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Physica A Statistical Mechanics and its Applications

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

Chi‐Fai Lo, K.L. Liu

Published Sep 1, 1999• 3 citations
Publisher
DOI
10.1016/s0378-4371(99)00214-9

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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.
In this paper we have investigated the eigen energy spectrum of the k-photon Jaynes-Cummings (JC) model without the rotating-wave approximation (RWA). Our analysis shows that for k > 2 the k-photon 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 JC model without the RWA is qualitatively different from the RWA counterpart which is valid for all values of k and the coupling parameter.