Validity of the rotating wave approximation in the driven Jaynes–Cummings model

Photon generation through decoherence in cavity QED: analytical analysis

“…The range of validity of RWA has been studied for a long time and the common sense [2,3,6] is that it is valid for a weak field amplitude, small g and small detuning |∆| ≪ 1, where ∆ ≡ ω 0 − ω. Several numerical studies exemplified the deviation of the dynamics of the RH compared to the one expected from the JCH [6,22,23,24,25], thereby demonstrating the breakdown of RWA in specific regimes. Alternative approximations have been also suggested in order to increase the validity of the RWA [26,27].…”

“…The system of equations ( 6) is not closed because of the dynamic variables ζ ≡ 2x 2 σ z and α ≡ (xp + px) σ z , which obey the corresponding differential equations. Therefore, this system of equations cannot be integrated exactly, although some numerical methods for its solution based on semi-Lie algebra have been proposed [24]. For simplicity, from now on we shall neglect the pure cavity dephasing, setting Γ ph = 0.…”

Rabi model beyond the rotating-wave approximation: Generation of photons from vacuum through decoherence

“…Therefore, the total energy of the system H is conserved and no violation of physical laws occur. Besides, recent works questioned the validity of the RWA [35,36,37] and proposed alternative analytical approximate methods [6,8]. Moreover, it was shown that the antirotating term is responsible for several novel quantum mechanical phenomena, such as quantum irreversibility and chaos [38,39], quantum phase transitions [40], implementation of Landau-Zener transitions of a qubit in circuit QED architecture [41,42], generation of atom-cavity entanglement [43,44], and simulation of the dynamical Casimir effect (DCE [45]) in semiconducting microcavities [46,47,48] or circuit QED [44].…”

A new perturbative expansion of the time evolution operator associated with a quantum system

“…The main point to understand is that the behavior of a single observable quantity does not contain, in general, all the 'information' encoded in the evolution operator. Several authors have investigated the contribution of the 'counter-rotating terms' in various quantum optical models, contribution which is completely ignored by the RWA; for instance, perturbative corrections to the energy spectrum [29], and corrections to the time evolution by means of path integral [30], perturbative [31,32,33] and numerical [34,35] techniques have been studied. However, as far as we know, our approach is the first systematic attempt at taking into account the corrections to the RWA evolution operator from a completely general point of view, which allows also to gain a deeper insight in the different roles played by the RWA and counter-rotating terms.…”