论文标题
结晶的schrödinger猫状态的符号断层造影概率分布
Symplectic tomographic probability distribution of crystallized Schrödinger cat states
论文作者
论文摘要
在量子力学的概率表示的框架内，我们研究了与n个侧面常规多边形对称性相关的通用高斯状态的叠加。换句话说，循环基（包含旋转对称性）和二面基（包含旋转和反转对称性）。我们获得Wigner函数和断层造影概率分布（符号和光学阶段图），以明确确定状态的密度矩阵作为高斯项的总和。获得的Wigner函数表明了非经典行为，即包含负值，而pogract图显示了每个状态的一系列最大值和最小值，其中关键点的数量反映了定义状态的组的顺序。我们讨论了正常概率分布的这种概括的一般特性。
Within the framework of the probability representation of quantum mechanics, we study a superposition of generic Gaussian states associated to symmetries of a regular polygon of n sides; in other words, the cyclic groups (containing the rotational symmetries) and dihedral groups (containing the rotational and inversion symmetries). We obtain the Wigner functions and tomographic probability distributions (symplectic and optical tomograms) determining the density matrices of the states explicitly as the sums of Gaussian terms. The obtained Wigner functions demonstrate nonclassical behavior, i.e., contain negative values, while the tomograms show a series of maxima and minima different for each state, where the number of the critical points reflects the order of the group defining the states. We discuss general properties of such a generalization of normal probability distributions.
