Evolution of the vacuum Rabi peaks in a many-atom system

Summary form only given. The two peaks of the vacuum Rabi splitting behave like simple harmonic oscillators for very weak excitation. The transmission spectrum of a cavity filled with a collection of two-level atoms shows this doublet and, for sufficiently high intensities, its evolution into a single peak. As the excitation increases anharmonicity grows in the oscillators to a point where frequency hysteresis appears in the transmission spectrum. The saturation of the transition of the two-level atoms is responsible for the nonlinearity that causes the anharmonicity. This work investigates the transition from the doublet into the singlet. We include the possibility of a detuning between the atomic and cavity resonances.