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Quantum correlations of light produced in spontaneous parametric frequency down-conversion process

Ievgen I. Arkhipov

Published Jan 1, 2017• 0 citations
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We consider the quantum state of light produced via direct parametric decay of pump photons into photon triples in a medium with cubic nonlinearity. For this state generated in the near-collinear frequency-degenerate regime, the third- and second-order Glauber's correlation functions are calculated and the intensity distribution over frequency and wave vector is found. It is shown that the number of photons generated into a single mode via the three-photon down-conversion is proportional to the width of the frequency-angular intensity distribution for the corresponding two-photon phase matching (spontaneous parametric down-conversion). The intensity of three-photon parametric down-conversion is shown to have an extremely broad frequency spectrum, even for a fixed angle of scattering.
“Ghost” imaging is a process utilizing entangled photon pairs, by which an image is produced indirectly, using photons that have never interacted with the object being imaged. We can do this by taking advantage of correlations inherent in Spontaneous Parametric Down Conversion (SPDC), which is used to produce these entangled photon pairs. SPDC is a classically forbidden process in which a photon of a high frequency is converted into a pair of photons. The change in frequency makes this a nonlinear process. Processes like absorption, reflection, refraction, and polarization are linear processes. These can affect the properties of a light field but cannot change the frequency. SPDC allows us to produce a pair of correlated photons. By utilizing a coincidence-counter, we will be able to measure photon pairs from the source beam arriving within a narrow time interval. With this restriction, we can limit our attention to these correlated photons. One of these photons, which does interact with the object to be imaged, is used to turn on a “camera” detecting the other photon. It is the correlations between these photons that allow for ghost imaging, the reconstruction of the image of an object, even though the object never interacts directly with those single photons that are going to our camera.