In Hong-ou-Mandel interferometers, it means the two photons exit the same output port of the beamsplitter and fall on a single detector but in the case of the Hanbury Brown and Twiss effect, does joint probability detection mean that both photons fall on the same detector or that they are detected simultaneously at two detectors?
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In HOM, you have two photons, one entering on each input of the beam splitter (BS). If they "overlap" in the BS, both will leave the BS on the same output port. The amplitudes of the two possiblities where the two photons leave the BS on different output ports have different sign and cancel each other.
In HBT, you want to measure the two-photon correlation function at the same location (for different or the same time). You use a BS to "split" the wave function an the location. This gives you the possibility to perform two measurements "at the same location". So, basically you measure the probability that a photon is at time t_1 at the location when at t_0 there was another one. Note that in HBT you only use one input port of the BS.
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$\begingroup$ Dr. Andrew Truscott from Australian National University said that bunching is an effect where two or more wavefunctions overlap and interfere. However you only see this interference only if the two particles are detected within the coherence length. The detectors must be separated by less than the coherence length or we get Poissonian distribution. My question is, does this bunching imply that the interfering photons fall on the same or different detectors at the same time? $\endgroup$ Commented Dec 3, 2016 at 5:46
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$\begingroup$ "As the width of the bunching peak is approximately the inverse of the spectral bandwidth, bunching of thermal sources can only be observed when the coherence length is smaller than the time resolution of the detectors." What is this, how do you explain this? $\endgroup$ Commented Dec 3, 2016 at 6:38