基于代数动力学方法实现一类相干态的构建

最近提出的一个构建相干态的方案中,需要精确求解一个时间相关的常微分方程.基于代数动力学理论,利用该方程具有的SU(1,1)动力学对称性,提出了对此方程在含时系数取任意函数形式时的统一的精确求解方法,并且得到了严格的解析解.运用这个精确解,就可以构造相应物理系统的精确相干态的具体表达式.给出了一个解例,即频率取"快变"函数的情形.利用得到的精确结果,讨论了这个系统的量子涨落(量子噪声)随时间演化的情况.针对动量算符不确定度随时间演化的曲线的性态,指出在制备这个系统压缩态时可以利用的一些性质.最后,讨论了这个量子系统的不确定关系随时间演化的情况.

Realization of the Construction of a Class of Coherent States Based on Algebraic Dynamics

In an approach to construct coherent states proposed recently, there is the requirement to solve a time-dependent ordinary differential equation (TDODE). Based on the consideration that the equation possesses SU(1,1) dynamical symmetry, we propose a uniform method for solving the TDODE exactly by means of the theory of algebraic dynamics, whatever the time-dependent frequency takes what form as a function of time. Then, after impacting the time-dependent frequency take a specific form, which is a sudden change function, we obtain the exact solution with the method. Next, we construct the corresponding coherent states with the help of this exact solution. Then the evolution of quantum fluctuation (quantum noise) is discussed. According to the property of the curve of the uncertainty of momentum operator, we point out some properties which can be utilized when preparing the squeezed states of this quntum system. At last, the evolution of the uncertainty relation with time is discussed.