Narrow Results

Phase synchronization between linearly and nonlinearly coupled systems with internal resonance is investigated in this paper. By introducing the conception of phase for a chaotic motion, we tune the linear coupling parameter to obtain the two Rössler oscillators in a synchronized regime and analyze the effect of a nonlinear coupling on the phase synchronized state. It demonstrates that the detuning parameter σ between the two natural frequencies ω₁ and ω₂ affects phase dynamics, and with the increase of the nonlinear coupling strength, for the primary resonance, the effect of phase synchronization between two sub-systems was decayed, while increasing with frequency ratio 1:2. Further investigation reveals that the transition of phase states between the two oscillators are related to the critical changes of the nonlinear coupling strength.

The influence of time dependence on the model which consists of two qubits interacting with a two-mode electromagnetic field of the parametric amplifier type is investigated. The analytical solution of the wave function is obtained. The quantum Fisher information, entanglement and population inversion for a time-dependent system are analyzed. The photon statistics of a single-mode are quantified by the evolution of the Mandel parameter. Our results showed that there exists a positive relationship between the time-dependent parameter and entanglement. In other words, the time-dependent parameter due to the degree of entanglement is increased. Also, the quantum quantifier is strongly affected by the time-dependent coupling parameter in the absence and presence of the detuning parameter. This enables new parameters to control the degree of entanglement and quantum Fisher information, especially in quantum communication.