A Class of Quasi-exact Solutions of Rabi Hamiltonian

A class of quasi-exactsolutions of the Rabi Hamiltonian, which describes a two-level atominteracting with a single-mode radiation field via a dipoleinteraction without the rotating-wave approximation, are obtained byusing a wavefunction ansatz. Exact solutions for part of thespectrum are obtained when the atom-field coupling strength and thefield frequency satisfy certain relations. As an example, the lowestexact energy level and the corresponding atom-field entanglement atthe quasi-exactly solvable point are calculated and compared toresults from the Jaynes-Cummings and counter-rotating cases of theRabi Hamiltonian.