Beyond adiabatic elimination: A hierarchy of approximations for multi-photon processes

. In multi-level systems, the commonly used adiabatic elimination is a method for approximating the dynamics of the system by eliminating irrelevant, nonresonantly coupled levels. This procedure is, however, somewhat ambiguous and it is not clear how to improve on it systematically. We use an integr...

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Bibliographic Details
Published in:European physical journal plus 2014-01, Vol.129 (1), p.12, Article 12
Main Authors: Paulisch, Vanessa, Rui, Han, Ng, Hui Khoon, Englert, Berthold-Georg
Format: Article
Language:English
Subjects:
Adiabatic flow
Amplitudes
Applied and Technical Physics
Approximation
Atomic
Complex Systems
Condensed Matter Physics
Differential equations
Mathematical analysis
Mathematical and Computational Physics
Molecular
Optical and Plasma Physics
Physics
Physics and Astronomy
Regular Article
Schrodinger equation
Theoretical
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Summary:. In multi-level systems, the commonly used adiabatic elimination is a method for approximating the dynamics of the system by eliminating irrelevant, nonresonantly 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 Schrödinger 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 provides significant improvements over standard adiabatic elimination, without much increase in complexity, and is furthermore not so sensitive to the choice of interaction picture. We illustrate these points with several examples.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/i2014-14012-8