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Mathematical Structure of Rabi Oscillations in the Strong Coupling Regime

Kazuyuki Fujii
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Abstract

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.

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Kazuyuki Fujii. 2002-11-20. Mathematical Structure of Rabi Oscillations in the Strong Coupling Regime. https://doi.org/10.1088/0305-4470/36/8/309

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