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arXiv:quant-ph/0206038 · Physical Review A

Spatial antibunching of photons with parametric down-conversion

W. A. T. Nogueira, Stephen Patrick Walborn, Sebastião Pádua, Carlos Henrique Monken

Published Nov 19, 2002• 9 citations
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Abstract

The theoretical framework behind a recent experiment by Nogueira et al. [Phys. Rev. Lett. 86, 4009 (2001)] of spatial antibunching in a two-photon state generated by collinear type-II parametric down-conversion and a birefringent double slit is presented. The fourth-order quantum correlation function is evaluated and shown to violate the classical Schwarz-type inequality, ensuring that the field does not have a classical analog. We expect these results to be useful in the rapidly growing fields of quantum imaging and quantum information.

DOI
10.1103/physreva.66.053810

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The theoretical framework behind a recent experiment by Nogueira et al. [Phys. Rev. Lett. 86, 4009 (2001)] of spatial antibunching in a two-photon state generated by collinear type-II parametric down-conversion and a birefringent double slit is presented. The fourth-order quantum correlation function is evaluated and shown to violate the classical Schwarz-type inequality, ensuring that the field does not have a classical analog. We expect these results to be useful in the rapidly growing fields of quantum imaging and quantum information.
In experiments with spontaneous parametric down conversion the near-field plane is usually defined as the output facet of the generating crystal. Experimentally, however, the spatial correlations are accessed via an imaging system and observed in a region around the image of the output facet. We show that the imaged two-photon field has a very rich transverse and longitudinal structure, which is determined by the phase-matching conditions. We observe many intriguing three-dimensional structures that demonstrate the presence of spatial antibunching, an extreme localization of twin photons, and spatial correlations that resemble Bessel beams in propagation. We link these observations with previous results in second harmonic generation and predict the presence of fourth-order phase singularities. Both experiments and theory are presented, yielding further insight into the nature of the two-photon field.
Control of spatial quantum correlations in bi-photons is one of the fundamental principles of Quantum Imaging. Up to now, experiments have been restricted to controlling the state of a single bi-photon, by using linear optical elements. In this work we demonstrate experimental control of quantum correlations in a four-photon state comprised of two pairs of photons. Our scheme is based on a high-efficiency parametric downconversion source coupled to a double slit by a variable linear optical setup, in order to obtain spatially encoded qubits. Both entangled and separable pairs have been obtained, by altering experimental parameters. We show how the correlations influence both the interference and diffraction on the double slit.
The quantum theory of fourth-order interference of light is presented in a general format and compared with classical wave theory. The conditions under which nonclassical phenomena occur are discussed. In particular, the interference between the quantum field and classical field may give rise to a nonclassical effect. For some special states of light, the interference pattern does not disappear even though one field is much stronger than the other, for which no classical analog exists. Fourth-order effects in the interference between two independent fields are analyzed in detail. It is pointed out that the fourth-order interference between independent fields will not disappear when the integration time of detection is of the order of the reciprocal bandwidth of the two light fields as long as the spectra of the two fields are symmetric around the same center frequency, and for some correlated fields, the interference does not vanish even if the detection time is much larger than the reciprocal bandwidth of the fields. A new type of fourth-order interference experiment involving a beam splitter is proposed in which local realism of the Einstein-Podolsky-Rosen form is violated for quantum mechanics. This general argument is then applied to the interference between two photons generated in the parametric down-conversion process. The possibility of violations of Bell's inequalities in interference experiments is investigated.
The quantum state for spontaneous parametric down-conversion was evaluated to include information about the transverse spatial characteristic of the down-conversion fields. This state was used to calculate the angular spectrum of down-conversion in the case of both single-channel and coincidence measurements, while retaining the characteristic nonclassical correlations. Actual transverse profiles for typical experimental parameters were evaluated numerically and measurements were performed with results that compared well with the numerical calculation. This theoretical spatial model was then applied nonrigorously to the case of induced coherence without induced emission. The theoretical results implied that there was a reduction in the degree of induced coherence due strictly to the spatial distribution of the down-conversion beams. This was interpreted as a result of increased distinguishability of the overlapping idler photons. Measurements were conducted which support these results qualitatively. In addition, the present theory explained an unexpected quantitative discrepancy between second- and fourth-order visibilities in previous induced-coherence experiments. This discrepancy was interpreted phenomenologically as a difference between intrinsic and nonintrinsic indistinguishability, and some implications towards quantum measurement theory and the role of the observer were suggested.