Introduction to the transverse spatial correlations in spontaneous parametric down-conversion through the biphoton birth zone

James Schneeloch*, John C. Howell

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

86 Scopus citations

Abstract

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.

Original languageAmerican English
Article number053501
JournalJournal of Optics (United Kingdom)
Volume18
Issue number5
DOIs
StatePublished - May 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016 IOP Publishing Ltd.

Keywords

  • SPDC
  • introduction
  • nonlinear quantum optics
  • position momentum correlation
  • spontaneous parametric down conversion

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