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Mathematical Structure of Rabi Oscillations in the Strong Coupling Regime
In this paper we generalize the Jaynes--Cummings Hamiltonian by making use of
some operators based on Lie algebras su(1,1) and su(2), and study a
mathematical structure of Rabi floppings of these models in the strong coupling
regime. We show that Rabi frequencies are given by matrix elements of
generalized coherent operators (quant--ph/0202081) under the rotating--wave
approximation.
In the first half we make a general review of coherent operators and
generalized coherent ones based on Lie algebras su(1,1) and su(2). In the
latter half we carry out a detailed examination of Frasca (quant--ph/0111134)
and generalize his method, and moreover present some related problems.
We also apply our results to the construction of controlled unitary gates in
Quantum Computation. Lastly we make a brief comment on application to Holonomic
Quantum Computation.Comment: Latex file, 24 pages. I added a new section (Quantum Computation), so
this paper became self-contained in a certain sens