论文标题
SU（1,1）指南针状态的子泛滥相位空间结构和灵敏度
Sub-Planck phase-space structure and sensitivity for SU(1,1) compass states
论文作者
论文摘要
我们通过确定双曲机上的普朗克量表可以将其视为Bargmann指数$ k $的倒数，从而研究了与SU（1,1）组相关的子Planck尺度结构。我们的讨论涉及Wigner函数的SU（1,1）版本，并且通过这些Wigner函数的图很容易看到量子干扰效应。具体而言，与$ \ \\ frac1 {\ frac1 {\ frac1 {\ sqrt {k}} $（1,1）的coart corration相比，四个perelomov su（1,1）相干状态（指南针）的叠加几乎产生的相位空间缩放的各向同性子planck结构将其作为$ \ frac1 {k} $与$ \ frac1 {\ frac1 {\ sqrt {k}} $缩放量表相比两个SU（1,1）相干状态（CAT状态）的叠加。我们表明，位移敏感性表现出相同的二次缩放缩放效果。
We investigate the sub-Planck-scale structures associated with the SU(1,1) group by establishing that the Planck scale on the hyperbolic plane can be considered as the inverse of the Bargmann index $k$. Our discussion involves SU(1,1) versions of Wigner functions, and the quantum-interference effect is easily visualized through plots of these Wigner functions. Specifically, the superpositions of four Perelomov SU(1,1) coherent states (compass state) yield nearly isotropic sub-Planck structures in phase space scaling as $\frac1{k}$ compared with $\frac1{\sqrt{k}}$ scaling for individual SU(1,1) coherent states and anisotropic quadratically improved scaling for superpositions of two SU(1,1) coherent states (cat state). We show that displacement sensitivity exhibits the same quadratic improvement to scaling.
