E Brion et al 2007 J. Phys. A: Math. Theor. 40 1033 doi:10.1088/1751-8113/40/5/011
E Brion, L H Pedersen and K Mølmer
Show affiliationsThis paper deals with different ways to extract the effective two-dimensional lower level dynamics of a lambda system excited by off-resonant laser beams. We present a commonly used procedure for elimination of the upper level, and we show that it may lead to ambiguous results. To overcome this problem and better understand the applicability conditions of this scheme, we review two rigorous methods which allow us both to derive an unambiguous effective two-level Hamiltonian of the system and to quantify the accuracy of the approximation achieved: the first relies on the exact solution of the Schrödinger equation, while the second resorts to the Green's function formalism and the Feshbach projection operator technique.
32.80.-t Photoionization and excitation
31.15.-p Calculations and mathematical techniques in atomic and molecular physics
78A60 Lasers, masers, optical bistability, nonlinear optics (See also 81V80)
Issue 5 (2 February 2007)
Received 9 October 2006, in final form 27 November 2006
Published 17 January 2007
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