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Physical Review A

Two-photon geometric optics

T. B. Pittman, Dmitry Strekalov, Давид Николаевич Клышко, Morton H. Rubin, Alexander V. Sergienko, Yanhua H. Shih

Published Apr 1, 1996• 205 citations
Publisher

Abstract

We report two-photon correlation experiments using spontaneous parametric down-conversion under a severe manipulation of the input pump field. Considering the case of passing the laser beam through a focusing lens before the down-conversion crystal, theoretical calculations and a series of imaging experiments demonstrate two-photon geometric optics effects. In particular, the imaging in coincidence counts of an aperture placed in one of the down-conversion beams is found to be the analog of a simple spherical mirror system, which displays a ``vacuum dispersion'' effect in that the object and image distances are wavelength weighted. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.2804

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We report two-photon correlation experiments using spontaneous parametric down-conversion under a severe manipulation of the input pump field. Considering the case of passing the laser beam through a focusing lens before the down-conversion crystal, theoretical calculations and a series of imaging experiments demonstrate two-photon geometric optics effects. In particular, the imaging in coincidence counts of an aperture placed in one of the down-conversion beams is found to be the analog of a simple spherical mirror system, which displays a ``vacuum dispersion'' effect in that the object and image distances are wavelength weighted. \textcopyright{} 1996 The American Physical Society.
The reported experiment is a two-photon optical imaging experiment1 in which a spontaneous-parametric-downconversion light beam, which consists of pairs of orthogonally polarized signal and idler photons, is split into two diverging beams by a polarization beam splitter, so that co- incidence detections may be performed between two distant photon-counting detectors. An aperture (mask) placed in front of one of the detectors is illuminated by the signal beam through a convex lens. Surprisingly, an image of this aperture is observed in the coincidence counting rate when the other detector is scanned in the transverse plane of the idler beam, even though both detectors’ single counting rates remain constant.
A theory of two-photon down-conversion in the presence of mirrors is developed and applied to recent observations of Herzog et al. [Phys. Rev. Lett. 72, 629 (1994)]. The experimentally observed results for counting and coincidence rates as functions of mirror-crystal separations are obtained, and it is shown how the same results may be derived in a simplified formulation that presumes phase-matched signal and idler modes. We account for the observed effects of the finite coherence length of the pump field as well as the signal and idler coherence lengths, which are much shorter than the pump coherence length and have a different physical origin. Our analysis also supports the interpretation of the phenomena observed as being analogous to the modification of single photon spontaneous emission of atoms in cavity QED. \textcopyright{} 1996 The American Physical Society.
The transverse correlation of triphoton entanglement generated within a single crystal is analyzed. Among many interesting features of the transverse correlation, they arise from the spectral function FFF of the triphoton state produced in the parametric processes. One consequence of transverse effects of entangled states is quantum imaging, which is theoretically studied in photon counting measurements. Klyshko's two-photon advanced-wave picture is found to be applicable to the multiphoton entanglement with some modifications. We found that in the two-photon coincidence counting measurement by using triphoton entanglement, although the Gaussian thin lens equation (GTLE) holds, the imaging shown in coincidences is obscure and has a poor quality. This is because of tracing the remaining transverse modes in the untouched beam. In the triphoton imaging experiments, two kinds of cases have been examined. For the case that only one object with one thin lens is placed in the system, we found that the GTLE holds as expected in the triphoton coincidences and the effective distance between the lens and imaging plane is the parallel combination of two distances between the lens and two detectors weighted by wavelengths, which behaves as the parallel combination of resistors in the electromagnetism theory. Only in this case, a point-point correspondence for forming an image is well-accomplished. However, when two objects or two lenses are inserted in the system, though the GTLEs are well-satisfied, in general a point-point correspondence for imaging cannot be established. Under certain conditions, two blurred images may be observed in the coincidence counts. We have also studied the ghost interference-diffraction experiments by using double slits as apertures in triphoton entanglement. It was found that when two double slits are used in two optical beams, the interference-diffraction patterns show unusual features compared with the two-photon case. This unusual behavior is a destructive interference between two amplitudes for two photons crossing two double slits.
We show that the two-photon state generated in the process of spontaneous parametric down-conversion in a thin crystal carries information about the angular spectrum of the pump beam. This information transfer allows one to control the transverse correlation properties of the down-converted fields by manipulating the pump field, with consequences for a broad class of experiments. The effect is demonstrated theoretically and experimentally, in connection with the formation of fourth-order images by the down-converted beams.