Kalka M, Spisak B J, Woźniak D, Wołoszyn M, Kołaczek D
Faculty of Physics and Applied Computer Science, AGH University of Krakow, al. Mickiewicza 30, 30-059, Krakow, Poland.
Department of Applied Mathematics, University of Agriculture in Kraków, ul. Balicka 253c, 30-198, Kraków, Poland.
Sci Rep. 2023 Sep 27;13(1):16266. doi: 10.1038/s41598-023-43421-2.
The phase-space approach based on the Wigner distribution function is used to study the quantum dynamics of the three families of the Schrödinger cat states identified as the even, odd, and Yurke-Stoler states. The considered states are formed by the superposition of two Gaussian wave packets localized on opposite sides of a smooth barrier in a dispersive medium and moving towards each other. The process generated by this dynamics is analyzed regarding the influence of the barrier parameters on the nonclassical properties of these states in the phase space below and above the barrier regime. The performed analysis employs entropic measure resulting from the Wigner-Rényi entropy for the fixed Rényi index. The universal relation of this entropy for the Rényi index equal one half with the nonclassicality parameter understood as a measure of the negative part of the Wigner distribution function is proved. This relation is confirmed in the series of numerical simulations for the considered states. Furthermore, the obtained results allowed the determination of the lower bound of the Wigner-Rényi entropy for the Rényi index greater than or equal to one half.
基于维格纳分布函数的相空间方法被用于研究三类被确定为偶态、奇态和尤尔克 - 斯托勒态的薛定谔猫态的量子动力学。所考虑的态由两个高斯波包叠加而成，这两个波包位于色散介质中一个光滑势垒的两侧，并相互靠近。针对势垒参数对这些态在势垒区域上下的相空间中非经典性质的影响，分析了这种动力学所产生的过程。所进行的分析采用了由固定雷尼指数的维格纳 - 雷尼熵得出的熵度量。证明了雷尼指数等于二分之一时该熵与被理解为维格纳分布函数负部度量的非经典性参数之间的普遍关系。在针对所考虑态的一系列数值模拟中证实了这种关系。此外，所获得的结果使得能够确定雷尼指数大于或等于二分之一时维格纳 - 雷尼熵的下限。
