Holographic Ghost Imaging and the Violation of a Bell Inequality B. Jack, 1 J. Leach, 1 J. Romero, 1 S. Franke-Arnold, 1 M. Ritsch-Marte, 2 S. M. Barnett, 3 and M. J. Padgett 1 1 Department of Physics and Astronomy, SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom 2 Division for Biomedical Physics, Innsbruck Medical University, A-6020 Innsbruck, Austria 3 Department of Physics, SUPA, University of Strathclyde, Glasgow G4 0NG, United Kingdom (Received 11 May 2009; published 20 August 2009) 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 un- ambiguously revealing the quantum nature of our ghost-imaging arrangement. DOI: 10.1103/PhysRevLett.103.083602 PACS numbers: 42.50.Tx, 03.65.Ta, 42.65.Lm Ghost imaging was proposed as an illustration of the quantum correlations between pairs of photons created in spontaneous parametric down-conversion [1,2]. The pho- tons in each pair are spatially separated, and each propa- gates along a distinct optical path. The optical image is revealed in the coincidences between pairs of such pho- tons, with only limited information available in counts from either one of the detectors alone. Since the first observations more than 10 years ago [3,4], the phenome- non has remained controversial, not because of any ques- tion concerning the experiments, but on whether or not ghost imaging is solely a quantum phenomenon [5–13]. A recent analysis of this question may be found in [14]. The debate on the quantum vs classical nature of ghost imaging has lead to other interesting two-photon imaging effects using classical sources [15]. It is quantum theory that provides our best current description of light and for us the question is not whether ghost imaging is a quantum phenomenon, but rather whether the consequences of its nonclassical nature can be observed. The first experiments on the nonlocality of entangled photons utilized optical polarization [16]. Ghost imaging, however, relates to measurements of transverse spatial modes. The spatial modes and their Fourier transform correspond to measurements of position and momentum, respectively, and hence relate to the original EPR paradox [17]. Previous experimental investigations with entangled sources show strong correlations in the near-field (position) and far-field (momentum) [7,8]. One way to determine whether these correlations are quantum in origin would be to test against a suitable Bell inequality. An experimen- tal investigation of Bell’s inequality is the standard method to test whether results can be explained through local hidden-variable theories. Violation of Bell-type inequal- ities have been demonstrated originally on polarization measurements [16] and subsequently on measuring corre- lations between spatial modes [18,19]. Crucially, previous to this Letter, a Bell violation approach has not been applied to analyzing ghost images. In terms of spatial modes, one can make the extension to helically-phased modes and their associated orbital angular momentum (OAM) (in analogy to the position-momentum relationship [20]). All helically-phased modes described by a phase profile expði‘Þ carry an OAM of ‘@ per photon [21,22]. At the quantum level, OAM has been shown to be an entangled property of down-converted photon pairs [23–25]. In classical imaging, various techniques give enhanced images. Many of these techniques were developed within microscopy and include dark field and phase contrast [26]. Traditionally each technique required different objective lenses or phase filters within the microscope. However, programmable spatial light modulators (SLMs) can be incorporated into the microscope to introduce specific phase filters so that all of these imaging modes can be sequentially implemented without any change of hardware [27]. For example, the use of spiral phase plates introduces modes with OAM which can result in images with edge enhancement [28,29]. In this Letter, we apply these edge enhancement tech- niques to ghost imaging and show how a phase filter, nonlocal with respect to the object, leads to enhanced coincidence images. Furthermore, we are able to achieve high-contrast images, which we can interpret as a violation of a Bell inequality—thus demonstrating the quantum nature of this implementation of ghost imaging. Our experimental system, shown in Fig. 1, is based upon a mode-locked (100 MHz) 355 nm pump source, which is weakly focussed into a 3 mm long BBO crystal, cut for degenerate type 1, noncollinear down conversion. Upon leaving the crystal, the signal and idler down-converted beams have a half-angle separation of 4  . The light in the plane of the crystal is imaged onto a phase object in the signal arm and a phase filter in the idler arm. The phase PRL 103, 083602 (2009) PHYSICAL REVIEW LETTERS week ending 21 AUGUST 2009 0031-9007= 09=103(8)=083602(4) 083602-1 Ó 2009 The American Physical Society