Exponentiation of certain Matrices related to the Four Level System by use of the Magic Matrix

Details Exponentiation of certain Matrices related to the Four Level System by use of the Magic Matrix Exponentiation of certain Matrices related to the Four Level System by use of the Magic Matrix

2007-01-15

arxiv.org/abs/quant-ph/0701092v3

Yokohama Math. J. 54(2007) 31-44

Physics

Quantum Physics

Latex ; 13 pages ; 2 figures ; substantial changes (including the title) made. To appear in Yokohama Mathematical Journal (200

Scientific paper

In this paper we show how to calculate explicitly the exponential of certain matrices, which are evolution operators governing the interaction of the four level system of atoms and the radiation, etc. We present a consistent method in terms of the magic matrix by Makhlin. As a closely related subject, we derive a closed form expression of the Baker-Campbell-Hausdorff formula for a class of matrices in SU(4), by use of the method developed by the present authors in quant-ph/0610009.

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