Question about the Mach-Zehnder experiment

[naffin]

Question about the Mach-Zehnder interferometer experiment

Let's consider a Mach–Zehnder interferometer with a significant difference in length between the two physical paths. The optical paths are set up such that the two beams interfere 100% destructively on one of the two detectors.

What happens when we turn on the light source ?
According to classical mechanics there is a transient situation during which only one of the two beams arrives at the last beam splitter, so before having interference between the two beams half of the photons goes to both the detectors.
After this situation we have 0% and 100% detections.

According to quantum mechanics each photon interferes only with itself, so my question is: how can quantum mechanics explain this experiment? What is the difference among photons emitted at different times? I would say there's no difference, because the preparation is the same.

 

[f95toli]

According to quantum mechanics each photon interferes only with itself

Not true, this is a common misunderstanding, which comes from a quote by Dirac (and in this case Dirac was wrong).

Anyway, if I understand your question the answer will simply be that it comes down to distinguishability: if the path length is so long that you could in principle obtain which-path information (due to the difference in arrival times) there will be no interference pattern.

I've seen experiments where this has been demonstrated directly by varying the path length and then comparing it with the time-constant tau of the "detector" (which as far as I remember was a trapped ion). the visibility goes down as the path length approaches ~c*tau;
it is a neat demonstration of SR and QM.

 

[San K]

Anyway, if I understand your question the answer will simply be that it comes down to distinguishability: if the path length is so long that you could in principle obtain which-path information (due to the difference in arrival times) there will be no interference pattern.

thanks f95toli ..however does the logic change in case of two-photon interference?

Someone had, about a month back, posted a link to a paper (two-photon interference), on this forum, where you could have a delay (between the paths) as well as interference. The paper was reliable/high-quality and I did not understand it fully. I am trying to reconcile that with the above information.

It did not talk about any limit on the path length. The paper has been located -

http://physics.nist.gov/Divisions/Div844/publications/migdall/psm96_twophoton_interference.pdf

It says -

In conclusion, the results of this experiment clearly demonstrate that two-photon interference effects can be
observed even when the optical paths in the interferometer have very different lengths, and the photons do not arrive
at the beam splitter at the same time.

In several earlier polarization experiments [6] the intuitively comforting notion of the photons overlapping at the beam splitter is
not at the heart of the interference, but a mere artifact of the particular geometry of the setups.

What is important is the indistinguishability of the two-photon amplitudes, which may be maintained or destroyed after the output of the interferometer.

another question: what does "indistinguishability of the two-photon amplitudes" mean? what are the various ways we can create it experimentally?

 

[naffin]

Not true, this is a common misunderstanding, which comes from a quote by Dirac (and in this case Dirac was wrong).

Anyway, if I understand your question the answer will simply be that it comes down to distinguishability: if the path length is so long that you could in principle obtain which-path information (due to the difference in arrival times) there will be no interference pattern.

I've seen experiments where this has been demonstrated directly by varying the path length and then comparing it with the time-constant tau of the "detector" (which as far as I remember was a trapped ion). the visibility goes down as the path length approaches ~c*tau;
it is a neat demonstration of SR and QM.

So the quantum mechanical description should be this one: if we start sending lots of photons at a time, the first of them will be detected with a probability of 50% on each detector because of the large difference in the two "possible paths", while the others will interfere among them producing the expected interference pattern.

 

[Cthugha]

What happens when we turn on the light source ?
[...]
So the quantum mechanical description should be this one: if we start sending lots of photons at a time, the first of them will be detected with a probability of 50% on each detector because of the large difference in the two "possible paths", while the others will interfere among them producing the expected interference pattern.

I would like to point out that the mere act of turning on a light source is not as trivial as one might consider it to be. Having interference in a Mach-Zehnder interferometer means that the time delay introduced by the different path lengths is less than the coherence time of the light source in question. Also, all photons emitted during the coherence time are indistinguishable and basically the exact emission time cannot really be determined on a timescale smaller than the coherence time. This sounds paradoxical as one one can measure the distance between the light source and the interferometer and calculate how long it takes light to travel that way. However, the emission process already happens inside the light source and for typical useful light sources with high coherence times - typically lasers - the light goes back and forth between two high quality mirrors for a period of time roughly comparable to the coherence time already inside the light source.

So basically switching on a light source having long coherence time in such a kind of experiment typically means that you do not get light out directly, but light gets feeded into a cavity from which it escapes with a statistical low escape rate which already causes a delay roughly comparable to the coherence time of the light. Nevertheless, many light sources show a behavior similar to what you described and have somewhat lowered coherence at times close to the turn-on process and approach a higher level of coherence when reaching steady state operation.

 

[San K]

Also, all photons emitted during the coherence time are indistinguishable and basically the exact emission time cannot really be determined on a timescale smaller than the coherence time. This sounds paradoxical as one one can measure the distance between the light source and the interferometer and calculate how long it takes light to travel that way.

Interesting information Cthugha.

I gather that the Coherence length, and hence coherence time, can be increased with better control over the environment (i.e. by reducing propagation factors such as dispersion, scattering, and diffraction)

for example it can be made equal to the distance between Earth and moon...which is roughly 1.2 seconds.

are we still not able to distinguish the photons if the difference is 1.2 seconds?

more importantly - is the two-photon interference happening without the photons ever meeting?