Darmstadt 2008 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 40: Quantengase (Bosonen I)
Q 40.3: Talk
Thursday, March 13, 2008, 14:30–14:45, 1A
Commuting Heisenberg operators in the Wigner representation — •Bettina Berg1, Lev Plimak1, Murray K. Olsen2, Michael Fleischhauer3, and Wolfgang P. Schleich1 — 1Institute of Quantum Physics, Ulm University, Germany — 2School of Physical Sciences, University of Queensland, Australia — 3Fachbereich Physik, Technische Universität Kaiserslautern, Germany
We discuss commuting Heisenberg operators as a response problem in the phase space. In the Wigner representation one calculates averages of symmetrically ordered two-time operator pairs [1]. As the quantities that are experimentally measured are the time-normally ordered correlation functions, we need a way of commuting Heisenberg operators at different times. For an operator pair, solution to this problem is given by Kubo’s linear response relation [2] expressing the commutator as a linear response function. This quantity can be found in the Wigner representation simply by adding sources to the “Langevin” equations in the phase space. By using the truncated Wigner representation [3], one can calculate the normally-ordered correlation functions approximately yet with relative ease. These techniques are demonstrated for the Bose-Hubbard model [4].
[1] L. I. Plimak, M. K. Olsen, M. Fleischhauer, M. J. Collett, Europhys. Lett. 56, 372 (2001). [2] R. Kubo, Lectures in Theoretical Physics, v. 1 (Wiley, New York, 1959). [3] M. J. Werner, P. D. Drummond, J. Comput. Phys. 132, 312 (1997). [4] D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, P. D. Zoller, Phys. Rev. Lett. 81, 3108 (1998).