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Physical Review A

Transfer of angular spectrum and image formation in spontaneous parametric down-conversion

Carlos Henrique Monken, P. H. Souto Ribeiro, Sebastião Pádua

Published Apr 1, 1998• 350 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.57.3123

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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.
We show that the transfer of the plane-wave spectrum of the pump beam to the fourth-order transverse spatial correlation function of the two-photon field generated by spontaneous parametric down-conversion leads to the conservation and entanglement of orbital angular momentum of light. By means of a simple experimental setup based on fourth-order (or two-photon) interferometry, we show that our theoretical model provides a good description for down-converted fields carrying orbital angular momentum.
Coherence properties of the down-converted beams generated in spontaneous parametric down-conversion are investigated in detail using an iCCD camera. Experimental results are compared with those from a theoretical model developed for pulsed pumping with a Gaussian transverse profile. The results allow us to tailor the shape of correlation area of the signal and idler photons using pump-field and crystal parameters. As an example, splitting of a correlation area caused by a two-peak pump-field spectrum is experimentally studied.
We present a theoretical and experimental analysis of the joint effects of the transverse electric field distribution and of the nonlinear crystal characteristics on the properties of photon pairs generated by spontaneous parametric downconversion (SPDC). While it is known that for a sufficiently short crystal the pump electric field distribution fully determines the joint signal–idler properties, for longer crystals the nonlinear crystal properties also play an important role. In this paper we present experimental measurements of the angular spectrum (AS) and of the conditional angular spectrum (CAS) of photon pairs produced by SPDC, carried out through spatially resolved photon counting. In our experiment we control whether or not the source operates in the short-crystal regime through the degree of pump focusing, and explicitly show how the AS and CAS measurements differ in these two regimes. Our theory provides an understanding of the boundary between these two regimes and also predicts the corresponding differing behaviors.
In this work we study, for the spontaneous parametric downconversion process, how the transverse amplitude of the pump may be transferred to one of the emitted photons in a given pair when heralded by the detection of the remaining photon. We present a theoretical description of this process along with a discussion of the short-crystal regime within which faithful transfer of the transverse amplitude occurs. We show experimental results for Gaussian and Bessel–Gauss pump beams. In both cases, we verify that the transverse amplitude mechanism occurs and for the former also shows the effects of a departure from the short crystal regime. For the latter we show that our heralded single photons exhibit a non-diffractive behavior, and for orders l = 1 and l = 2 we show that these heralded single photons are in fact vortices with orbital angular momentum transferred from the pump.
We demonstrate, both experimentally and theoretically, a method that allows us to modify the spatial properties of photon pairs produced by the process of spontaneous parametric down-conversion (SPDC) with an apertured, zeroth-order Bessel-Gauss beam. Concentrating on the use of a half-plane aperture, we show that the phase-matching conditions for non-paraxial pump beams can be controlled by simply changing the aperture orientation. Partially blocking the pump beam, leads to a selection of either one of two individual cones that form a dual-cone SPDC angular spectrum, or a portion of both of them. We can likewise determine the shape and orientation of the conditional angular spectrum. This control of the SPDC spatial properties could be useful for quantum information processing protocols.
We present an experimental and theoretical study of type I, frequency-degenerate spontaneous parametric down-conversion (SPDC) with a Bessel-Gauss pump in which we include both paraxial and nonparaxial pump beam configurations. We present measurements of the SPDC angular spectrum (AS), of the conditional angular spectrum (CAS) of signal-mode single photons as heralded by the detection of an idler photon, and of the transverse wave-vector signal-idler correlations (TWC). We show that as the pump is made increasingly nonparaxial, the AS acquires a nonconcentric double-cone structure, with the CAS shape depending on the azimuthal location of the heralding detector, while the signal-idler wave-vector correlation region splits into characteristic doublet stripes, representing as yet unexplored nontrivial, nonlocal quantum correlations between the signal and idler photons. Our work provides further understanding of SPDC with a particular class of structured pump beams, and we believe that the controlled presence of double wave-vector correlations represents an interesting resource for photon-pair quantum-state engineering.