The Properties Of Entanglement For The System Of Trapped Ions And Nonlinear Coupler Inside The Optical Cavity

Quantum entanglement is not only a basic question in quantum mechanics,but also have an important significance in quantum information science.We study the generation of entangled motional coherent state of two distant ions trapped in two cascaded cavities, in which the motional mode of the each ion is coupled to the respective cavity field via a linear-mixing interaction. The master equation is solved analytically by use of the characteristic function method. It is found that the generated entangled coherent state resulted from the initial preparation of an even coherent state is more robust than that from an odd coherent state under the dissipation of the cavity.We also study the property of two-mode squeezed and entangled light generated in a nonlinear coupler inside an optical cavity. We solve analytically the master equation of the two-mode field, with the method of characteristic function. It shows that the state of the two-mode field is a two-mode Gaussian one. We find that, under some conditions, the two-mode cavity field exhibits stable two-mode squeezing and continuous variable entanglement. The degree of the squeezing and entanglement is dependent on the damping rate of the cavity field and the coupling constants between the two modes.