Mathematical Structure of Rabi Oscillations in the Strong Coupling Regime
Kazuyuki Fujii · 2002
In this paper we generalize so--called 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 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.