The light produced by parametric down-conversion shows strong spatial entanglement that leads to violations of EPR criteria for separability. Historically, such studies have been performed by scanning a single-element, single-photon detector across a detection plane. Here we show that modern electron-multiplying charge-coupled device cameras can measure correlations in both position and momentum across a multi-pixel field of view. This capability allows us to observe entanglement of around 2,500 spatial states and demonstrate Einstein–Podolsky–Rosen type correlations by more than two orders of magnitude. More generally, our work shows that cameras can lead to important new capabilities in quantum optics and quantum information science.

Conventional imaging systems rely upon illumination light that is scattered or transmitted by the object and subsequently imaged. Ghost-imaging systems based on parametric down-conversion use twin beams of position-correlated signal and idler photons. One beam illuminates an object while the image information is recovered from a second beam that has never interacted with the object. In this Letter, we report on a camera-based ghost imaging system where the correlated photons have significantly different wavelengths. Infrared photons at 1550 nm wavelength illuminate the object and are detected by an InGaAs/InP single-photon avalanche diode. The image data are recorded from the coincidently detected, position-correlated, visible photons at a wavelength of 460 nm using a highly efficient, low-noise, photon-counting camera. The efficient transfer of the image information from infrared illumination to visible detection wavelengths and the ability to count single photons allows the acquisition of an image while illuminating the object with an optical power density of only $100\mathrm{pJ}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$. This wavelength-transforming ghost-imaging technique has potential for the imaging of light-sensitive specimens or where covert operation is desired.

Correlated photon imaging, popularly known as ghost imaging, is a technique whereby an image is formed from light that has never interacted with the object. In ghost imaging experiments, two correlated light fields are produced. One of these fields illuminates the object, and the other field is measured by a spatially resolving detector. In the quantum regime, these correlated light fields are produced by entangled photons created by spontaneous parametric down-conversion. To date, all correlated photon ghost imaging experiments have scanned a single-pixel detector through the field of view to obtain spatial information. However, scanning leads to poor sampling efficiency, which scales inversely with the number of pixels, N, in the image. In this work, we overcome this limitation by using a time-gated camera to record the single-photon events across the full scene. We obtain high-contrast images, 90%, in either the image plane or the far field of the photon pair source, taking advantage of the Einstein–Podolsky–Rosen-like correlations in position and momentum of the photon pairs. Our images contain a large number of modes, >500, creating opportunities in low-light-level imaging and in quantum information processing.

We discuss the use of the transverse spatial degrees of freedom of photons propagating in the paraxial approximation for continuous-variable information processing. Given the wide variety of linear optical devices available, a diverse range of operations can be performed on the spatial degrees of freedom of single photons. Here we show how to implement a set of continuous quantum logic gates which allow for universal quantum computation. In contrast with the usual quadratures of the electromagnetic field, the entire set of single-photon gates for spatial degrees of freedom does not require optical nonlinearity and, in principle, can be performed with a single device: the spatial light modulator. Nevertheless, nonlinear optical processes, such as four-wave mixing, are needed in the implementation of two-photon gates. The efficiency of these gates is at present very low; however, small-scale investigations of continuous-variable quantum computation are within the reach of current technology. In this regard, we show how novel cluster states for one-way quantum computing can be produced using spontaneous parametric down-conversion.

The propagation of transverse spatial correlations of photon pairs through arbitrary first-order linear optical systems is studied experimentally and theoretically using the fractional Fourier transform. Highly correlated photon pairs in an Einstein-Podolsky-Rosen-like state are produced by spontaneous parametric down-conversion and subject to optical fractional Fourier transform systems. It is shown that the joint detection probability can display either correlation, anticorrelation, or no correlation, depending on the sum of the orders $\alpha$ and $\beta$ of the transforms of the down-converted photons. We present analytical results for the propagation of the perfectly correlated EPR state and numerical results for the propagation of the two-photon state produced from parametric down-conversion. We find good agreement between the theory and experiment.

We investigate the nonlinear mixing of orbital angular momentum in type-II second-harmonic generation with arbitrary topological charges imprinted on two orthogonally polarized beams. Starting from the basic nonlinear equations for the interacting fields, we derive the selection rules determining the set of paraxial modes taking part in the interaction. Conservation of orbital angular momentum naturally appears as the topological charge selection rule. However, a less intuitive rule applies to the radial orders when modes carrying opposite helicities are combined in the nonlinear crystal, an intriguing feature confirmed by experimental measurements.