The transverse spatial effects observed in photon pairs produced by parametric down-conversion provide a robust and fertile testing ground for studies of quantum mechanics, non-classical states of light, correlated imaging and quantum information. Over the last 20 years there has been much progress in this area, ranging from technical advances and applications such as quantum imaging to investigations of fundamental aspects of quantum physics such as complementarity relations, Bell's inequality violation and entanglement. The field has grown immensely: a quick search shows that there are hundreds of papers published in this field, some with hundreds of citations. The objective of this article is to review the building blocks and major theoretical and experimental advances in the field, along with some possible technical applications and connections to other research areas.

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We report a quantum eraser experiment which actually uses a Young double-slit to create interference. The experiment can be considered an optical analogy of an experiment proposed by Scully, Englert and Walther(SEW) [Nature 351, 111 (1991)]. One photon of an entangled pair is incident on a Young double-slit of appropriate dimensions to create an interference pattern in a distant detection region. Quarter-wave plates, oriented so that their fast axes are orthogonal, are placed in front of each slit to serve as which-path markers. The quarter-wave plates mark the polarization of the interfering photon and thus destroy the interference pattern. To recover interference, we measure the polarization of the other entangled photon. In addition, we perform the experiment under "delayed erasure" circumstances.42.50. Ar, 42.25.Kb

We report an experiment to generate entangled states of D-dimensional quantum systems, qudits, by using transverse spatial correlations of two parametric down-converted photons. Apertures with D slits in the arms of the twin photons define the qudit space. By manipulating the pump beam correctly, the twin photons will pass only by symmetrically opposite slits, generating entangled states between these different paths. Experimental results for qudits with D = 4 and 8 are shown. We demonstrate that the generated states are entangled states.

A fourth-order Young interference experiment was done to demonstrate a practical way to measure the de Broglie wavelength of a two-photon wave packet. A two-photon collinear beam is generated by type-II spontaneous parametric down-conversion. By modifying the transverse field profile of the pump laser beam that generates the two-photon beam we demonstrate that it is possible to measure the de Broglie wavelength of the single-photon constituents of the two-photon wave packet, the de Broglie wavelength of the two-photon wave packet as a whole and an ill defined intermediate de Broglie wavelength between the two cases. [S0031-9007 (99)08826-2] PACS numbers: 42.50.Ar, 03.65.BzIn a recent article, Jacobson et al.[1] have shown theoretically that the measured de Broglie wavelength of an object is dependent on its internal structure as well as on the detection system. Motivated by a recent experiment [2,3] with molecules they proposed an idealized interferometer that is capable of measuring the de Broglie wavelength of an incident multiphoton wave packet as a whole. For an ensemble of photons with average number n and wavelength l 0 , the de Broglie wavelength is l 0 n . Their proposed Mach-Zehnder interferometer has an "effective" beam splitter (BS) that is a function of a parameter x that varies from 0 (BS does not divide the composite system in constituent quanta) to 1 (BS divides the composite system in its constituent quanta). A calculation done with an incident state jc 0 ͘ j2, 0͘ (two photons incident in one of the ports and zero photons in the other) shows that the oscillation period of the interferometer varies from l 0 ͑x 1͒, corresponding to single-photon interference, to l 0 2 ͑x 0͒, corresponding to two-photon interference. It is interesting to notice that for intermediate values of x the de Broglie wavelength is not well defined, even though the state energy is well defined.In this article, we demonstrate that we can measure the de Broglie wavelength of a two-photon wave packet (biphoton) with a Young double-slit experiment. The incident two-photon wave packet is generated collinearly from a nonlinear crystal by the process of spontaneous parametric down-conversion. The photons transmitted by the double slit form a fourth-order pattern which is a superposition of two Young interference patterns with different periodicity