Holographic Ghost Imaging and the Violation of a Bell Inequality

We demonstrate the contrast enhancement of images within a ghost-imaging system by use of nonlocal phase filters. We use parametric down-conversion as the two-photon light source and two separated phase modulators, in the signal and idler arms which represent different phase filters and objects, respectively. We obtain edge enhanced images as a direct consequence of the quantum correlations in the orbital angular momentum (OAM) of the down-converted photon pairs. For phase objects, with differently orientated edges, we show a violation of a Bell-type inequality for an OAM subspace, thereby unambiguously revealing the quantum nature of our ghost-imaging arrangement.

Figure 1

Experimental setup. The phase object is stepped across the beam and imaged onto the single-mode fiber. At each position the local form of the object can be treated as a simple phase step of appropriate orientation and coincidence measurements are made for different reference holograms. The details of the experimental setup are explained in the main text.

Figure 2

(a) Phase object. (b) Single channel counts from the object detector. (c)–(f) Coincidence images of the phase object shown in (a), using reference holograms shown in insets. Note that although the object can still be discerned in (b), the edge visibility is only $\approx 2:1$, as compared with greater than $35:1$ for the ${\ell }_{\mathrm{ref}}=0$ case (c), and $13:1$ for the ${\ell }_{\mathrm{ref}}=1$ case (d).

Figure 3

(a)–(d) Coincidence images for reference orientations of 0°, 45°, 90°, and 135°, respectively. By plotting the azimuthal intensity variations in each image (e), one can see the sinusoidal pattern in coincidence, and appropriate phase shift for each analyzer hologram. The image data are averaged radially over 6 pixels and azimuthally by binning over 3°; see the dashed lines in (a).