Eur. Phys. J. D (2014) 68: 173
https://doi.org/10.1140/epjd/e2014-50138-y

Regular Article

The two-mode multi-photon intensity-dependent Rabi model

Institute of Theoretical Physics and Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong SAR, P.R. China

^a e-mail: cflo@phy.cuhk.edu.hk

Received: 22 February 2014
Received in final form: 20 March 2014
Published online: 27 June 2014

Abstract

We have investigated the energy eigen-spectrum of the two-mode k-photon intensity-dependent Rabi (IDR) model for k ≥ 2. Our analysis shows that the model does not have eigenstates in the Hilbert space spanned by the eigenstates of the two-mode k-photon intensity-dependent Jaynes-Cummings (IDJC) model, which is obtained by applying the rotating-wave approximation (RWA) to the two-mode k-photon IDR model. That is, the two-mode k-photon IDR model is ill-defined for k ≥ 2, and it is qualitatively different from the RWA counterpart which is valid for all values of k, implying that the counter-rotating term does drastically alter the nature of the RWA counterpart. Hence, the previous study of the effect of the counter-rotating term in the two-mode k-photon IDJC model via the time-dependent perturbation expansion is completely invalid.