耦合腔系统双光子过程中的纠缠特性

The entanglement properties in the system of two double-level atoms trapped in two coupled cavities

研究原子与耦合腔相互作用系统,考虑每个腔囚禁一个二能级原子,并且原子通过双光子跃迁与腔场发生共振相互作用,通过解薛定谔方程导出了系统态矢的演化规律;利用负本征值度量两个子系统间的纠缠,研究两原子间和原子与腔场间的纠缠演化,讨论了两腔场间耦合系数变化对纠缠的影响。研究结果表明:随腔场间耦合系数增大,原子间的纠缠和原子与腔场间纠缠均表现出从不规则振荡向准周期性演化的转变,当腔场间耦合系数大于一定值后它们均呈现出准周期性演化规律;而曲线平均值呈现时而增大时而减小的过程,表明它们与腔场耦合系数间存在非线性关系;另一方面,当腔场间耦合系数较小时,原子与腔场间纠缠还呈现出崩塌和恢复现象。

We consider a system consisting of two two-level atoms interacting with two coupled cavities via a two-photon hopping.Two atoms are individually trapped in two coupled cavities.The evolution of the state vector of the system is given by solving the Schrodinger equation.Negativity is used to quantify the degree of entanglement.By means of the numerical calculations,we investigate the temporal evolution in the entanglement between atoms and that between atom and cavity.Through comparing the results of different cavity-cavity coupling coefficients,the influence of cavity-cavity coupling coefficient on the entanglement is discussed.The obtained results show that the atom-atom entanglement and atom-cavity entanglement both display the evolution which is from the irregular oscillations to quasi-periodic oscillation with the cavity-cavity coupling coefficient increasing.The average value of atom-atom entanglement and that of atom-cavity entanglement sometimes increase and sometimes decrease.It shows that there is non-linear relationship between atom-atom entanglement and cavity-cavity coupling coefficient,or between atom-cavity entanglement and cavity-cavity coupling coefficient.On the other hand,when the cavity-cavity coupling coefficient is small,the entanglement between atom and cavity exhibits the phenomenon of collapse and recovery.