How close can 2 coherent photons be?

[bwana]

By coherent photons, I mean ones that are in phase (like what comes out of a laser). I would guess that they can be no closer than the size of the atom that emitted them. If adjacent atoms simultaneously emitted photons, that would give the minimum separation. For the photons to be any closer, the atoms would have to be staggered. But then they would be offset in the direction of light travel and result in phase differences.

Is there a way to measure this? It would require sensors more closely packed than the wavelength. I was reading that only recently have metamaterials been developed where patterns can be inscribed in metal smaller than a wavelength.

 

[pallidin]

Well, I do not have an answer, but I understand your question and consider it a good one for general purposes.

 

[Andy Resnick]

By coherent photons, I mean ones that are in phase (like what comes out of a laser). I would guess that they can be no closer than the size of the atom that emitted them. If adjacent atoms simultaneously emitted photons, that would give the minimum separation. For the photons to be any closer, the atoms would have to be staggered. But then they would be offset in the direction of light travel and result in phase differences.

Is there a way to measure this? It would require sensors more closely packed than the wavelength. I was reading that only recently have metamaterials been developed where patterns can be inscribed in metal smaller than a wavelength.

Photons don't really have a size. However, it's possible to write down the mutual coherence between two photons that vary slightly in frequency, direction of propagation, or both.

The mutual coherence function $\Gamma$ is a statistical property of the system, but can be written down as something like:

$$\Gamma =\frac{<E(r,t)E^{*}(r+s, t+ \tau)>}{<I(0,0)>}$$.

http://scienceworld.wolfram.com/physics/MutualCoherenceFunction.html

For some situations (two fully coherent sources, two mutually incoherent sources), the MCF is easy to evaluate. In general, the form can be found by the vanCittert-Zernicke theorem.

If two photons differ *slightly* from each other, the MCF is approximately of the form sin(x)/x: a sinc function. So the mutual coherence will decrease as the properties differ, but becoming zero only at specific points in parameter space. The MCF can be measured easily enough (interferometric telescopes require this information) with a Young's interferometer and/or a Michaelson interferometer.

My reference text is Mandel and Wolf's book, but it's in my office. If I think of it, I'll follow-up this post.

 

[bwana]

thank you for your considered replies. however, by size i should have more specifically stated wavelength. For example, the radius of a helium atom is 32 pm (=.032 nm, =.000032 microns) However the wavelength of light generated by Helium Neon Gas Laser is much larger.
Specifically, the transition from upper 3s to 3p and 3s to 3p levels generate the laser of wavelengths 6328*10^-10 m (red color) and 3.39 microns respectively,Transition from 2s to 2p level generate laser beam of wavelength 1.15 microns.

My naive statement then is that the distance between photons (emitted in phase from adjacent helium atoms) should be 64 pm. However, the wavelength of the light emitted is much greater. How far apart are photons REALLY? Can this be measured to a greater precision than the wavelength of the light ?

For example, Could the distance separating photons be measured by looking at the interference caused by shining a second identical laser onto the spot of the first laser? As one laser is slowly moved from left to right, the intensity of the spot where the two beams are coincident should fluctuate as interference changes from constructive to destructive. The distance the laser has to be moved to go from maximum to minimum intensity should be the distance separating the photons.

Perhaps this question has already been asked/answered more intelligently but I cannot find it with commonly available search engines on the net.

 

[Andy Resnick]

My naive statement then is that the distance between photons (emitted in phase from adjacent helium atoms) should be 64 pm. However, the wavelength of the light emitted is much greater. How far apart are photons REALLY? Can this be measured to a greater precision than the wavelength of the light ?

I don't understand what you are asking. It is true that the wavelength of emitted light is often much larger than the object emitting the light. But 'size' is not a physical property of photons.

For example, Could the distance separating photons be measured by looking at the interference caused by shining a second identical laser onto the spot of the first laser?

Yes- this is called measuring the mutual coherence of the sources. If the lasers are independent, the sources are mutually incoherent. The vanCittert-Zernicke theorem shows that as the light propagates, the mutual coherence changes, giving rise to a spatially correlated field:

http://www.ncra.tifr.res.in/gmrt_hpage/Users/doc/WEBLF/LFRA/node19.html

http://spiedl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PSISDG002525000001000148000001&idtype=cvips&gifs=yes&ref=no

 

[bwana]

thanks again.