为了研究非线性对囚禁离子沿两个正交方向的振动模式之间的互相关函数的影响, 采用理论分析和数值计算相结合的方法, 对单个2维三能级囚禁离子与两个经典驻波激光相互作用的非线性双光子Jaynes-Cummings模型进行了严格求解, 并对囚禁离子沿两个正交方向的振动模式之间的互相关函数进行了数值分析。结果表明,当初始平均量子数较小时, 反关联效应随Lamb-Dicke参量的增大先是增强然后减弱, 但是关联效应却随Lamb-Dicke参量的增大一直增强。随着初始平均量子数的增大, 反关联效应会减弱直至消失;表征非线性效应的Lamb-Dicke参量和初始振动运动平均量子数对交叉关联有明显的影响。

采用线性化近似方法计算了单模激光系统的光强关联函数，讨论了光强关联函数随时间的演化关系，发现光强关联函数呈现周期振荡的现象.关联函数振荡的幅度和周期不受量子噪音强度、抽运噪音强度和交叉关联程度的影响,输入信号频率会改变关联函数振荡的周期和幅度，但不改变振荡的平衡位置,量子噪音强度会改变振荡极值的位置,四个参量都改变关联函数衰减的初始值，但关联函数对时间周期调制频率不敏感.

用线性化近似方法计算了噪声间关联程度λ受时间周期调制下单模激光系统的光强关联时间T, 结果表明, 无论λ=0, λ>0或λ<0, T随量子噪声强度D和抽运噪声强度Q的变化均呈单调增长且最终趋于饱和(T＝1), 只是当λ<0时T随Q的变化曲线出现一极小值(存在抑制现象); 当λ=0时, T不随时间周期调制频率Ωλ变化, 当λ>0和λ<0, Ωλ取值小时T-Ωλ曲线出现高频振荡, 随着Ωλ值增大振荡频率变低, 振幅变小, 最后趋于与λ=0的T值一致。

Considering a single-mode laser system with cross-correlated additive colored noise and multiplicative colored noise, we study the effects of correlation among noises on the normalized intensity correlation function C(s). C(s) is derived by means of the projection operator method. The effects of the self-correlation time \tau1 of the additive colored noise, \tau2 of the multiplicative colored noise, and the effect of the cross-correlation time \tau0 between the two noises on C(s) are discussed by numerical calculation. For the case of positive correlation (\lambda&gt;0), it is found that when a0&gt;0 the normalized intensity correlation function C(s) increases with the increase of \tau0 or \tau2, and with value of \tau0 or \tau2 becoming larger, C(s) comes to saturation. With increasing the self-correlation time \tau1 of the additive noise, a minimum and a maximum will appear on curve of C(a) as a0&gt;0. If a0&lt;0, C(s) decreases with the increase of \tau0, \tau1, and \tau2.

A single-mode laser system with colored cross-correlated additive and multiplicative noise terms is considered. By the means of projection operator method, we study the effects of the cross-correlation time 'tau' and the cross-correlation intensity 'lambda' between noises on the normalized intensity correlation function C(s). It is found that if 'lambda'&gt;0 ('lambda'&lt;0), the normalized intensity correlation function C(s) increases (decreases) with increasing the cross-correlation time 'tau', and at large value of 'tau', the variation of the normalized intensity correlation function C(s) becomes small. With the increase of the net gain a0, C(s) exhibits a maximum when 'lambda' is larger. However, a minimum and a maximum appear on C(s) curves with the increase of a0 when 'lambda' becomes smaller and smaller.