoherent pumping) affect the dynamical behavior of an Ising model? Surprisingly, unlike the case of a coherent drive, this incoherent driving can be incorporated (at the level of a Markovian master equation) without approximation in any dimension. The underlying reason why a solution exists will be emphasized, and applications to characterizing and improving upon entanglement generation in open spin systems will also be discussed.
Ising models, and the physical systems in which they are realized, play a central role in the generation of 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 this paper, we present a detailed theoretical framework for studying the dynamics of such systems in response to being driven into essentially arbitrary (but unentangled) non-equilibrium states. The central feature of these calculation—exact expressions for arbitrary time-ordered correlation functions—is then used to study the effect of Markovian decoherence. In particular, we derive exact expressions for the dynamics of spin-spin correlation functions in the presence of both T1 (dephasing) and T2 (longitudinal spin relaxation) type decoherence processes. Even though the decoherence is local, an interaction mediated backaction allows its effects to propagate throughout the system, drastically amplifying the degradation of quantum correlations. In addition to identifying the mechanism of this deleterious effect, our solution points toward a possible scheme to mitigate it via measurement based coherent feedback.
Host: Jim Freericks