Nonlinear multiquantum Jaynes-Cummings model with counter-rotating terms

Abstract

In this paper we have investigated the eigenenergy spectrum of the nonlinear k-quantum Jaynes-Cummings (JC) model without the rotating-wave approximation (RWA). Our analysis has shown that the nonlinear k-quantum JC model without the RWA does not have eigenstates in the Hilbert space spanned by the number states, i.e. the model becomes ill-defined. Hence, the nonlinear k-quantum 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.