发表机构
Khalifa University of Science and Technology; KU Research Center for Intelligent Computing, Networks and Sensing (ICONS); Institute of Physics of the Czech Academy of Sciences（哈利法科学技术大学; KU智能计算、网络与传感研究中心; 捷克科学院物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对对称双莫尔斯振子的基态，分析了势几何参数A与排序参数s对相空间准概率表示的影响，为非线性相空间方法提供了精确基准。
AI 中文摘要
相空间与准概率方法在量子技术中发挥关键作用，可表征局域性、非高斯性、非经典资源及粗粒化特性。本文对对称双莫尔斯振子的最低准精确基态开展了表示一致性分析：参数A改变势几何与物理状态，而Cahill–Glauber排序参数s仅改变固定密度算子的表示及相空间分辨率。尽管当0<A<1时势为双阱结构，但精确基态振幅在原点处为单峰且位于内部势垒上方；当A趋近于1时，合并的势阱仍为局部四次型而非简谐型。我们获得了Wigner函数与Weyl特征函数的闭式表达式：Wigner函数显示出A依赖的位置与动量局域性交换，且保留负区域，可证明非经典性，对于该纯态还可证明非高斯性；Weyl函数提供傅里叶对偶描述，生成对称排序矩与累积量，并得到完整的s排序层级。当s<0时，各向同性高斯平滑会抑制精细变号结构，同时保留大尺度局域包络；Husimi端点非负但不意味着经典性，而Glauber–Sudarshan P表示仍为分布形式，不定义正则正相干态混合。因此，随A增大Wigner负区域视觉范围减小并非经典化：A控制物理几何，而s控制同一非高斯、非经典结构在互补表示中的呈现方式。这种分离为非线性相空间方法提供了精确基准。
英文摘要
Phase-space and quasiprobability methods now play operational roles in quantum technologies, characterizing localization, non-Gaussianity, nonclassical resources, and coarse-graining. We develop an exact, representation-consistent analysis of the lowest quasi-exact ground state of the symmetric double-Morse oscillator. In the double-Morse potential, the dimensionless parameter $A$ controls the separation of the minima and the central barrier, thereby changing the physical ground state. At fixed $A$, the Cahill--Glauber parameter $s$ labels the quasiprobability $W_A^{(s)}(q,p)$: $s=0$, $-1$, and $1$ give the Wigner, Husimi $Q$, and Glauber--Sudarshan $P$ representations, respectively. Although the potential is double-welled for $0<A<1$, the exact ground-state amplitude is single-peaked at the origin and lies above the barrier; as $A$ approaches unity, the merged well remains locally quartic rather than harmonic. Closed analytical expressions are obtained for the Wigner function and Weyl characteristic function. The Wigner function displays the $A$-dependent exchange between position and momentum localization and retains negative regions, certifying nonclassicality and, for this pure state, non-Gaussianity. The Weyl function is its Fourier dual, generates symmetrically ordered moments and cumulants, and yields the full $s$-ordered hierarchy. For $s<0$, isotropic Gaussian smoothing suppresses fine sign-changing structure while preserving the large-scale localization envelope. The Husimi endpoint is nonnegative without implying classicality, whereas the $P$ representation remains distributional. Thus, $A$ controls the physical phase-space geometry, while $s$ controls how the same non-Gaussian and nonclassical state is resolved across complementary representations
Comments13 pages, 5 figures
