Nonequilibrium dynamics of spin-boson models from phase-space methods

Published on Sep 5, 2017in Physical Review A3.14
· DOI :10.1103/PHYSREVA.96.033607
Asier Piñeiro Orioli6
Estimated H-index: 6
(Heidelberg University),
Arghavan Safavi-Naini19
Estimated H-index: 19
+ 1 AuthorsAna Maria Rey62
Estimated H-index: 62
Sources
Abstract
An accurate description of the nonequilibrium dynamics of systems with coupled spin and bosonic degrees of freedom remains theoretically challenging, especially for large system sizes and in higher than one dimension. Phase space methods such as the Truncated Wigner Approximation (TWA) have the advantage of being easily scalable and applicable to arbitrary dimensions. In this work we adapt the TWA to generic spin-boson models by making use of recently developed algorithms for discrete phase spaces [Schachenmayer, PRX 5, 011022 (2015)]. Furthermore we go beyond the standard TWA approximation by applying a scheme based on the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations [Pucci, PRB 93, 174302 (2016)] to our coupled spin-boson model. This allows in principle to study how systematically adding higher order corrections improves the convergence of the method. To test various levels of approximation we study an exactly solvable spin-boson model which is particularly relevant for trapped-ion arrays. Using TWA and its BBGKY extension we accurately reproduce the time evolution of a number of one- and two-point correlation functions in several dimensions and for arbitrary number of bosonic modes.
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From the contents: A Historical Introduction.- Quantum Statistics.- Quantum Langevin Equations.- Phase Space Methods.- Quantum Markov Processes.- Applying the Master Equation.- Amplifiers and Measurement.- Photon Counting.- Interaction of Light with Atoms.- Squeezing.- The Stochastic Schrodinger Equation.- Cascaded Quantum Systems.- Supplement.- Bibliography.- Author Index.- Index.
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