Fig.1. Biphoton correlation radius versus the distance from the crystal. Insets: shapes of the spatial correlation function at different points of the dependence. 
Preparation of entangled photons with small correlation times and transverse lengths is a key problem in the realization of interaction between twophoton light and material quantum objects, such as atoms or ions. We have proposed a method for generating biphotons with extremely narrow spatial intensity correlation functions. The method is based on the spatial variation of linear or nonlinear properties of the crystal where biphotons are generated via spontaneous parametric downconversion. As a result, the crystal acts as a `nonlinear lens’, creating twophoton light with a spatially converging intensity correlation function. Figure 1 shows the dependence of the transverse correlation length (correlation radius) of the biphoton versus the distance from the crystal (red line). The insets show the shapes of the spatial correlation functions at different distances from the crystal. This ‘transverse compression’ effect is similar to the time compression of chirped pulses due to their propagation through dispersive media.
Fig. 2. A 'ring' of parametric downconversion obtained by averaging over 2000 frames of an ICCD camera. 
It is planned to observe this effect in experiment using a singlephoton CCD camera (ICCD) for the measurement of spatial intensity correlation functions. As the first step, it is necessary to develop the technique of measuring spatial intensity correlation functions with an array singlephoton detector. Towards this, we have performed a test measurement of the spatial intensity correlation function of a pseudothermal light source based on a rotating groundglass disc, as well as of a parametric downconversion source. The measurement is in the singlephoton regime, i.e., each pixel of the ICCD camera either fires, registering a photon, or does not fire. Our first results demonstrate the feasibility of such a measurement. Figure 2 shows the farfield distribution of the parametric downconversion intensity at the degenerate wavelength 709 nm, recorded by summing over 2000 frames of an ICCD camera. Note that each frame contains only singlephoton events, the probability of a single pixel firing being below 0.02. By processing the frames, we can measure the spatial correlations.
Multiphoton states of light (MPL) are, in principle, available via their conditional preparation from squeezed vacuum generated via parametric downconversion. However, a huge problem consists of the lack of reliable photonnumber resolving detectors. As a substitute, one uses timemultiplexing detectors but here we choose a different strategy, which is space multiplexing.
It is planned to produce three, four, and higherphoton states via conditional preparation, using spontaneous parametric downconversion with intermediate gain values. Characterization of the produced state will be through the measurement of a higherorder Glauber’s intensity correlation function depending on the intensity, similar to the way it was done in [1]. The correlation functions of different orders will be measured by illuminating many pixels of the ICCD by a single mode of parametric downconversion radiation. Different pixels will then play the role of different detectors, and their correlated counts will provide the same information as a multiport Hanbury BrownTwiss interferometer.
1. M. Avenhaus, K. Laiho, M.V. Chekhova, and C. Silberhorn, Accessing Higher Order Correlations in Quantum Optical States by Time Multiplexing, PRL 104, 063602 (2010).
