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Q: Fachverband Quantenoptik und Photonik
Q 30: Poster II
Q 30.4: Poster
Tuesday, March 3, 2009, 16:30–19:00, VMP 9 Poster
Time-normally ordered correlation functions in the Wigner representation — •Bettina Berg1, Lev I. Plimak1, Anatoli Polkovnikov2, Murray K. Olsen3, Michael Fleischhauer4, and Wolfgang P. Schleich1 — 1Institute of Quantum Physics, Ulm University, Germany — 2Department of Physics, Boston University, USA — 3ARC Centre of Excellence for Quantum-Atom Optics, University of Queensland, Australia — 4Fachbereich Physik, Technische Universität Kaiserslautern, Germany
Applicability of the so-called truncated Wigner approximation (−W) [1] is extended to multitime averages of Heisenberg field operators.
We develop a path-integral approach in phase-space based on the symmetric operator ordering. This results in a new class of averages of the Heisenberg operators which we call time-symmetric. The −W emerges as an approximation within this path-integral approach.
Furthermore, we show how the time-symmetric averages calculated by −W can be converted to the time-normal order by relating commutators of Heisenberg operators to response of the system. For two-time commutators, this is nothing but Kubo’s renowned formula for the linear response function [2]. The latter can be easily calculated numerically by introducing “quantum jumps” into phase-space trajectories [3].
[1] M. J. Werner, P. D. Drummond, J. Comput. Phys. 132, 312 (1997). [2] R. Kubo, Lectures in Theoretical Physics, v. 1 (Wiley, New York, 1959). [3] M.K. Olsen et al., Phys. Rev. A62, 023802, (2000); A. Polkovnikov, Phys. Rev. A68, 053604 (2003).