Multimode Hong-Ou-Mandel interference

We consider multimode two-photon interference at a beam splitter by photons created by spontaneous parametric down-conversion. The resulting interference pattern is shown to depend upon the transverse spatial symmetry of the pump beam. In an experiment, we employ the first-order Hermite-Gaussian modes in order to show that, by manipulating the pump beam, one can control the resulting two-photon interference behavior. We expect these results to play an important role in the engineering of quantum states of light for use in quantum information processing and quantum imaging.Comment: 4 pages, 6 figures, submitted to PR

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

Optical Bell-state analysis in the coincidence basis

Many quantum information protocols require a Bell-state measurement of entangled systems. Most optical Bell-state measurements utilize two-photon interference at a beam splitter. By creating polarization-entangled photons with spontaneous parametric down-conversion using a first-order Hermite-Gaussian pump beam, we invert the usual interference behavior and perform an incomplete Bell-state measurement in the coincidence basis. We discuss the possibility of a complete Bell-state measurement in the coincidence basis using hyperentangled states [Phys. Rev. A, \textbf{58}, R2623 (1998)].Comment: 5 pages, 5 figure

Multimode Hong-Ou-Mandel Interferometry

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.Comment: 20 pages, 14 figures, Brief Review to be published in Modern Physics Letters

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