Study on Dynamics of N Level System of Atom by Laser Fields

Details Study on Dynamics of N Level System of Atom by Laser Fields Study on Dynamics of N Level System of Atom by Laser Fields

2005-12-16

arxiv.org/abs/quant-ph/0512126v2

Contemporary Mathematics and Its Applications (in Russian), 44(2007), 3-15

Physics

Quantum Physics

Latex; 20 pages; 3 figures. The paper was corrected considerably by use of (quant-ph/0604115)

Scientific paper

This paper is an extension of Fujii et al (quant--ph/0307066) and in this one we again treat a model of atom with n energy levels interacting with n(n-1)/2 external laser fields, which is a natural extension of usual two level system. Then the rotating wave approximation (RWA) is assumed from the beginning. To solve the Schr{\" o}dinger equation we set the {\bf consistency condition} in our terminology and reduce it to a matrix equation with symmetric matrix $Q$ consisting of coupling constants. However, to calculate $\exp(-itQ)$ {\bfexplicitly} is not easy. In the case of three and four level systems we determine it in a complete manner, so our model in these levels becomes realistic. In last, we make a comment on Cavity QED quantum computation based on three energy levels of atoms as a forthcoming target.

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