Science
In reply to the discussion: Quantum Entanglement, Dark Counts, Coincidence Detection [View all]caraher
(6,278 posts)If you want polarization entangled beams with Type II, you basically have one cone of H polarization and another cone of V polarization, and along the lines of intersection a given photon is equally likely to "belong" to the H cone or the V cone. So the state you get is something like |HV> + |VH>, where the first letter is the polarization of the photon emitted along one intersection line and the second letter is the polarization of the photon emitted simultaneously along the other line. The pump beam, as always, is along a line halfway between them (for equal-wavelength photons).
If you tilt that crystal, for a given wavelength, the cones change opening angles and central directions. In Type II collinear downconversion, the cones that used to intersect along 2 lines now have just one line of intersection.
In general you can get more photons just by using a longer crystal, but there are limits. And there is what's known as temporal walkoff - one polarization moves ahead of the other polarization. One way to correct for that is to follow your BBO with a second BBO crystal, rotated 90 degrees, with half the length. This overlaps your H and V wave packets.
A typical temporal walkoff is about 100 fs for a crystal of about 1 mm length. That may or may not matter, depending on the experiments you want to do. For this experiment I don't think it matters at all, since you plan to have very different path lengths for the two photons anyway