When is the two-level approximation untenable in issues of Decoherence?

Abstract

We examine the conditions in favor and necessity of a realistic multileveled description of a decohering quantum system. Under these conditions approximate techniques to simplify a multileveled system by its first two levels is unreliable and a realistic multilevel description in the formulation of decoherence is unavoidable. In this regard, our first crucial observation is that, the validity of the two level approximation of a multileveled system is not controlled purely by {\it sufficiently low temperatures}. We demonstrate using three different environmental spectral models that the type of system-environment coupling and the environmental spectrum have a dominant role over the temperature. Particularly, zero temperature quantum fluctuations induced by the Caldeira-Leggett type linear coordinate coupling can be influential in a wide energy range in the systems allowed transitions. The second crucial observation against the validity of the two level approximation is that the decoherence times being among the system's short time scales are found to be dominated not by the resonant but {\it non-resonant} processes. We demonstrate this in three stages. Firstly, our zero temperature numerical calculations reveal that, the calculated decoherence rates including relaxation, dephasing and leakage phenomena show, a linear dependence on the spectral area for all spectral models used, independent from the spectral shape within a large environmental spectral range compared to the quantum system's energies. Secondly, within the same range, the decoherence times only have a marginal dependence on the translations of the entire frequency spectrum. Finally, the same decoherence rates show strong dependence on the number of coupled levels by the system-environment coupling.