The multiquantum q-deformed Jaynes–Cummings model with the counter-rotating terms

In this paper we have investigated the eigenenergy spectrum of the k-quantum q-deformed Jaynes–Cummings (JC) model without the rotating-wave approximation (RWA). Our analysis has shown that the k-quantum q-deformed 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-quantum q-deformed JC model without the RWA is qualitatively different from the RWA counterpart which is valid for all values of k and the coupling parameter. In other words, the counter-rotating terms do drastically alter the nature of the system.