Observations of unusual diffraction and interference by two-photon correlation measurements are reported. The signal and idler beams produced by spontaneous parametric down-conversion are sent in different directions, and detected by two distant pointlike photon counting detectors. A double slit or a single slit is inserted into the signal beam. Interference-diffraction patterns are observed in coincidences by scanning the detector in the idler beam. PACS numbers: 42.50.Dv, 03.65.Bz Spontaneous parametric down-conversion (SPDC) [1]is the most effective source of two-photon light, consisting of pairs of correlated photons. The essentially quantum nature of the corresponding two-photon state [2,3] has been confirmed in a number of two-photon correlation experiments [4]. This quantum feature allows us to demonstrate an unusual two-photon effect [5], which looks very strange from the classical point of view. The SPDC light beam, which consists of two orthogonal polarization components (usually called signal and idler), is split by a polarization beam splitter into two beams, and detected by two distant pointlike photon counting detectors for coincidences (see Fig. 1). A Young's double-slit

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Single-crystal holmium and gadolinium layers have been grown on yttrium substrates using the molecular beam epitaxy technique and their structures investigated using high resolution x-ray scattering. The experiments were performed using a Philips MRD diffractometer in Oxford, and with the XMaS facility at the ESRF. Holmium layers with a thickness below T c = 115 Å give scattering that is characteristic of a pseudomorphic film structure with the same in-plane lattice parameter as the yttrium substrate to within 0.05%. For layers thicker than T c , there is a sharp reduction in misfit strain due to the creation of edge dislocations. The transverse lineshape of the holmium peaks exhibits a two-component lineshape for thicknesses above T c , but below about 500 Å. Above 500 Å the lineshape of the transverse scans becomes Gaussian and is characteristic of a mosaic crystal.The gadolinium layers show no sharp change of strain for layers as thick as 2920 Å and the transverse peak shape remained similar for all films. This is characteristic of pseudomorphic film growth and a failure to nucleate dislocations.

Two types of interference were observed using two-photon spontaneous parametric radiation from two nonlinear interaction regions. Two experimental setups analogous to the Young and Mach-Zehnder interferometers were used. An interesting feature of the two-photon Young interference is the opposite conditions for its observation by two different methods: by measuring intensity of light at a single frequency and by measuring correlation of intensities at two conjugated frequencies ͑method of coincidences͒. Two-photon Mach-Zehnder interference resembles the Ramsey method of separated fields, which is used in beam spectroscopy. A simple macroscopic quantum model agrees well with the experimental results and enables their interpretation in terms of ''biphotons'' carrying information about the pump phase. ͓S1050-2947͑97͒03210-1͔

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