Abstract
A Hamiltonian, that describes the interaction between a two-level atom (su(2) algebra) and a system governed by su(1,1) Lie algebra besides two external interaction, is considered. Two canonical transformations are used, which results into removing the external terms and changing the frequencies of the interacting systems. The solution of the equations of motion of the operators is obtained and used to discuss the atomic inversion, entanglement, squeezing and correlation functions of the present system. Initially the atom is considered to be in the excited state while the other systems is in the Perelomov coherent state. Effects of the variations in the coupling parameters to the external systems are considered. They are found to be sensitive to changing entanglement, variance and entropy squeezing.
Highlights
It is well known that the interaction between atom and electromagnetic field plays crucial role in the quantum optics
On the other hand the interaction between three electromagnetic fields represents an important nonlinear parametric interaction, which has played a significant role in several physical phenomena of interest, such as stimulated and spontaneous emissions of radiation, coherent Raman and Brillouin scattering
Note that the interaction between three electromagnetic fields can be transformed into either parametric amplifier or parametric frequency converter; the first type leads to amplification of the system energy while the second type leads to the energy exchanges between modes
Summary
It is well known that the interaction between atom and electromagnetic field plays crucial role in the quantum optics. Note that the interaction between three electromagnetic fields (which is of nonlinear type) can be transformed into either parametric amplifier or parametric frequency converter; the first type leads to amplification of the system energy while the second type leads to the energy exchanges between modes.1–8 This depends on the nature of the used approximation. J± and Jz are the angular momentum operators which belongs to su[2] Lie algebra In this case the Hamiltonian is converted to the Tavis-Cummings model. These two extra classical terms can be interpreted as the exhibition of the effect of the parametric amplification represented by su[1, 1] Lie algebra, while the other term plays the role of external driving force in sense of su[2] Lie algebra This will be achieved by studying the degree of entanglement and the entropy as well as the different types of squeezing..
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