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 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 full matrix
diagonalization.Comment: 8pages, 1 figure, LaTeX. Accepted for publication in J. Phys. B: At.
Mol. Opt. Phy
