A progressive diagonalization scheme for the Rabi Hamiltonian
Feng Pan, Xin Guan, Yin Wang, Jerry Paul Draayer · Journal of Physics B Atomic Molecular and Optical Physics · 2010
A diagonalization scheme for the Rabi Hamiltonian, which describes a qubit interacting with a single-mode radiation field via a dipole interaction, is proposed. It is shown that the Rabi Hamiltonian can be solved almost exactly using a progressive scheme that involves a finite set of one variable polynomial equations. The scheme is especially efficient for the lower part of the spectrum. Some low-lying energy levels of the model with several sets of parameters are calculated and compared to those provided by the recently proposed generalized rotating-wave approximation and a full matrix diagonalization.