Mach-Zehnder Experiment: Wave-Particle Duality Demonstrated

[jeremyfiennes]

TL;DR Summary

Essence of Mach-Zehnder xpt

Can the essence o the Mach-Zehnder experiment be resumed as shown, to emphasize the analogy with the double-slit experiment? When the beams are brought together on a screen they form an interference pattern (no which-path inormation; wave behaviour). If the screen is removed and replaced by two photon detectors, individual photons appear in either one detector or the other, but never both simultaneously (which-path inormation available; particle behaviour).

 

[vanhees71]

There's also no which-way information in the right scenario since all that has changed is to substitute the screen by photon detectors. What should have been changed, however, is the source, because with a light bulb you can never have single-photon states (they emit thermal radiation, which is never a one-photon Fock state, no matter how dim you ever make it). The point is that if you do the experiment with one-photon Fock states, you get always only one of the photon detectors registering one photon but never two registering "half a photon". Thus for photons the intereference pattern reflects the detection probability for one photon.

 

[jeremyfiennes]

Thanks. The light bulbs are symbolic single-photon sources: I should have added that. So with a screen as the final target, the single photons build up to an overall intererence pattern, as in the double-slit experiment with single photons. And with the two photon detectors as the final target, individual photons are found in one detector or the other, but never both. Correct?

 

[PeterDonis]

with a screen as the final target, the single photons build up to an overall intererence pattern

In the diagram you give, yes, but the diagram you give is not a diagram of a Mach-Zehnder interferometer, because it is missing a critical component: a second half-silvered mirror (or "beam splitter", as it is more often called) at the upper right corner. In a "base" MZI, which has that second beam splitter present, but no other components, you do not get an interference pattern at all: all of the photons go to the right after passing the second beam splitter (because of the way the phases on the two paths match up), so putting a screen in is pointless, and with photon detectors all of the photons will go to the detector on the right, and none to the detector upwards.

The main purpose of MZIs, as I understand it, is, knowing the "base" state above, to put other components in one or both of the paths that can affect the phase of the photons, in order to see how doing that affects the output. For example, if you shift the phase on one of the two paths by 180 degrees, all of the photons now go up instead of to the right after the second beam splitter. If you shift the phase half as much, by 90 degrees, the photons go 50-50 each way after the second beam splitter. And so on. So by putting components whose phase shift you don't know in one or the other of the two paths, you can test how much they shift the phase.

 

[jeremyfiennes]

Ok. Thanks. I am aware of the second beam splitter. I wanted to simplify it down to the point where it becomes an equivalent to the double-slit experiment, with an interference pattern showing wave properties, and one or the other, but not both, photon detectors firing showing particle properties.

 

[PeterDonis]

I wanted to simplify it down to the point where it becomes an equivalent to the double-slit experiment

Can you find a reference where this has actually been done, experimentally?

 

[jeremyfiennes]

I had fondly imagined it had. But from your question, I am now wondering.

 

[vanhees71]

One classic experiment in the early history of quantum optics involving single photons, beam splitters, and a Mach Zehnder interferometer is

P. Grangier, G. Roger and A. Aspect, Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Light on Single-Photon Interferences, EPL 1, 173 (1986)
https://iopscience.iop.org/article/10.1209/0295-5075/1/4/004/meta

One should note that before the mid 1980ies there was not much true evidence for specific effects that are only correctly described with the quantized electromagnetic fields. Almost all experiments believed to show field quantization are as well describable in the semiclassical approximation, where only the detector material is treated as quantized (e.g., the photo effect a la Einstein 1905 is completely understandable by describing the electromagnetic field as classical interacting with a bound electron; the same holds for the Compton effect). The first theoretical hint for field quantization was Einstein's derivation of the Planck formula for black-body radiation by kinetic theory, where Einstein had to assume that besides the (semi-)classical effects of absorption and induced emission also another transition mechanism is at work, which is spontaneous emission, according to which an excited state of an atom must also decay under emission of a photon without any other radiation present. This is the most simple effect really showing field quantization.

The difficulty for the early experimenters was the lack of efficient single-photon sources, i.e., sources where you have for sure a single photon, i.e., a with certainty prepared single-photon Fock state of the em. field. As in the above famous example in the early days of the mid 1980ies the experimenters used atomic cascades as single-photon sources.

The interest was also high at this time because of Bell's work about possible hidden-variable interpretations of quantum theory. Famously Aspect, also using atom cascade photon sources was the first to experimentally demonstrate the violation of Bell's inequality hinting at the impossibility of any local deterministic hidden-variable theory explaining the effects predicted by QT in terms of stronger-than-classical correlations described by entangled states.

 

[jeremyfiennes]

Thanks. I am beginning to see that the whole question is considerably more complicated than I had originally imagined.

 

[jeremyfiennes]

"The photo effect a la Einstein 1905 is completely understandable by describing the electromagnetic field as classical interacting with a bound electron; the same holds for the Compton effect."

Can you give me some not-too-mathematical references or this?
Thanks

 

[vanhees71]

It's maybe too mathematical, but here it is:

https://www.physicsforums.com/insights/sins-physics-didactics/

For a less mathematical but more science-historical perspective concerning the difficult notion of photons, see

https://www.amazon.com/dp/B07FP2ZVRG/?tag=pfamazon01-20

 

[jeremyfiennes]

Thanks. I will look them both up.