A Rabi Oscillation in Four and Five Level Systems

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In this paper we consider a general model of an atom with n energy levels interacting with n-1 external (laser) fields which is a natural extension in the two and three level systems. We exactly solve the Schr{\" o}dinger equation to obtain a Rabi oscillation when n = 4 and 5, which will constitute a quantum logic gate of Quantum Computation based on four and five level systems.
Latex file ; 14 pages ; 1 figure ; many typos corrected. To appear in Yokohama Mathematical Journal

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