Characterization of atomic state evolution in the JC and anti-JC models: spin-displaced field modes in the quantum Rabi model

Abstract

In this article, characterization of the atomic state evolution in the Jaynes-Cummings (JC) and anti-Jaynes-Cummings (aJC) models means using the reduced atomic state degree of purity, concurrence and spin excitation number to determine the ranges and critical values of the mean photon number and frequency detuning parameters at which the atom is in a disentangled pure, mixed or entangled state. By unifying the mean photon number amplitude and detuning parameters in a simple relation, leaving the mean photon number as the only variable parameter, we have discovered a beautiful natural evolution property where the atom is in a uniformly mixed state describing symmetrical stable evolution of collapses and revivals of the degree of purity and concurrence, one above and the other below, a uniformly mixed state axis through points of equal degree of purity and concurrence at 1√