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Physical Review A

Conditional Talbot effect using a quantum two-photon state

Itamar Vidal, Solange Bessa Cavalcanti, E. J. S. Fonseca, J. Miguel Hickmann

Published Sep 22, 2008• 14 citations
Publisher

Abstract

We study the interference patterns obtained from the superposition of two Bessel beams originated from a quantum two-photon state produced by a spontaneous parametric down-conversion process. Due to the nondiffracting character of the light beam, a self-imaging effect is found along the propagation direction for second-order interference patterns with periodicity proportional to $\ensuremath{\lambda}∕2$, characterizing a two-photon Talbot effect. Conditional interference patterns in the longitudinal plane are theoretically shown as well.

DOI
10.1103/physreva.78.033829

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Superimposed Bessel beams self-imaging effect is investigated using photon pairs produced by a spontaneous parametric down-conversion source, instead of classical light. Results show that the photon pairs transmitted by the two annular slits form an interference pattern analogous to the ones produced by the Talbot effect, which can be explained using a theory based on the angular spectrum transference from the pump field to the photon pairs.

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Sarayut Deachapunya, Sorakrai Srisuphaphon, Pituk Panthong +3 more

We demonstrate the quantum Talbot effect using pairs of single photons produced by parametric down conversion. In contrast to the previous works, we use a programmable spatial light modulator to behave as a diffraction grating. Thus, the investigation of the Talbot diffraction patterns under the variation of grating structure can be easily performed. The influence of spectral bandwidth of the down-converted photons on the diffraction pattern is also investigated. A theoretical model based on the wave nature of photons is presented to explain the Talbot diffraction pattern under varying conditions. The measured diffraction patterns are in good agreement with the theoretical prediction. We are convinced that our study improves the understanding of the quantum Talbot effect.

arXiv:1605.07563•May 24, 2016•0 citations
We study the interference patterns obtained from the superposition of two Bessel beams originated from a quantum two-photon state produced by a spontaneous parametric down-conversion process. Due to the nondiffracting character of the light beam, a self-imaging effect is found along the propagation direction for second-order interference patterns with periodicity proportional to \ensuremathλ∕2\ensuremath{\lambda}∕2\ensuremathλ∕2, characterizing a two-photon Talbot effect. Conditional interference patterns in the longitudinal plane are theoretically shown as well.
We demonstrate the quantum Talbot effect using a beam of single photons produced by parametric down conversion. In contrast to the previous works, we use a programmable spatial light modulator to behave as a diffraction grating. Thus, the investigation of the Talbot diffraction patterns under the variation of grating structure can be easily performed. The influence of spectral bandwidth of the down-converted photons on the diffraction pattern is also investigated. A theoretical model based on the wave nature of photons is presented to explain the Talbot diffraction patterns under varying conditions. The measured diffraction patterns are in good agreement with the theoretical prediction. We are convinced that our study improves the understanding of the quantum Talbot effect.
The Talbot effect in quantum physics is known to produce intricate patterns in the probability distribution of a particle, known as ``quantum carpets,'' corresponding to the revival and replication of the initial wave function. Recently, it was shown that one can encode a DDD-level qudit in such a way that the Talbot effect can be used to process the DDD-dimensional quantum information [Far\'{\i}as et al., Phys. Rev. A 91, 062328 (2015)]. Here we introduce a scheme to produce free-propagating ``entangled quantum carpets'' with pairs of photons produced by spontaneous parametric down-conversion. First we introduce an optical device that can be used to synthesize arbitrary superposition states of Talbot qudits. Sending spatially entangled photon pairs through a pair of these devices produces an entangled pair of qudits. As an application, we show how the Talbot effect can be used to test a DDD-dimensional Bell inequality. Numerical simulations show that violation of the Bell inequality depends strongly on the amount of spatial correlation in the initial two-photon state. We briefly discuss how our optical scheme might be adapted to matter wave experiments.
Summary form only given. We demonstrate a proof-of-principle experiment of quantum lithography utilizing parametric down-converted photons and a transmission grating, and show that the diffraction of a multiphoton state can be also explained by the concept of the photonic de Broglie wave. Pairs of frequency-degenerate photons were collinearly generated by spontaneous parametric down-conversion (SPDC) in a 5 mm long KNbO/sub 3/ (KN) crystal pumped by the second harmonic light of a single longitudinal mode Ti:sapphire laser operating at 861.5 nm. The photon pairs were diffracted by a transmission grating (slit width: 125 /spl mu/m, period: 250 /spl mu/m), placed just after the KN crystal. In this geometry, each photon pair passes together through one of the grating slits. By rotating a mirror, we recorded spatial diffraction-interference patterns at a two-photon detector consisting of two avalanche photodiodes. For comparison, we also observed diffraction-interference patterns of chaotic light from a tungsten lamp using the same apparatus.
We demonstrate the quantum Talbot effect using pairs of single photons produced by parametric down conversion. In contrast to the previous works, we use a programmable spatial light modulator to behave as a diffraction grating. Thus, the investigation of the Talbot diffraction patterns under the variation of grating structure can be easily performed. The influence of spectral bandwidth of the down-converted photons on the diffraction pattern is also investigated. A theoretical model based on the wave nature of photons is presented to explain the Talbot diffraction pattern under varying conditions. The measured diffraction patterns are in good agreement with the theoretical prediction. We are convinced that our study improves the understanding of the quantum Talbot effect.