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. Lastly we make a brief comment on application to Holonomic Quantum Computation. ∗E-mail address : [email protected]