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arXiv:1003.1249 · Physical Review A

Transverse coherence of photon pairs generated in spontaneous parametric down-conversion

Martin Hamar, Jan Peřina, Ondřej Haderka, Václav Michálek

Published Apr 21, 2010• 45 citations
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Abstract

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.

DOI
10.1103/physreva.81.043827

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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.
The correlation properties of the pump field in spontaneous parametric down-conversion are crucial in determining the degree of entanglement of generated signal and idler photons. We find theoretically that continuous-variable entanglement of the transverse positions and momenta of these photons can be achieved only if the coherence of the pump beam is sufficiently high. The positions of signal and idler photons are found to be correlated, even for an incoherent pump. However, the momenta of the signal and idler photons are not anti-correlated, even though transverse momentum is conserved.
Measurement of photon-number statistics of fields composed of photon pairs generated in spontaneous parametric down-conversion pumped by strong ultrashort pulses is described. Finite detection quantum efficiencies, noises as well as possible loss of one or both photons from a pair are taken into account. Measured data provided by an intensified CCD camera are analyzed along the developed model. The joint signal-idler photon-number distribution is obtained using the expectation maximization algorithm. Covariance of the signal and idler photon-numbers exceeds 98%. Entanglement area of the correlated photon pairs is determined.
Abstract The correlation properties of the pump field in spontaneous parametric down-conversion are crucial in determining the degree of entanglement of generated signal and idler photons. We find theoretically that continuous-variable entanglement of the transverse positions and momenta of these photons can be achieved only if the coherence of the pump beam is sufficiently high. The positions of signal and idler photons are found to be correlated, even for an incoherent pump. However, the momenta of the signal and idler photons are not anti-correlated, even though transverse momentum is conserved.
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.
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.
In parametric down-conversion, a nonlinear crystal is pumped by a laser and spontaneous emission takes place in signal and idler modes according to the phase-matching conditions. A seed laser can stimulate the emission in the signal beam if there is mode overlap between them. This also enhances the emission in the idler beam, affecting its coherence properties. While the degree of coherence of the idler field as a function of the seed power has already been studied, the transverse coherence length has not yet been properly investigated. The transverse coherence length is a key parameter of optical beams that determines the beam divergence, for example. Here, we present a theoretical and experimental investigation of the transverse coherence length in stimulated down-conversion. In addition, we make a connection between stimulated down-conversion and partially coherent sources like the Gaussian-Schell model beams, and show that in general the idler field cannot be described with this model.