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Physical Review A

Azimuthal correlation of photon pairs generated in spontaneous parametric down-conversion

Vygandas Jarutis, Saulius Juodkazis, Vygantas Mizeikis, Hiroaki Misawa

Published Oct 30, 2007• 0 citations
Publisher

Abstract

Correlations between the entire conical spatial modes of signal and idler beams in a type II spontaneous parametric down-conversion (SPDC) under ultrashort pulse pumping are examined experimentally and theoretically. Statistical properties and theoretical analysis of ``path-entangled'' states formed using these beams suggest that the quantum state of SPDC photon pairs cannot be represented by a pure ensemble of identically prepared pairs.

DOI
10.1103/physreva.76.043845

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Correlations between the entire conical spatial modes of signal and idler beams in a type II spontaneous parametric down-conversion (SPDC) under ultrashort pulse pumping are examined experimentally and theoretically. Statistical properties and theoretical analysis of ``path-entangled'' states formed using these beams suggest that the quantum state of SPDC photon pairs cannot be represented by a pure ensemble of identically prepared pairs.
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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.
A theory is presented for the quantum state of photon pairs generated from spontaneous parametric down-conversion nonlinear process. In this theory, the influence of the final sizes of nonlinear optical crystals on optical eigenmodes is explicitly taken into consideration. It was found that these photon pairs are not in entangled quantum states. Polarization correlations between the signal beam and the idler beam are explained. It is also shown that the two photons generated from SPDC are not spatially separated, therefore the polarization correlation between the signal and idler beams is not an evidence for quantum non-locality.
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.
Summary form only given. Entangled photons are the workhorse of quantum information technology and cryptography. So far, the emphasis has been on entanglement of the polarization state (for type II down conversion), or of the wave vectors of the degenerate signal and idler pair (for type I down conversion). A subject of current interest is entanglement in the spatial domain, i.e. nontrivial, spatially extended, correlation between signal and idler. A prime example of this being the discussion regarding the conservation and entanglement of orbital angular momentum in spontaneous parametric down conversion. We report our very first measurements of the signal-idler correlation in type I down conversion, employing a frequency-doubled femtosecond Ti:sapphire laser as our source of pump photons, and a fourth generation intensified CCD as our "multi-element single-photon detector" With pump pulses at /spl lambda/ = 400 nm of approximately 2 nJ energy and 250 fs duration directed at a 0.5 mm long BBO crystal we detect roughly one pair in every four frames.