B Kim and Scully delayed eraser, interference curve form

[jeremyfiennes]

TL;DR Summary

They say they obtained a standard interference curve. But they didn't.

Ref https://arxiv.org/abs/quant-ph/9903047.
They say the form of their no-which-path-info interference curves (figs 3,4) is "standard". But a standard interference curve has a zero base line. Their base line is a humped curve of the form of their Fig.5, but with about 1/3 of its height.
They give no explanation or comment. Is there any?

 

[hutchphd]

Summary:: They say they obtained a standard interference curve. But they didn't.

But a standard interference curve has a zero base line.

This is likely just Lambert's taw in action somehow. Were there subsequent papers? This is a twenty year old Phys Rev Letter so there should be.

 

[Cthugha]

I am not sure I get your question. Do you wonder why the pattern shows the sinc envelope instead of a flat one or do you wonder why the interference pattern does not exactly go to 0?

The envelope of the interference pattern is the standard sinc shape. In the special case of narrow slits this reduces to an effectively flat base line, but that is not the standard (or at least not the general) case. The slits used in the paper had a width of 300 microns and cannot really be considered narrow.

If you wonder why the interference pattern does not go to 0: The detector D0 has a finite width and the SPDC light will not be perfect and background-free. It is not too surprising that the interference pattern does not reach full visibility.

 

[jeremyfiennes]

Thanks. Yes, the minima of a standard interference pattern are all zero. But these follow a 'hump' shape curve. As if the no-which-path-info case points (interference) had got contaminated with points from the which-path-info (hump) case.

 

[Cthugha]

Well, the hump shape itself is really just the envelope given by the shape of the single slit diffraction patterns. Indeed, for perfect visibility of the interference pattern, the minima should go to zero, but for non-perfect interference visibility, it is expected that the minimum absolute count rate follows the shape of the envelope as the reduction in intensity is a relative one.

As for the origin of the non-perfect interference itself: The interference pattern is formed by coincidence counts. When the authors put D0 at the peak of the hump, they find about 160 coincidences within 240000 detections at D0. The probability that some background light accidentally arrives at D1 or D2 while D0 clicks (or vice versa that some background light arrives at D0 while D1 or D2 click) is quite high. Any of such erroneous detections will reduce the visibility of the interference pattern.

 

[jeremyfiennes]

Thanks. I imagine that they set the detector D0 at some point along the screen (x-axis). And then counted the coincidences of signal photons there with idler photons in the other detectors. R03 and R04 (coincidences with idlers in D3 or D4: which-path info) should give humped curves, which they apparently did (fig.5). R01 and R02 (coincidences with idlers in D1 or D2: no which-path info) should have given a standard interference pattern. In the caption to fig.3 they say it did. This is what I am questioning. For D0 at a 'null' (dark) point on the screen, there should have been no coincidences with D1 or D2 (interference case). You suggest it could have been due to stray light hitting the screen (D0). Possible. But in that case the minima offet would be random, and not the definite hump curve they got. Some systematic effect seems to be involved.

 

[Cthugha]

You suggest it could have been due to stray light hitting the screen (D0). Possible. But in that case the minima offet would be random, and not the definite hump curve they got. Some systematic effect seems to be involved.

That is just my suggestion for effects that might take place beyond those already mentioned by the authors. As the authors state :
"Finally, after we take into account the finite size of the detectors and the divergence of the pump beam, the interference visibility is found to be in satisfactory agreement with observation."Essentially the DCQE experiment works like a non-local momentum filter. For a standard double slit a standard interference pattern does not necessarily go to 0. You need light with well defined momentum (angle) to see a well defined interference pattern with perfect visibility. The larger the spread of momenta inside your beam is, the less interference visibility you get. In DCQE, you have light that intrinsically shows a huge spread in momenta, but you may use one detector as a momentum filter. Postselecting on this set of detections will result in photons having quite well defined momentum on the other side of the experiment. How well the momentum is defined, depends on the size of the detectors and the divergence of the pump beam (as the latter sets the uncertainty of the initial momentum before conversion). This filter will certainly not be as perfect as placing a pinhole and create the interference pattern expected of the degree of filtering obtained. I think you are misinterpreting what the term "standard interference pattern" is supposed to mean.

 

[jeremyfiennes]

Thanks -- though I'm not sure I completely grasped all you said. But I think my query is more basic. For the screen detector D₀ at an interference pattern zero, for idler photons arriving in D₁ or D₂ (no which slit info) there should be no D₀ photons, except as you say for strays. In fact there are almost exactly half what one would expect in the 'humped' case (which slit info, idlers detected in D₃ or D₄). See diagram. This seems to be systematic, and harly attributable to chance.

 

[Cthugha]

Ok, maybe let me phrase it more directly:

For the screen detector D₀ at an interference pattern zero, for idler photons arriving in D₁ or D₂ (no which slit info) there should be no D₀ photons, except as you say for strays.

This is completely wrong. Of course there should be photons there. The interference pattern is NOT expected to go to zero for the exact reasons mentioned by the authors. The standard double slit is a momentum measurement. You can easily see that yourself if you can prepare a simple double slit:
Shine a light source at it at from far away at normal incidence: you will see a double slit pattern.
Shine the same light source at it from far away at a different angle: you will see a different double slit pattern, where the position of the peaks is shifted.
Do the same thing from a third angle: you will again see a different double slit pattern.

The reason for this is simple: each different momentum (angle) corresponds to a different path length difference from the light source to the two slits. You will see this phase difference as a shift of the interference pattern. If you now move the light source closer to the slits and if the light source has a finnite size, you will notice that the visibility of the interference pattern will go down. The reason for this is simple: you just average over the scenarios above. Light emitted from the left end of the light source will have some well defined path length difference to the two slits. Light emitted from the center of the light source will have another well defined path length difference. Light emitted from the right end of the light source will have another well defined path length difference. These path length differences correspond to different interference patterns and you will measure the superposition of all of them, which is an interference pattern with reduced visibility. You will only get full visibility if the momentum of the incoming beam is well defined, which means that all light arrives at a single angle and the light source can be considered as point-like.

In the SPDC paper, the pump beam already has a finite divergence, which directly means that there will be some range of emission angles and the momentum of the incoming photons is not well defined. Therefore one necessarily gets a weighted average over all the interference patterns corresponding to the different emission angles involved, which is the interference pattern with reduced visibility which you see in the paper. It is NOT expected that the count rate will go to zero.

 

[EPR]

The reason for this is simple: each different momentum (angle) corresponds to a different path length difference from the light source to the two slits. You will see this phase difference as a shift of the interference pattern.

Isn't this observed phenomenon of shifting to left or right of the interference pattern exactly an observation of the process of decoherence(i.e. loss of wave coherence)?

 

[Cthugha]

Well, it may be.
The double slit in itself is a classical measurement that measures spatial coherence (which means how point-like the light source appears to the slit). Whether the light field was already spatially incoherent initially (which corresponds to a finite size of the light source) or whether the light source lost spatial coherence during propagation (e.g. due to propagation through a scattering medium, other interactions or decohering processes): both is possible depending on the experimental scenario.

 

[jeremyfiennes]

Ok. Thanks.