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If I have two time varying voltages, \$V_1\$ and \$V_2\$ coming from two light detectors, how would I go about 'multiplying' the two signals with an electronic circuit?

The voltages vary \$\pm 5V\$ against a mean of ~6 V at a frequency around 1 GHz. The idea is to subtract the mean value so the voltages swing positive and negative. Multiplication and summation at this point gives some measure of the coherence of the signals. If both are positive then multiplication is obviously positive, if both are negative then you also get a positive output. If they are coherent then they should swing +/- together. Some summation over time gives a measure of the coherence.

Basically it's an attempt to replicate the Hanbury-Brown and Twiss effect.

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  • \$\begingroup\$ The signals can be coherent (phase locked) but 90 deg out of phase and the average product will still be zero. \$\endgroup\$
    – Olin Lathrop
    Commented Jun 27, 2012 at 13:05
  • \$\begingroup\$ The incoming signal is essentially random, so phase considerations are not so important. \$\endgroup\$
    – Nic
    Commented Jun 27, 2012 at 13:09
  • \$\begingroup\$ @OlinLathrop, if you are multiplying something like that and they are out of phase you normally are expecting a 0. \$\endgroup\$
    – Kortuk
    Commented Jun 27, 2012 at 13:18
  • \$\begingroup\$ 1 GHz. Um! In fact Um[tm] :-). Digital sampling would need to be at several GHZ+, say 10 GHz which is getting "difficult". Later, maybe, but probably not :-). || I'm not so sure of their comment "if the source consists of a single atom which can only emit one photon at a time, simultaneous detection in two closely spaced detectors is clearly impossible. " The validity of both 'clearly' and 'impossible' are possibly not clear :-) \$\endgroup\$
    – Russell McMahon ♦
    Commented Jun 27, 2012 at 13:57

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Without getting into the physics / coherence / phases discussion, I'll just point out that analog multipliers exist and can be pretty fast. (Also see "mixers" in the RF world, but four-quadrant operation and linearity might get compromised in the quest for bandwidth.)

Check out Analog Devices' multipliers, which go up to 2GHz.

It sounds like you're essentially interested in the DC / near-DC content of the product signal. Your sensors and multiplier have to handle the "around 1GHz", but the rest of the signal chain after the multiplier can be as slow as the length of the "coherence"/correlation effect you're trying to measure. (Slower is better from a noise perspective. Don't forget that even on paper, two uncorrelated random signal sources may and will show a non-zero cross-correlation when you're examining only a finite-length time sample.)

Out of curiosity, where in the physics does the 1GHz number come from? Mean photon inter-arrival time?

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  • \$\begingroup\$ 1GHz represents the typical intensity fluctuations of a thermal source. In the low light limit then yes, this would be co-incident photon arrival time \$\endgroup\$
    – Nic
    Commented Jun 28, 2012 at 21:14

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