Are there limits to the size of the double-slit experiment? Can we in principle emit single photons with lower and lower values of hf and consequently increase the spacing between the slits?
Are there any limits to doing this in theory? What are the practical limits?
What is the lowest hf that has ever been experimentally tried to date?
There is no theoretical limit insofar as the difference in path length for each slit is lower than the coherence length. In pactice, the limit is the size of the beam.
A particle can interfere in a double slit if the distance of the slits is smaller than the compton length of the particle L= h / m c. the More the energy of the particle increase, the more closer the slits: in general they must be closer than D < h c / E. Since the photon is massless it can also interfere for slits very far away, if E= h f is small.
Hi Derek, for photons, you can use Maxwell's theory and the classical theory of diffraction and interference. Essentially, whenever the classical theory predicts interference fringes, you will see that photons will arrange accordingly on the screen.
However, I am aware of nice double-slit experiments with electrons and not with photons using the electron microscope. To the best of my knowledge, Merli, Missiroli and Pozzi were the first to observe the effect back in 1974-1976. There is a web site devoted to their experiment: http://l-esperimento-piu-bello-della-fisica.bo.imm.cnr.it/english/index.html
Later, this experiment was repeated at Hitachi and, apparently, the Japanese group did not know of the Italian result: http://www.hitachi.com/rd/portal/research/em/doubleslit.html
I hope this answer helps.
Enrico
So why has no-one done the experiment with a very low hf? Are there experimental limitations on single photon sources?
Sources might not be a problem. Decreasing the power of an antenna could work.
One limitation might be the availability of good single-photon detectors in the far-infrared and radio frequency range.
http://www.nature.com/nature/journal/v403/n6768/abs/403405a0.html
http://arxiv.org/ftp/arxiv/papers/1209/1209.5774.pdf
This is a very interesting problem and I would appreciate an answer from someone who is working on these devices experimentally.
Interferences between C60 fullerene molecules have been observed. What is the Compton wavelength?
Dear Claude,
When mass goes up the wavelength gets shorter so electrons and fulleranes are out of theme. The question was about low energy, long waves, therefore pure classical limit. This is a very interesting question. When the photon stops being a real quantum object? My intuition is that the size of wavelength does not matter (so it can be a kilometer) but its identity, i.e. how much stuff changes on this one kilometer. Because the speed is the same and large so if you start changing the media to differentiate different portions of a quanta you should see decoupling and loss of signal. That would be a cool experiment.
Derek, thanks for a cool question.
As mentioned above, people have done this with electrons, but in 1999 people showed that buckyballs also exhibit the same expected wave interference. So it would appear that even collections of many fundamental particles still act as a single object and all the wave interference properties appear to be intact.
@Peter. That isn't the question. As Boguslaw correctly points out, the question is about *long* wavelengths.
Where are the experiments at long wavelengths, and if there aren't any what has been the theoretical or experimental limitation?
A lot of good answers here, but I think that the key limitation to the question is that detecting single photons becomes increasingly difficult as the photon energy decreases. It is possible to detect single microwave photons in circuit QED systems, but I am not aware of any work being done to in-couple the free-space photons into such a system - which would be very hard IMO. As mentioned several times above, however, the interference effects for long-wavelength photons would exist if the classical interference is seen, so the largest systems would presumably be the very long baseline interferometers used in radio wave detection. But of course, if you are trying to simultaneously prove the photonic effect, then the single photon energy would be too hard to detect.
I would guess (although I haven't checked) that the lowest energy photons would have been seen with superconducting transition edge detectors. These can apparently work at least at the THz regime, although I don't know if photon statistics have been observed there or not. Assuming that the detectors work, then just as @Enrico Sales mentions, there should be no problem in getting the antennas to low enough power. Keep in mind, however, that a standard antenna will not give single photon output statistics.
In addition to @Enrico's links, I found this rather good reference on detectors:
Susumu Komiyama, Single-Photon Detectors in the Terahertz Range, IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 17, NO. 1, Page 54, JANUARY/FEBRUARY 2011
It seems harder to find publications on true THz single photon sources, although I'd guess you could probably do it with quantum dot/SET type structures.
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