Research ArticlePHYSICS

Imaging Bell-type nonlocal behavior

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Science Advances  12 Jul 2019:
Vol. 5, no. 7, eaaw2563
DOI: 10.1126/sciadv.aaw2563
  • Fig. 1 Imaging setup to perform a Bell inequality test in images.

    A BBO crystal pumped by an ultraviolet laser is used as a source of entangled photon pairs. The two photons are separated on a beam splitter (BS). An intensified camera triggered by a SPAD is used to acquire ghost images of a phase object placed on the path of the first photon and nonlocally filtered by four different spatial filters that can be displayed on an SLM (SLM 2) placed in the other arm. By being triggered by the SPAD, the camera acquires coincidence images that can be used to perform a Bell test.

  • Fig. 2 Full-frame images recording the violation of a Bell inequality in four images.

    (A) The four coincidence counting images are presented, which correspond to images of the phase circle acquired with the four phase filters with different orientations, θ2 = {0° , 45° , 90° , 135°}, necessary to perform the Bell test. Scale bars, 1 mm (in the plane of the object). (B to E) The coincidence counts graphs as a function of the orientation angle θ1 of the phase step along the object are presented. As shown, these results are obtained by unfolding the ROIs represented as red rings and are extracted from the images presented in (A). The blue dots in the graphs are the coincidence counts per angular region within the ROIs, and the red curves correspond to the best fits of the experimental data by a cosine-squared function. (B) to (E) correspond to phase filter orientations θ2 of 0°, 45°, 90°, and 135°, respectively.

  • Fig. 3 Full-frame single image recording the violation of a Bell inequality.

    (A) The coincidence counting single image acquired through our protocol is presented, which corresponds to an image of the same phase circle acquired with the four phase filters with different orientations, θ2 = {0° , 45° , 90° , 135°}, necessary to perform the Bell test. Scale bar, 1 mm (in the plane of the object). (B) The correspondence between the phase filters used and the particular observation of the object acquired in the single image are highlighted. The four ROIs used to treat the single image are also highlighted in (B). (C) The coincidence counts graphs as a function of the orientation angle θ1 of the phase step along the object for the four different orientations of the phase filters are presented. These graphs are obtained solely by extracting the coincidence counts in the single image presented in (A).

  • Fig. 4 Full-frame single image recording the violation of a Bell inequality and implementing the scanning of the phase circle.

    (A) The raw sum of the coincidence counting single image acquired through our protocol is presented, which corresponds to an image of the same phase circle acquired with the four phase filters with different orientations, θ2 = {0° , 45° , 90° , 135° }, necessary to perform the Bell test. (B) The image obtained by de-scanning each of the images given the chosen position for the phase circle is presented. We can use this latter image to perform an evaluation of the Bell parameter S and to demonstrate the nonlocal behavior.

Supplementary Materials

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Detailed experimental setup
    • Section S2. Classical simulations
    • Fig. S1. Detailed experimental setup.
    • Fig. S2. Simulated image for realistic parameters.
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