Non-Markovian quantum dissipation in the Kraus representation

¹ Institute of Theoretical Physics, University of Amsterdam Valckenierstraat 65, NL-1018 XE Amsterdam, The Netherlands
² Institute of Physical Chemistry, University of Zurich Winterthurerstrasse 190, CH-8057 Zurich, Switzerland

Received: 27 April 2005
Accepted: 29 June 2005

Abstract

In order to describe the evolution of a quantum system that is coupled to a reservoir, a non-phenomenological Kraus map is constructed. At time zero, system and reservoir are not entangled. In the perturbative series for the density operator of the system all reservoir correlation functions are factorised into products of pair-correlation functions. This allows for a resummation of the perturbative series up to infinite order. The density operator can be expressed in terms of an auxiliary system operator that satisfies an analytically tractable integral equation. Hence, the difficulties caused by integral kernels of Nakajima-Zwanzig type are circumvented. Assuming an interaction between system and reservoir of the Jaynes-Cummings form, one shows that the Kraus map is capable of generating Rabi oscillations of a two-level atom. If the reservoir is a continuum, the Kraus map reproduces the Wigner-Weisskopf theory of spontaneous emission.