Quantum Imaging

The process of frequency down-conversion in a nonlinear crystal is known to display strong quantum correlations between the down-converted signal and idler fields. Its large angular emission bandwidth permits to create entanglement among a large number of spatial modes of the optical field and make it a natural candidate to display quantum correlation in the spatial domain. In the nineties, Belinskii et al. investigated the possibility of using this property of spatial entanglement of the down-converted elds in order to obtain detailed information on an object (typically a transparency creating an image) inserted in the path of one of the two beams, say of the signal. They considered a regime of low conversion eciency, where at most a single pair of photons is produced by each laser pulse. By making a "bucket" detection of the signal photon that excludes any position measurement, and by scanning the position of the idler photon, which, in principle, does not contain any direct information on the object, they demonstrated a kind of magic reconstruction of the object image, achieved by doing coincidence counts of the signal and idler photons [3]. We have demonstrated that this technique can be implemented even in a high gain regime, when the number of down-converted photons can be large. This is made possible by the fact that the position-momentum entanglement of single photon pairs survives when considering macroscopic fields, in the form of highly non-classical spatial correlation between signal and idler fields. We studied different imaging schemes, which can be used to obtain both the near and the far field image (i.e. the diraction pattern) of the object and formulated a fully analytical theory. Although the efficiency of image reconstruction should in principle increase when using many photons, we had to face the problem of the "visibility" of the correlation effect that make the imaging possible. To this end, we have developed a numerical model of the experiment, based on stochastic simulations of the system Wigner function. This permits a realistic description of the system, including eects such as the nite size of the pump beam prole and its pulse duration, and allows us to evaluate the conditions under which an ecient image reconstruction is possible.