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The Effect of Phases on Time-Dependent Three Coupled Quantum Systems
M. M. Nassar and M. Sebawe Abdalla

In this communication we study a time-dependent quantum system consists of parametric amplifier and frequency converter terms. The Hamiltonian model we have introduced contains three coupling parameters in addition to three phases pump. The time-dependent dynamical operators have been obtained by solving the equations of motion in Heisenberg picture. The results are employed to discuss the nonclassical properties of the system. The main concentration was on studying the variation would occur in the system behavior resultant of changing the phases pump. It has been shown that if the system is initially in the coherent states an increase in the phases value leads to chaotic behavior. Furthermore, for large value of the coupling parameters l1 and l2 (both coupling are response of the parametric amplifier terms) the system gets sensitive for any variations in the phases pump and the nonclassical phenomenon becomes pronounced.

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