Semiclassical theory of field-induced thermal transition rate with application to output coupling of a Bose-Einstein gas at finite temperature

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Abstract
Electromagnetically induced output coupling of a trapped Bose-Einstein gas at finite temperatures into propagating or bound matter waves is equivalent in many ways to molecular processes such as photodissociation at finite temperature. We develop a semiclassical approximation for the transfer rate of a thermal distribution of atoms or molecules between two potential surfaces under the influence of an external electromagnetic field. To leading order, the result is an integral over phase space, restricted by energy conservation and weighted by the initial thermal phase-space distribution. The validity of the method is demonstrated by a set of examples. Applying the theory to the case of weak output coupling of a magnetically trapped atomic Bose-Einstein gas at finite temperature into a loosely confined or unconfined state, we give quantitative predictions for the spectrum of transition rates in real situations. An asymmetric broadening of the spectrum of transitions relative to the expected spectrum of transitions at zero temperature is obtained, which may be related to the asymmetric spectral broadening observed recently in a similar situation.