Exact solutions are obtained for a collective model of two identical two-level atoms interacting with a quantized bimodal field with intensity-dependent coupling terms in a lossless cavity. A unitary transformation method is used to solve the time-dependent problem that also gives the eigensolutions of the interaction Hamiltonian. The atomic population dynamics and the dynamics of the photon statistics of the two cavity modes are studied. We present evidence of cooperative effects.

In this investigation, the effect of Zr substitution at the Ti site of the CaCu3Ti4O12 on the electrical properties has been studied. Samples with composition x = 0.00, 0.10 and 0.30 have been synthesized by the solid state ceramic route in the system CaCu3Ti4−xZrxO12. Powder x-ray diffraction data showed the formation of a single phase solid solution. The structure remains cubic similar to an undoped sample. The Seebeck coefficient, α, is measured on a thick pellet in the temperature range 500–800 K and is found to be negative in this temperature range, indicating n-type conduction in the temperature range of measurement. Dc resistivity, ρdc, and ac conductivity, σac, were measured to understand the mechanism of conduction. Immittance analysis is used to separate the contributions of the grains and grain boundaries to the total observed resistance. From the temperature and frequency dependence of ac conductivity, it is concluded that at and around room temperature conduction occurs due to thermally activated rotation of dipoles while at high temperature it occurs due to excitation of charge carriers at the conduction band edge and hopping at energies close to it. From the immittance analysis it is observed that activation energies of conduction for grains and grain boundaries are almost equal indicating the same mechanism of conduction.

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In the present paper, the eigenfunctions and eigenvalues of the Hamiltonian of the interacting system have been obtained in two generalized Jaynes Cummings models separately, one in which the transition are mediated by two different modes of photon in the ladder configuration and the other involving two mode multi-photon interaction between the field and the atom. Effect of intensity dependent coupling between the field and the atom in both the above-mentioned cases have been investigated. Graphical features of the time dependence of population inversion have been analyzed when one of the field modes is prepared initially in a coherent state while the other one in a vacuum state.The unitary transformation method presented here for the special case of exact resonance not only solves the time-dependent problem but also provides the eigensolutions of the interacting Hamiltonian at the same time.Keywords Jaynes-Cummings (J-C) model · Rotating wave approximation (RWA) · Unitary operatorT · Two-mode ladder model · Two-mode k-photon interaction (2k interaction) ladder model · Intensity dependent coupling · Atomic population inversion W (t)