2015/02/28 by James Schneeloch, John C. Howell, John C Howell · 3 citations
Engineering · Physics and Astronomy · #Amplitude #Coherence (philosophical gambling strategy) #Degenerate energy levels #Laser-Matter Interactions and Applications #Nonlinear Optical Materials Studies #Parametric statistics #Photon #Photorefractive and Nonlinear Optics #Quantum optics #Spontaneous parametric down-conversion #Transverse plane #quant-ph
paper · pdf · doi:10.1088/2040-8978/18/5/053501
published as J. Opt. 18 053501 (2016) · 17 pages, 6 figures, 1 table (essential typos corrected in birth zone formulae)
openalex publication_date 2016/04/04 · openalex created_date 2016/06/24 · arxiv created 2018/02/27 · arxiv updated 2018/03/01 · openalex updated_date 2026/08/05
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.