香农熵的位置($S_{\rvec}$)和动量($S_{\pvec}$)空间,以及它们的总和($S_t$)的单位归一化密度的He,Li $^+$和Be $^{2+}$离子,空间上被限制在一个不可穿透的球形外壳的中心定义的半径$r_c$。基态和一些选定的低激发态,\emph{viz.,} 1 sns(n $=$ 2-4)$^3$ S,1个SNP(n $=$ 2-3)$^3$ P,1 s3 d $^3$ D在密度泛函方法中被考虑,该方法利用基于功函数的交换势以及两个相关势(局部Wigner型参数化泛函以及更多涉及的非线性梯度和Laplacian依赖的Lee-Yang-Parr泛函)。通过广义伪谱(GPS)方法,使用最佳空间离散方案求解径向Kohn-Sham(KS)方程。详细的系统分析的限制系统(相对于相应的自由系统)已执行这些量相对于$r_c$在表格和图形的形式,\emph{with and without}电子相关。由于压缩,前述状态中的熵的模式的特征在于中间和较低$r_c$区域处的各种交叉。电子关联的影响在较弱的约束极限中更为明显,并且随着约束强度的增加而衰减。仅交换的结果非常好,可以提供一个体面的定性讨论。熵不确定性关系提供的下界在所有情况下都成立。观察到其他一些新的有趣的功能。
英文摘要:
Shannon entropy in position ($S_{\rvec}$) and momentum ($S_{\pvec}$) spaces, along with their sum ($S_t$) are presented for unit-normalized densities of He, Li$^+$ and Be$^{2+}$ ions, spatially confined at the center of an impenetrable spherical enclosure defined by a radius $r_c$. Both ground as well as some selected low-lying singly excited states, \emph{viz.,} 1sns (n $=$ 2-4) $^3$S, 1snp (n $=$ 2-3) $^3$P, 1s3d $^3$D are considered within a density functional methodology that makes use of a work-function-based exchange potential along with two correlation potentials (local Wigner-type parametrized functional as well as the more involved non-linear gradient- and Laplacian-dependent Lee-Yang-Parr functional). The radial Kohn-Sham (KS) equation is solved using an optimal spatial discretization scheme via the generalized pseudospectral (GPS) method. A detailed systematic analysis of the confined system (relative to corresponding free system) has been performed for these quantities with respect to $r_c$ in tabular and graphical forms, \emph{with and without} electron correlation. Due to compression, the pattern of entropy in aforementioned states gets characterized by various crossovers at intermediate and lower $r_c$ regions. The impact of electron correlation is more pronounced in weaker confinement limit, and appears to decay with rise in confinement strength. The exchange-only results are quite good to provide a decent qualitative discussion. The lower-bounds provided by entropic uncertainty relation holds good in all cases. Several other new interesting features are observed.
Fisher Information Measures under Lattice Combined Paul Trap
Universiti Malaysia Perlis(马来西亚玻璃市大学);Prince of Songkhla University(宋卡王子大学);Centre of Excellence Advanced Communication Engineering (ACE), Universiti Malaysia Perlis(马来西亚玻璃市大学先进通信工程卓越中心)
Single-ion addressing via trap potential modulation in global optical fields
迄今为止,离子量子位的单独寻址主要依赖于经由电磁场空间梯度或经由离子传输操作产生的离子之间的局部拉比或跃迁频率差。或者,可以通过利用全局驱动场中的局部相位差来合成任意局部单量子比特门。在这里,我们报告了使用全局门激光场中的轴向势调制在双离子晶体中对$^{40}$ Ca $^+$离子的单独寻址。我们通过一个量子位随机基准测试,对每个共同捕获的离子应用不同的随机序列来表征所得到的门性能。我们确定了主要的误差来源,并将结果与单离子实验进行比较,以更好地了解我们的实验局限性。这些实验形成了一个基础的通用控制的两个离子,限制在同一个势阱,与一个单一的门激光束。