AI 中文总结
本文比较二维高斯波包的光子局域化度量，发现朗道-派尔斯波函数等三种度量可描述光子局域探测概率，且三者在单光子波包演化中保持相近。
AI 中文摘要
我们针对二维高斯波包，对不同的光子局域化度量标准展开比较研究。研究发现，若波包演化时间超过其动量空间宽度倒数的数倍，所有度量标准会开始合并。然而，朗道-派尔斯（Landau-Peierls）波函数会产生最大的正偏移量<r>-ct>0，而波包的标量傅里叶变换则产生最小的偏移量，且最快收敛至<r>-ct=0。我们还通过由离子阱中离子构成的模型探测器，探讨光子的局域探测问题，该位置依赖的探测概率由散射矩阵推导得出。研究发现，光子的局域探测概率可通过三种所提出的局域化度量标准表示，即朗道-派尔斯波函数、能量波函数与霍顿（Hawton）密度，这三种度量标准在单光子波包的整个时间演化过程中也始终保持相近。
英文摘要
We compare different measures for photon localization in terms of two-dimensional Gaussian wave packets. We find that all measures start to coalesce if the wave packet has evolved for times which are larger than a few times the inverse momentum-space width of the package. However, the Landau-Peierls wave function yields the largest positive offset <r>-ct>0 while the scalar Fourier transform of the wave packet yields the smallest offset and converges towards <r>-ct=0 fastest. We also discuss local detection of photons through a model detector consisting of ions in ion traps. The position-dependent detection probabilities are inferred from the scattering matrix. We find that the local detection probability for photons can be expressed in terms of three of the proposed localization measures, viz. the Landau-Peierls wave function, the energy wave function, and the Hawton density. Those three porposals also remain close throughout the time evolution of the single-photon wave packet.
Comments10 pages, 5 figures
