Wave packet methods in cavity QED

Abstract

The Jaynes-Cummings model, with and without the rotating wave approximation, is expressed in the conjugate variable representation and solved numerically by wave packet propagation. Both cases are then cast into systems of two coupled harmonic oscillators, reminiscent of coupled bound electronic potential curves of diatomic molecules. Using the knowledge of such models, this approach of the problem gives new insight of the dynamics. The effect of the rotating wave approximation is discussed. The collapse-revival phenomenon is especially analyzed in a non-standard manner. Extensions of the method is briefly mentioned in terms of a three-level atom and the Dicke model.

Quantum interference structures in trapped-ion dynamics beyond the Lamb-Dicke and rotating wave approximations

“…For a one-dimensional system, as the one we consider, it resembles an idealized diatomic molecule for which only two coupled bound electronic states are taken into account. A similar analogy, but between a diatomic molecule and a cavity QED model, was pointed out in [28,29], works that also made use of the wave packet method. As the standard viewpoints and methods applied in quantum optics and molecular physics are rather different, we discuss them and their relation in some depth with the aim to facilitate branching out and combining the two research fields.…”

“…This introduces three different time scales of the interaction, suggesting an application of the RWA. It is known, however, that the validity of the RWA does not solely depend on the involved time scales, but also on the relative amplitudes of the coupling parameters [28,29]. In particular, only for ion-field couplings much smaller than the ion level separation and vibrational spacingλη sin(φ) ≪ Ω, ω and λ cos(φ) ≪ Ω, ω, -is the RWA justified.…”