When generating entangled photons by means of Spontaneous Parametric Down-Conversion SPDC, the usual assumption is that the two photons are created at the same time. I have not been able to find any papers which discuss this assumption, nor experimental papers in which the delay has been measured.
I'm looking for (A) papers which discuss the above, or (B) measure the above. What follows describes what we are doing in the lab.
Our setup is type I SPDC using a 90 mW CW diode laser operating at 402 nm, with two pieces of BBO with the optic axes at 90 degrees. We use high efficiency interference filters to remove light that is away from the degenerate wavelength, which is 804 nm.
In our experiment we are finding that the quantum efficiency (pair correlation) increases very rapidly as the temporal binning is increased from a few hundred picoseconds to a few nanoseconds, flattening out around 10 ns. The corresponding Poisson statistics for "accidental pairs" should grow linearly with the increase of temporal binning, and our experiments with non-entangled light are consistent with the Poisson statistic estimates.
For example, with 135,000 counts per second on detector 1, and 146,000 counts per second on detector 2, the Poisson statistic for pair detection is 95 pairs per second for 10 ns binning, but the actual pair rate is 37,000 pairs per second, which is a quantum efficiency of over 26%.
The quantum efficiency declines as the temporal binning is reduced; at 240 ps the quantum efficiency is about 2%.
Our timer-counter clocks at 81 ps per tick; 81 ps of time corresponds to a distance of (300 um/ps x 81 ps) = 24.3 mm, or about an inch. 10 ns corresponds to 3 meters, or about 10 feet. The single-photon detectors are symmetrically placed, and essentially have identical distances to the BBO crystal, about 1200 mm.
We are currently running some additional experiments, gathering data for a series of temporal bin durations so that we can plot the rate of increase with increased time.
Answer
The assumption that the photons are created at the same time is a good one: you're looking for the problem in the wrong place.
What you've observed is almost certainly due to technical details of the detectors you're using. There is a time interval between when a detector absorbs a photon and when you get the electrical signal indicating this happened (latency); more importantly, this time interval also has a variance (jitter). These values can be on the order of nanoseconds depending on the type of detectors you're using.
One more thing: assuming you do have a small enough jitter to resolve relative timing of events by better than 10ns (quite likely you do), did you try readjusting the relative delay between the signals from the two detectors after reducing the time bin sizes? Maybe the two detectors' time bins are "misaligned" by a few nanoseconds: at 10ns the bins are so large that this misalignment doesn't matter.
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