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arXiv 1502.06996quant-ph
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双光子自发参量下转换中的横向空间相关

Introduction to the Transverse Spatial Correlations in Spontaneous Parametric Down-Conversion through the Biphoton Birth Zone

James Schneeloch, John C. Howell

摘要:

作为自发参量下转换(SPDC)的空间方面的教程,我们提出了一个详细的第一性原理推导的光子对在简并共线SPDC的横向相关宽度。这个宽度定义了双光子出生区的大小,当以被破坏的泵浦光子的位置为条件时,信号光子和闲频光子可能会在该区域被发现。在此过程中,我们讨论了量子光学计算的振幅的SPDC过程,以及其简化形式的近共线简并相位匹配。在此之后,我们将展示如何用双高斯波函数来近似这种双光子振幅,并简要讨论这种双高斯波函数的测量统计(以及随后的便利性)。接下来,我们使用这种近似来得到横向相关宽度的简化估计,并将其与更精确的计算和实验结果进行比较。最后,我们讨论了双光子出生区的概念,用它来发展一阶空间相干性和双光子相关性之间的权衡SPDC的直觉。

英文摘要:

As a tutorial to the spatial aspects of Spontaneous Parametric Downconversion (SPDC), we present a detailed first-principles derivation of the transverse correlation width of photon pairs in degenerate collinear SPDC. This width defines the size of a biphoton birth zone, the region where the signal and idler photons are likely to be found when conditioning on the position of the destroyed pump photon. Along the way, we discuss the quantum-optical calculation of the amplitude for the SPDC process, as well as its simplified form for nearly collinear degenerate phase matching. Following this, we show how this biphoton amplitude can be approximated with a Double-Gaussian wavefunction, and give a brief discussion of the measurement statistics (and subsequent convenience) of such Double-Gaussian wavefunctions. Next, we use this approximation to get a simplified estimation of the transverse correlation width, and compare it to more accurate calculations as well as experimental results. We then conclude with a discussion of the concept of a biphoton birth zone, using it to develop intuition for the tradeoff between the first-order spatial coherence and bipohoton correlations in SPDC.

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