Energy and momentum entanglement in parametric downconversion

We present a simple treatment for the phenomenon of parametric downconversion considering the coherent scattering of one pump photon into a photon pair by 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 the system entanglement.Comment: 6 pages, 2 figures. v3: Minor changes on the text. Some references were include

Hong-Ou-Mandel interferometer with cavities: theory

We study the number of coincidences in a Hong-Ou-Mandel interferometer exit whose arms have been supplemented with the addition of one or two optical cavities. The fourth-order correlation function at the beam-splitter exit is calculated. In the regime where the cavity length are larger than the one-photon coherence length, photon coalescence and anti-coalescence interference is observed. Feynman's path diagrams for the indistinguishable processes that lead to quantum interference are presented. As application for the Hong-Ou-Mandel interferometer with two cavities, it is discussed the construction of an optical XOR gate

Cancellation of atmospheric turbulence effects in entangled two-photon beams

Turbulent airflow in the atmosphere and the resulting random fluctuations in its refractive index have long been known as a major cause of image deterioration in astronomical imaging and figures among the obstacles for reliable optical communication when information is encoded in the spatial profile of a laser beam. Here we show that using correlation imaging and a suitably prepared source of photon pairs, the most severe of the disturbances inflicted on the beam by turbulence can be cancelled out. Other than a two-photon light source, only linear passive optical elements are needed and, as opposed to adaptive optics techniques, our scheme does not rely on active wavefront correction.Comment: 5 pages, 3 figure

Experimental observation of spatial antibunching of photons

We report an interference experiment that shows transverse spatial antibunching of photons. Using collinear parametric down-conversion in a Young-type fourth-order interference setup we show interference patterns that violate the classical Schwarz inequality and should not exist at all in a classical description.Comment: 4 pages, 7 figure

Geometrically induced singular behavior of entanglement

We show that the geometry of the set of quantum states plays a crucial role in the behavior of entanglement in different physical systems. More specifically it is shown that singular points at the border of the set of unentangled states appear as singularities in the dynamics of entanglement of smoothly varying quantum states. We illustrate this result by implementing a photonic parametric down conversion experiment. Moreover, this effect is connected to recently discovered singularities in condensed matter models.Comment: v2: 4 pags, 4 figs. A discussion before the proof of Proposition 1 and tomographic results were included, Propostion 2 was removed and the references were fixe

Conservation and entanglement of Hermite-Gaussian modes in parametric down-conversion

We show that the transfer of the angular spectrum of the pump beam to the two-photon state in spontaneous parametric down-conversion enables the generation of entangled Hermite-Gaussian modes. We derive an analytical expression for the two-photon state in terms of these modes and show that there are restrictions on both the parity and order of the down-converted Hermite-Gaussian fields. Using these results, we show that the two-photon state is indeed entangled in Hermite-Gaussian modes. We propose experimental methods of creating maximally-entangled Bell states and non-maximally entangled pure states of first order Hermite-Gaussian modes.Comment: 9 pages, 4 figures. Corrections made as per referee comments, references updated. Submitted PR