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We present a simple treatment of the phenomenon of spontaneous parametric downconversion consisting of the coherent scattering of a single pump photon into an entangled photon pair inside a nonlinear crystal. The energy and momentum entanglement of the quantum state of the generated twin photons are seen as a consequence of the fundamental indistinguishability of the time and the position in which the photon pair is created inside the crystal. We also discuss some consequences of photon entanglement. [ABSTRACT FROM AUTHOR]

The Bialynicki-Birula-Sipe photon wave function formalism is extended to include the interaction between photons and continuous non-absorptive media. When the second quantization of this formalism is introduced, a new method for describing the quantum interactions between light and matter emerges. As an example of the application of the method, an expression for the quantum state of the twin photons generated by parametric downconversion is derived in agreement with previous treatments, but with a more intuitive interpretation. [ABSTRACT FROM AUTHOR]

We report an experiment to generate and propagate two entangled spatial qudits, $\mathcal{D}$-dimensional quantum systems, using spontaneous parametric down-conversion. The manipulation, via pump beam, of the transverse spatial correlation between the photon pairs is explored. Inserting apertures with $\mathcal{D}$-slits in the arms of the down-converted photons, we associate the qudit space with the $\mathcal{D}$ possible paths followed by each photon. Experimental results for qudits with $\mathcal{D} = 4$ and 8 are shown. We demonstrate that the generated states cannot be classically correlated. We also show the propagation of entangled states of spatial qudits. Their free-space distribution is performed at the laboratory scale and the propagated states maintain a high fidelity with their original form. [ABSTRACT FROM AUTHOR]

We review recent theoretical and experimental works where are proposed and demonstrated how to use photon pairs created by spontaneous parametric down-conversion to generate entangled states of D-dimensional quantum systems, or qudits. This is the first demonstration of high-dimensional entanglement based on the intrinsic transverse momentum entanglement of the type-II down-converted photons. The qudit space is defined by an aperture made up of an opaque screen with D slits (paths), placed in the arms of the twin photons. By manipulating the pump beam profile we can prepare different entangled states of these possible paths. We focus our attention on an important case for applications in quantum information: the maximally entangled states. Experimental results for qudits with D=4 and D=8 are shown and measuring a two-photon conditional interference, we also demonstrate the nonclassical character of the correlations. [ABSTRACT FROM AUTHOR]

We review some recent experiments based upon multimode two-photon interference of photon pairs created by spontaneous parametric down-conversion. The new element provided by these experiments is the inclusion of the transverse spatial profiles of the pump, signal and idler fields. We discuss multimode Hong–Ou–Mandel interference, and show that the transverse profile of the pump beam can be manipulated in order to control two-photon interference. We present the basic theory and experimental results as well as several applications to the field of quantum information. [ABSTRACT FROM AUTHOR]

We discuss how it is possible to manipulate quantum spatial properties of light beams by using the transfer of the angular spectrum. Twin beams from the parametric down-conversion can be prepared in a state that carries two different quantum images. At the same time, the twin photons can be entangled in polarization. This preparation allows the selection between the detection of each one of the images at a time or a mixture by performing proper projections onto polarization sub-spaces. As another example, we show how to produce a light beam presenting spatial anti-bunching through the control of the entangled angular spectrum and reflections. [ABSTRACT FROM AUTHOR]

We show that a bright-field defocused microscope is effectively a phase-contrast microscope, but with advantages over the conventional one and maintaining the same optical resolution. In a multilayered transparent object, the height amplitude (static and dynamic) of each interface can be measured separately with nanometer sensitivity. By scanning the position of the objective focal plane in relation to the surfaces of a red blood cell, we obtain quantitative information on height fluctuations from each surface individually, which can be analyzed with our model of a defocused microscope and compared with theoretical models. [ABSTRACT FROM AUTHOR]