The multiquantum intensity-dependent Jaynes–Cummings model with the counterrotating terms

In this paper we have investigated the eigen energy spectrum of the k-photon intensity-dependent Jaynes–Cummings (JC) model without the rotating-wave approximation (RWA). Our analysis shows that for k⩾2 the k-photon intensity-dependent JC model without the RWA does not have eigenstates in the Hilbert space spanned by the photon number states, i.e. the model becomes ill-defined. Hence, the k-photon intensity-dependent JC model without the RWA is qualitatively different from the RWA counterpart which is valid for all values of k and the coupling parameter. As a consequence, previous studies of the effects of the counterrotating terms in the k-photon intensity-dependent JC model for k⩾2 are all invalid.