利用有序算符内的积分技术和热纠缠态表象,导出了线性共振力作用下扩散过程中密度矩阵主方程的解,给出密度算符的演化公式.并求出了真空态和单光子叠加态Wigner函数的解析表达式.采用数值计算方法,描绘了Wigner函数的演化曲线,以及负部体积随耗散时间的演化曲线.通过对Wigner函数演化曲线的分析,讨论了耗散过程和线性共振力作用对其量子特性的影响.研究结果表明:随耗散时间延长,真空态和单光子叠加态的Wigner函数负值范围和负值深度都在逐渐减小,直至消失;另一方面,线性共振力会使Wigner函数发生平移.

The diffusion master equations of density operators under action of linear resonance force were concisely solved by virtue of thermo entangled state representation and the technique of integration within an ordered product of operators.The evolution formula of the field density operator was given,and the Wigner function evolution formula which is in superposition of vacuum state and single-photon state initially was obtained.By numerically calculating the Wigner function was plotted,and the evolution of negative volume of Wigner function with dissipation time was calculated.Through the analysis of the Wigner function,the effect of decoherence on nonclassical property of the state was discussed.Numerical results show that the negativity area size and the depth of negativity of its Wigner function decrease until vanish with dissipation time.In addition,on the other hand,Wigner function can be slipped under the action of linear resonance force.