Proposal for a peculiar double-slit experiment

[Pelion]

Hi to all who might respond,

Consider the 'peculiar' double-slit setup below.
There is a double-slit configuration such that the two slits are never open at the same time. That is: whenever the top slit is open for a certain interval, Ts, the bottom slit is closed for the same interval and vice versa; the configuration toggles continuously between these two states. Let's assume that we have a pulsed sub-single-photon source whose broad-band pulse coherence time, Tp, is much less than Ts. The source targets the double-slit in the following manner: it splits each pulse (which contains at most one photon) into two time bins, synchronized with the opening/closing of the slits, separated by an interval Ts, such that the first time-bin pulse passes at the half-time of when the top slit is open while the second time-bin pulse passes at the half-time of when the bottom slit is open. Thus, a photon never experiences both slits open. Suppose that, just before the detection screen, we place a narrow-band spectral filter such that the coherence time of photons that pass the filter, Tf, is much larger than the slit toggling interval Ts...Will we see an interference pattern, since now it is impossible, even in principle, to determine through which slit a photon passed? Does this gedanken experiment have any implications (positive or negative) pertaining to the 'Standard' or the 'Bohmian' interpretations of QM?
Demetrios

 

[PeterDonis]

Will we see an interference pattern

No.

since now it is impossible, even in principle, to determine through which slit a photon passed?

You are misinterpreting the concept of "photon". See below.

it splits each pulse (which contains at most one photon) into two time bins

A "photon" doesn't work this way. What you are describing is not one pulse split into two time bins. What you are describing is two pulses, each of which "sees" only one slit open.

 

[Pelion]

No.
You are misinterpreting the concept of "photon". See below.
A "photon" doesn't work this way. What you are describing is not one pulse split into two time bins. What you are describing is two pulses, each of which "sees" only one slit open.

There is, at most, one photon per emitted source pulse, which is then split in two pulses separated by a time delay Ts, thus the photon is in a superposition of being in the 'early' pulse or the 'late' pulse of each pulse-doublet...that is not the controversial aspect of the proposal and neither the cause of 'no interference'...if there isn't any interference, then that is due to another, essential cause (unlike your statement)

 

[PeterDonis]

There is, at most, one photon per emitted source pulse, which is then split in two pulses separated by a time delay Ts, thus the photon is in a superposition of being in the 'early' pulse or the 'late' pulse of each pulse-doublet

Do you have a reference for this? It doesn't look to me like something that is possible.

 

[Pelion]

Do you have a reference for this? It doesn't look to me like something that is possible.

...here is a good reference and easy to access: Google "Time-bin encoding photon" and you'll get the Wiki article on time bin encoding of single photons.

 

[PeterDonis]

Google "Time-bin encoding photon" and you'll get the Wiki article on time bin encoding of single photons.

That got me this:

https://en.wikipedia.org/wiki/Time-bin_encoding

Wikipedia is not always a reliable source, but on a quick perusal and comparison with the references given (which are indeed peer-reviewed papers), this one looks OK. (But bear in mind that I am not an expert in this field.) However, I still don't see how it justifies your claim that there will be an interference pattern in your experiment.

This is a "B" level thread so the full math involved here is beyond the thread level. But heuristically: in the standard double slit experiment, we have (in the usual approximation used) a plane wave coming from a source that reaches both slits at the same time; the interference pattern on the detector is then a function of the relative distances from each slit at each point on the detector. I.e., it's a function of the position of the point on the detector relative to each slit.

In your case, the alternatives are two pulses, separated and with negligible overlap in time, each of which only goes through one slit. So there is no interference based on the position of a given point on the detector relative to each slit, because such interference would require overlap in time between the two alternatives (in the standard experiment the two alternatives go through their respective slits at exactly the same time). Essentially, the lack of overlap in time between the two pulses is sufficient to decohere the two alternatives so they can't interfere with each other.

 

[PeterDonis]

the lack of overlap in time between the two pulses is sufficient to decohere the two alternatives so they can't interfere with each other

Note that this is not a general statement, it's a statement about the specific measurement that is being made. Other measurements could be made that would create overlap between the two alternatives and would allow interference (for example, as the article notes, you could pass the photon through a second MZ interferometer). But those would not be double slit experiments.

 

[Pelion]

That got me this:

https://en.wikipedia.org/wiki/Time-bin_encoding

Wikipedia is not always a reliable source, but on a quick perusal and comparison with the references given (which are indeed peer-reviewed papers), this one looks OK. (But bear in mind that I am not an expert in this field.) However, I still don't see how it justifies your claim that there will be an interference pattern in your experiment.

This is a "B" level thread so the full math involved here is beyond the thread level. But heuristically: in the standard double slit experiment, we have (in the usual approximation used) a plane wave coming from a source that reaches both slits at the same time; the interference pattern on the detector is then a function of the relative distances from each slit at each point on the detector. I.e., it's a function of the position of the point on the detector relative to each slit.

In your case, the alternatives are two pulses, separated and with negligible overlap in time, each of which only goes through one slit. So there is no interference based on the position of a given point on the detector relative to each slit, because such interference would require overlap in time between the two alternatives (in the standard experiment the two alternatives go through their respective slits at exactly the same time). Essentially, the lack of overlap in time between the two pulses is sufficient to decohere the two alternatives so they can't interfere with each other.

...that is why there is a narrow-band filter just before the detection screen: the purpose of the tight spectral filtering is exactly to 'stretch' the coherence time of each pulse of a doublet such that, for the photon subset that is filtered, there is significant overlap in time...this erases our possible knowledge of what pulse from each doublet produced a count on the screen...for instance: if the initial pulse coherence times were 0.1 picoseconds, the slit toggling 1ps, and the pulse coherence time of the filtered photons 10ps, then there is overlap between the 'early' and 'late' time bins for the subset of photons that makes it to the detection screen, and we purportedly have an instance of quantum erasure.

 

[PeterDonis]

that is why there is a narrow-band filter just before the detection screen ... there is overlap between the 'early' and 'late' time bins for the subset of photons that makes it to the detection screen, and we purportedly have an instance of quantum erasure.

Hm. I see what you're getting at, but I'm still not sure if it is workable, and I'm not familiar enough with the detailed math in this field to be able to analyze the setup. Again, do you have any references that discuss an experiment like this?

 

[Pelion]

Hm. I see what you're getting at, but I'm still not sure if it is workable, and I'm not familiar enough with the detailed math in this field to be able to analyze the setup. Again, do you have any references that discuss an experiment like this?

...nope, because I am proposing it as something potentially 'new'...but it seems to me we have two single-slit diffraction patterns that are initially disjoint in time but, after spectral filtering, they overlap coherently to produce the interference pattern...maybe I will attempt a mathematical description, but first I wanted to see if there were any blatant flaws in the reasoning...

 

[PeterDonis]

nope, because I am proposing it as something potentially 'new'

Well, unless you can find some mathematical analysis of the scenario, I don't see how we can have any further useful discussion. Personal speculations are off limits here at PF; we need to have some kind of mainstream source (textbook or peer-reviewed paper), or at least some kind of actual math based on mainstream QM.

 

[PeterDonis]

As no references appear to be available, this thread is closed.