Einstein-Podolsky-Rosen Paradox in Twin Images

Abstract

Spatially entangled twin photons provide both promising resources for modern quantum information protocols, because of the high dimensionality of transverse entanglement 1,2 , and a test of the Einstein-Podolsky-Rosen (EPR) paradox 3 in its original form of position versus impulsion. Usually, photons in temporal coincidence are selected and their positions recorded, resulting in a priori assumptions on their spatio-temporal behavior 4 . Here, we record on two separate electron-multiplying charge coupled devices (EMCCD) cameras twin images of the entire flux of spontaneous down-conversion. This ensures a strict equivalence between the subsystems corresponding to the detection of either position (image or near-field plane) or momentum (Fourier or far-field plane) 5 . We report the highest degree of paradox ever reported and show that this degree corresponds to the number of independent degrees of freedom 6,7 or resolution cells 8 , of the images.In 1935, Einstein, Podolsky and Rosen (EPR) showed that quantum mechanics predicts that entangled particles could have both perfectly correlated positions and momenta, in contradiction with the so-called local realism where two distant particles should be treated as two different systems. Though the original intention of EPR was to show that quantum mechanics is not complete, the standard present view is that entangled particles do experience nonlocal correlations 9,10 . It can be shown that the spatial extent of these correlations corresponds to the size of a spatial unit of information, or mode, offering the possibility of detecting high dimensional entanglement in an image with a sufficient number of resolution cells 2,4 . However, in most experiments the use of single photon detectors and coincidence counting leads to the detection of a very few part of selected photons, generating a sampling loophole in fundamental demonstrations. High sensitivity array detectors have been used outside the single photoncounting regime in order to witness the quantum feature of light, showing the possibility of achieving larger signal-tonoise ratio than in classical imaging 11,12 . However, the EPR paradox is intimately connected to the particle character of light and its detection should involve single photon imaging, possible either with intensified charge coupled devices (ICCD) or, more recently, EMCCDs 13 . ICCDs exhibit a lower noise but have also a lower quantum efficiency than EMCCDs and a more extended spatial impulse response. ICCD are therefore convenient to isolate pairs of entangled photons 14 , as shown in a recent experiment: an ICCD triggered by a single photon detector was used to detect heralded photons in various spatial modes 15 .On the other hand, because of their higher quantum efficiency EMCCDs allow efficient detection of quantum correlations in images, as demonstrated some years ago by measuring sub-shot-noise correlations in far-field images of spontaneous parametric down-conversion (SPDC) 16,17 . More recently, two experiments intended to achieve the demonstra...

Conical refraction: fundamentals and applications

“…For the case of linear momentum entangled photons, entanglement detection is not an easy task, since transverse positions must be measured, e.g., by using a single photon CCD camera [146,260]. In contrast, detection of polarization entanglement is much simpler, since only linear polarizers and single photon detectors are needed.…”

“…The signal and idler photons generated in the SPDC process have been reported to be entangled in many different degrees of freedom such as polarization [244,257], frequency [258], linear momentum [259], transverse position [260] and orbital angular momentum [250]. In our case, we use a BBO uniaxial crystal to produce type-I SPDC photons with the same polarization and frequency and we pay attention to correlations in linear momentum.…”

Quality of spatial entanglement propagation

“…Fitting in this way, rather than, say, directly evaluating the variances and effective radii of curvature [34], yields a Gaussian approximation that more accurately reflects both the peak probability density and its full width at half maximum (FWHM) [12]. This is essentially what is done experimentally: measure the biphoton probability distribution and fit the result to a Gaussian to determine σ-and σ+ [14,16,[35][36][37]. For σ-= 5.5 μm and σ+ = 100 μm, this procedure yields FIG.…”

“…(11) of (1.89/1.0) 2 = 3.57. To confirm this behavior, we performed experiments using an electron multiplying CCD (EMCCD) camera, which has both single-photon sensitivity and massively parallel measurement capabilities, making it convenient for biphoton measurements [14,[37][38][39]. A spatially filtered 405 nm CW laser beam pumps a type I SPDC crystal (BBO, L = 3 mm), generating near-collinear entangled photons, and nearly degenerate pairs are selected via spectral filter.…”

Einstein-Podolsky-Rosen Entanglement of Narrow-Band Photons from Cold Atoms

“…By using two-photon quantum ghost imaging and interference [20,21], we demonstrate explicitly that the narrowband photon pairs violate the separability criterion, confirming EPR positionmomentum entanglement. We further demonstrate continuous variable EPR steering for positions and momenta of the two photons [22][23][24][25][26][27][28]. To the best of our knowledge, this is the first experimental demonstration of EPR entanglement and EPR steering of position-momentum degrees of freedom of narrowband photon pairs, well suited for spatially-multiplexed quantum information processing, storage of quantum images, quantum interface involving hyper-entangled photons, etc [29][30][31][32][33][34].…”