Vanessa Paulisch, Rui Han, Hui Khoon Ng, Berthold-Georg Englert
In multi-level systems, the commonly used adiabatic elimination is a method for approximating the dynamics of the system by eliminating irrelevant, non-resonantly coupled levels. This procedure is, however, somewhat ambiguous and it is not clear how to improve on it systematically. We use an integro-differential equation for the probability amplitudes of the levels of interest, which is equivalent to the original Schr\"odinger equation for all probability amplitudes. In conjunction with a Markov approximation, the integro-differential equation is then used to generate a hierarchy of approximations, in which the zeroth order is the adiabatic-elimination approximation. It works well with a proper choice of interaction picture; the procedure suggests criteria for optimizing this choice. The first-order approximation in the hierarchy is found to be sufficient for practical purposes, and is not so sensitive to the choice of interaction picture. We illustrate the method for a single three-level atom and a pair of three-level atoms with Rydberg blockade.
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http://arxiv.org/abs/1209.6568
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