I How Can Multi-Particle Interference Help Clarify Quantum Mechanics?

[Killtech]

i want to get a better understanding of quantum mechanics (specifically for the multiple particle case) and came to a point where looking deeper into the theory won't yield the answers i seek. so to my discomfort i fear i'd need to look at experimental results to extend my understanding.

so my first question simple interference experiments should hopefully answer. there are a lot of experiments that use half mirrors to split up a particle to conduct self-interference with it later in one way or another (e.g. quantum bomb tester). i am looking for experiments that instead of the half mirror splitting use another independent particle of same type for the interference instead. i imagine it might be difficult to consistently produce pairs of particles of the same wavelength and phase to yield proper interference results but i suppose there are enough tricky physicist that got it done one way or another.

any links would by helpful, thanks.

 

[BvU]

The S in laser stands for stimulated. Identical particles a-plenty ! If it will help you understand QM is another matter, though..

 

[ZapperZ]

there are a lot of experiments that use half mirrors to split up a particle to conduct self-interference with it later in one way or another (e.g. quantum bomb tester). i am looking for experiments that instead of the half mirror splitting use another independent particle of same type for the interference instead. i imagine it might be difficult to consistently produce pairs of particles of the same wavelength and phase to yield proper interference results but i suppose there are enough tricky physicist that got it done one way or another.

It is unclear on what exactly you are looking for. Are you looking for another interference-type experiment that uses something else other than photons? The double slit experiment with electrons, neutrons, etc.. are quite common already. Is this what you are seeking?

Zz.

 

[Killtech]

for the start i am looking for a overview of existing experiments that involve multiple particles - whatever kind - in some kind of setup where interference takes place (or doesn't due to wave-function collapse). however the interference should specifically occur between two different particle waves such that reducing the experiment to a single particle would not show exhibit the same behavior. therefore i am not sure a double slit experiment is useful for that matter.

or maybe i'll try with a series of gedankenexperiments: first take a photon, split it with a half mirror into two rays and then combine them in such a way that interference happens (destructive or constructive). basically the quantum bomb tester without a bomb - therefore the interference should always take place. now change the experimental setup in such a way that instead of using two rays of the same photon created through a half-mirror i want to use two independent and identical photons instead. is it possible to get any kind of wave interference between two separate waves? what will i measure?

 

[BvU]

You have funny ideas about photons. You can't split them into two rays. Perhaps you should look at the Feynman lectures, in particular part 1 here. It's worth the time investment -- and it's fun.

 

[Killtech]

You have funny ideas about photons. You can't split them into two rays. Perhaps you should look at the Feynman lectures, in particular part 1 here. It's worth the time investment -- and it's fun.

don't be picky about my wording as it's not the point. it's just how i call the behavior of a single photon sent through a half mirror.

 

[ZapperZ]

for the start i am looking for a overview of existing experiments that involve multiple particles - whatever kind - in some kind of setup where interference takes place (or doesn't due to wave-function collapse). however the interference should specifically occur between two different particle waves such that reducing the experiment to a single particle would not show exhibit the same behavior. therefore i am not sure a double slit experiment is useful for that matter.

T.L. Dimitrova and A. Weis, Am. J. Phys. v.76, p.137 (2008).

Zz.

 

[Killtech]

thanks for the reference but this isn't what i am looking for (also i cannot view the paper from the AAPT page so finding it elsewhere proves a bit tricky). anyway, that experiment is merely demonstrating the default particle wave duality of QM within one experiment but i don't see where a interference between two independent photons would take place. the presentation of the wave nature doesn't exclude the possibility that it is just the result of many self-interference photons overlapping.

perhaps my problem is that bringing two independent photons into interference might not be allowed by QM and therefore i am looking for a negative result experiment which can be harder to find?

 

[DrClaude]

Maybe this is what you are after: https://en.wikipedia.org/wiki/Hanbury_Brown_and_Twiss_effect

 

[zonde]

perhaps my problem is that bringing two independent photons into interference might not be allowed by QM and therefore i am looking for a negative result experiment which can be harder to find?

There can be interference between two independent photon beams:
Interference of Independent Photon Beams
And there can be interference between two identical photons:
Hong–Ou–Mandel effect

 

[Killtech]

There can be interference between two independent photon beams:
Interference of Independent Photon Beams
And there can be interference between two identical photons:
Hong–Ou–Mandel effect

thank you very much, this is exactly the information i was looking for! specifically the Hong-Ou-Mandel effect is useful for some simple thought experiments.

however this brings me to my next question. since physicists are a bit sloppy in the formulation what counts as a measurement (thus triggers a collapse of the wave function) and what doesn't - or at least i find it quite troublesome to find exact definitions for this - i wonder whether such a two photon interference is sufficient to trigger a collapse because technically a con-/destructive overlapping of waves is not the result of an interaction between them (disregarding some higher order photon-photon scattering which shouldn't be relevant here).

the reason i am trying to understand what reality does in such cases is because i am trying to understand which degrees of freedom of the wave function are irreducible (i.e. required to describe reality always correctly) and which are just mathematical artifacts and such two particle interference experiments could potentially be very useful for that.

 

[zonde]

i wonder whether such a two photon interference is sufficient to trigger a collapse because technically a con-/destructive overlapping of waves is not the result of an interaction between them

I find it useful to view HOM interference in beamsplitter as collapse. After all both photons end up in one of the spatially distinct outputs of beamsplitter.
And take note that this interference is different from usual interference in double slit or Mach–Zehnder interferometer. When you change path length for one photon withing one wavelength there is no change in observed effect (in Mach–Zehnder interferometer you will observe shifting between constructive/destructive interference). And you can not explain this as random phases between photon pairs as this would predict only half of maximum visibility.

 

[Killtech]

I find it useful to view HOM interference in beamsplitter as collapse. After all both photons end up in one of the spatially distinct outputs of beamsplitter.
And take note that this interference is different from usual interference in double slit or Mach–Zehnder interferometer. When you change path length for one photon withing one wavelength there is no change in observed effect (in Mach–Zehnder interferometer you will observe shifting between constructive/destructive interference). And you can not explain this as random phases between photon pairs as this would predict only half of maximum visibility.

that is interesting and it seems that indeed multi particle interference yields quite the insight i was looking for.

okay, now i have another question. i can now construct a gedanken-experiment that regardless of its outcome seems to contradict quantum mechanics in one way or another and i was hoping to get a clarification here where i am thinking wrong.

so consider the following setup: take a two independent photon beams (let's call them A and B) and direct At to a half mirror (HA). direct one outgoing ray towards a detector (DA) while use the other to do conduct a HOM interference with a second photon beam B with another half mirror HB. my question now is what will i measure? the trivial idea behind this setup is to detect the presence of the wave function originating from beam A and therefore detect whether it has collapsed or not. if i understand the theory correctly then detector DA should collapse the A wave function in any case due to Renningers negative result wave collapse.

therefore i'd expect two possible outcomes:
1) the wave function indeed collapses non-locally but only after it has reached DA. therefore moving DA further away from HA such that the beam travel distance is longer then the from HA to HB. in this case i will always measure HOM interference. but if the DA is moved closer then HOM interference will only take place in case DA detects nothing. therefore i would be able to measure the position of DA in a non local way and albeit just binary i would theoretically be able to transfer information instantly independently of the distance. this contradicts QM.

2) the wave function does not collapse regardless of DAs position. in that case the axioms of measurement are simply incorrect and the wave function itself (probably never) collapses but instead always follows the time evolution given by Schrödinger (or later QM equations of motions) and it's only the probability that collapses. but if the probability is not fully determined by the wave function it would require additional degrees of freedom in the theory. considering that the probability is specifically required only for particle detection it carries all the particle properties. so considering von-Bohm's particle trajectories it might be convenient to just use this as a first attempt to describe these additional degrees of freedom theoretically. therefore this experiment could possibly be used to falsify or confirm Bohms idea. note that this outcome would not contradict Bells experiments as it only shows that this particular experiment non-local aspects are not required.

so in any case to my understanding i get into conflict with QM axioms. the general problem here is that was i want to measure here is not any particle property which QM axioms are build around - but instead i want to measure the wave function directly. if i interpret QM correctly this is strictly forbidden by the axiom that requires measurable observables to correspond to linear Operators. therefore i wonder what operator this gedangen-experiment measurment corresponds to - since there is not know algorithm i know of to calculate the observable-operator from a experimental setup. on the other hand my attempts to find operators for wave function measurement always yielded that i would need to a non linear one (quadratic IIRC). then again i question what kind of experimental evidence is this axiom (observables=linear) build on anyway since it does seem rather difficult to verify such an exclusion postulate. on the other hand a whole lot of QM interpretation seems to be implicitly founded on it.