Jaynes-Cummings Model in Counter Propagating Waves Basis: Large Numbers of Excitations

The Jaynes-Cummings (JC) model is presented based on quantized counterpropagating waves, characteristic of a ring resonator. This model, in addition to the Hamiltonian and the operator of the number of excitations, includes an interference operator whose eigenvalues imitate the term cos 2kz of the classical picture of the field. The average number of photons, dispersion, the Mandel parameter Q, and atomic-photon entanglement in states with certain excitations are considered. The collapses and revivals are revealed, which in the standard JC model are present only in states with an indefinite number of excitations. It is shown that photons at the boundary energy levels are antibunched (with Q ≈ –1/2) regardless of the system’s parameters, and photons of other energy levels are grouped to the degree that grows with the total number of photons.