# What happens if we use two lasers for interference?

1. Jul 6, 2010

### Glen Bartusch

Consider the following:
Two point-sources of lased light, one 600nm and the other 602nm. Each is collimated to form a beam 100 microns in diameter; thus, each forms a well-collimated laser beam.
Aim each beam at each slit in a double-slit setup (each slit is 10 microns wide and 100 microns long, separated by 60 microns), so that one beam is aimed at one slit, and the other beam is aimed at the other slit.
The apparatus is such that one beam must go thru one slit and the other beam must go thru the other slit.

Question: will we see a diffraction pattern characteristic of double-slit diffraction? If not; why not?

2. Jul 6, 2010

### Creator

What is the distance from slit to the screen?

3. Jul 6, 2010

### mgb_phys

Does that matter?

hint - what does interference mean?

4. Jul 6, 2010

### Glen Bartusch

THe answer to my question may seem obvious to you (I'm not sure), but I sincerely don't know what will happen.
I don't know whether a diffraction pattern will or will not be seen. REason being is that two distinct sources of light are being used, however slight the distinction may be.
what's your take? do we see the pattern? why/why not?

5. Jul 6, 2010

### mgb_phys

To get an interference pattern you need the same photon to pass though both slits - two lasers don't give you the same photon

6. Jul 7, 2010

### jVincent

You can calculate this just using regular electromagnetism, and I belive you would see some interference provided that each laser has a long coherence length, and that the phase difference between them is stable for long times.

If the reason for your question is something in the lines of "Do photons from different sources interfere", the answer is yes, provided they are indistinguishable (share all quantum numbers, polarization, emission modes etc.). This has been demonstrated in Hong Ou Mandel measurements performed where single photons from two seperate InAs quantum dots where brought to interfere at a beamsplitter interface.

7. Jul 13, 2010

### Antiphon

Actually you will get a diffraction pattern. You do not need to use the same laser.

If they are the same wavelength the diffraction pattern will be stationary in space. If the frequencies (wavelengths) differ then the diffraction pattern will strobe around.

8. Jul 13, 2010

### Andy Resnick

Unless your sources are mutually coherent, you will not form an interference pattern. If the two sources are mutually coherent (which means they are not independent sources), you will generate an interference pattern.

I don't know of many schemes that bring one laser (or any source) into coherence with another:

Last edited by a moderator: May 4, 2017
9. Jul 13, 2010

### Andy Resnick

It's not just the coherence length, but yes- this is mutual coherence.

10. Jul 13, 2010

### Creator

Actually that is not true. The way the OP described it each laser was sent through its OWN slit and therefore each laser WILL produce its own diffraction pattern ... its called 'single slit interference".
And due to the close proximity of the two slits, the two resultant inteference patterns will overlap.

So more precisely, to answer the OP question as to whether the resultant pattern will be like a two slit interference will require more precise info, one of which will be the distance to the screen....which is one of the parameters that will determine how much the minimums (or maximums) of each laser (of different wavelength) will overlap.

The formula in the small angle approximation for EACH single slit diffraction is:
tan T = y/L......where T is the angle made from a line of length L from the slit to the middle of the maximum ON THE SCREEN (L = distance to the screen) and with a line to the first minimum. "y" is the distance ON the screen from first min. to max.

for example....see here for a good tutorial: http://www.math.ubc.ca/~cass/courses/m309-03a/m309-projects/krzak/index.html
and see the 2nd to last eqn. on the page...which I gave above.

From there; the final equation on the same site shows the wavelength (lambda) dependence and is given by :

y = (L x lambda) / a .....
where 'a' is the slit diameter which was appropriately given by the original poster. L = distance to the screen. lambda = wavelength of laser.

So, the OP gave all the necessary and appropriate information (including the width of the slit) EXCEPT for the distance to the screen L.....which would become necessary to determine the overlap of the mins. and maxes. from EACH of the SINGLE SLIT DIFFRACTION PATTERNS (in order to see if it approximates a double slit pattern) ....which seemed to be his question.

However, Glen, having said all that, since the width of the slit is so large relative to the wavelength (and the wavelengths of each are so close) that the diffraction angle to the first minimum will be very large (large envelope) and there will probably be little 'out of phase' overlap ...making it distinct from a typical two-slit pattern.

Creator

Last edited: Jul 14, 2010
11. Jul 14, 2010

### jostpuur

Here's my thread about roughly the same problem: photons, particles and wavepackets (The opening post is in fact the first post I ever wrote here )

12. Jul 14, 2010

### unusualname

It should be noted that Dirac's (famous) quote about a photon interfering only with itself turned out to be wrong, and was demonstrated as far back as 1963:

G. Magyar and L. Mandel, “Interference fringes produced by superposition of two independent maser light beams,” Nature (London) 198 (1963), 255

Here's a blog with a discussion:

http://skullsinthestars.com/2008/09/12/interference-between-different-photons-never-occurs-not-1963/

as mentioned above, you need to maintain a constant phase relationship between the two beams, which may be difficult to maintain in practice over long periods.

13. Jul 14, 2010

### jostpuur

IMO it's not wrong. It's only slightly hypothetical.

From the blog:

No, the claim is ambiguous! It's tricky situation:

It is true that interference between different photons does not exist, but...

... and then individual photons have their own wave functions spread to various places so that interference can occur.

14. Jul 14, 2010

### unusualname

I think people are still arguing over it, but I didn't think modern QFT had a problem with the EM field from distinct sources interacting to produce two-particle interference (in the case of bosons)

Here's a paper from 2006 with some discussion and lots of references:

Two-photon interference with two independent pseudo-thermal sources
http://arxiv.org/abs/quant-ph/0610101

15. Jul 14, 2010

### |squeezed>

Interference of two different lasers may occur. This has been verified experimentally in various settings. However this does not mean that all "kinds"* of 'em can interfere.

* states

For a detailed explanation take a look at p.37-38 of "Quantum optics" by D. F. Walls, Gerard J. Milburn.

Dirac's book is great but it is very concise and sometimes misleading.

16. Jul 14, 2010

### Cthugha

Well, it is not necessarily wrong, but can be misleading. Sometimes, when I give talks at conferences with a broader audience I motivate my experimental approach using a slide with the following two quotes from great physicists:

(P. A. M. Dirac, The Principles of Quantum Mechanics.)

(Roy J. Glauber, Quantum Optics and Heavy Ion Physics)

Glauber then goes on to argue that it is never photons interfering, but probability amplitudes of processes involving photons. However, if one wants to attribute interference to the photons themselves, Dirac's quote is in some way right. Interference between several photons can occur, but if it does, the photons are indistinguishable under the given conditions. Therefore they do not qualify as DIFFERENT photons.

Funny that they got this published calling it "independent" pseudo-thermal sources. The rotating ground-glass disks are feeded by the same laser.

Another very impressive experiment concerning two-photon interference is given in
"Interference of dissimilar photon sources" (A. J. Bennett et al, Nature Physics 5, 715 - 717 (2009))

This paper is also available at Arxiv:
http://arxiv.org/pdf/1006.0820v1"

Last edited by a moderator: Apr 25, 2017
17. Jul 14, 2010

### jostpuur

This appears to be a very interesting topic. I'm getting increasingly bitter about how this was omitted in my education. I never heard anything about this in the courses, and didn't encounter it in the books I read. When I came to PF to ask about this problem in 2007, I was under a belief that I was nearly the only person in the world who is interested in this topic. Now it seems this is a hot topic like wave function collapse or relativistic mass. That means, a kind of a topic on which lot of opinions exist.

18. Jul 15, 2010

### Cthugha

Optical coherence theory was developed rather late. Glauber's famous papers came in the sixties. The first experiment in this direction was the HBT experiment which came in the fifities - and sparked some controversy. Usually quantum optical coherence theory will just make it to specialized courses at universities having at least some focus on optics. Otherwise it is indeed omitted quite often.

However, I think the recent "birthdays" in this field added to its attractivity - in 2000 we had 100 years of light quanta and the Nobel prize going to Glauber (his Nobel speech of the same name is a great introduction into the topic) and in this year we have the 60th birthday of the laser.

19. Jul 15, 2010

### unusualname

Yes, it seems that after all the success of QED and subsequent field theories the question about what is actually doing the interfering in the case of photons has been neglected over the years.

You pointed out the rather vague comment in the last paragraph of that blog I linked to about a subsequent experiment showing that interference between the two maser sources was still present even when there was high probability of only one photon being emitted between detections.

What is not in dispute is that there can be no way of knowing which of the two sources any of these single photons came from if the interference is to be observed.

If we follow Cthugha's suggestion and interpret this phenomenon as an interference of probability amplitudes (contributed from each source) then it makes sense - whether there is one photon or many they will be distributed according to the probability amplitudes.

However, note that this definitely can't be interpreted as a photon interfering with only itself (since we have two probability amplitudes interfering).

But then what causes the probability amplitudes?

And here's where it gets difficult, the notion of a wavefunction of a photon is not even well-defined, it hasn't been needed since QED has been more than sufficient for analysing the quantum properties of photons.

But if you are happy with a non-local wavefunction associated with a photon, then the analysis in terms of probability amplitudes interfering is almost trivial.

I hesitate because the plausible modern construction of a photon wavefunction interprets it as the wave described by the Maxwell field equations (eg see http://arxiv.org/abs/quant-ph/0604169), but that wave propagates at velocity c, and we need something faster or non-local.

Any suggestions?

20. Jul 15, 2010

### Cthugha

I am not be too sure about that. If you consider the basic double slit experiment with photons (or electrons - it does not matter much) shot one at a time and aim at an explanation in terms of probability amplitudes, you will also get two probability amplitudes interfering: One for taking the left slit, one for taking the right slit. Nevertheless most people would agree that there is only one photon involved despite the presence of two probability amplitudes.

Btw. I suppose this is why Glauber wanted to move away from attributing interference to the photons themselves. If you just consider the initial and final states and have all possibilities to get from one to the other interfere, you solve several ambiguities and misleading interpretations which could occur.

21. Jul 15, 2010

### Glen Bartusch

What's a probability amplitude? Is it an observable? Is it part of the E/M spectrum at all? How are these probability amplitudes related to momentum, wavelength, energy? Since electrons must possess them as well as photons, they must not necessarily travel at c, correct?

22. Jul 15, 2010

### Cthugha

Just another name for a well known thing. In general a probability amplitude is just a complex number. If you take its absolute square, you get a probability density. If you are familiar with basic quantum mechanics this is pretty much the meaning of the wave function.
$$\left|\psi (r) \right|^2$$ gives the probability density to find some particle at position r.
$$\psi (r)$$ is then considered to be the wavefunction of this particle and is technically speaking a probability amplitude.

Considering light, this is easy to formulate for classical light. Here the probability amplitude is given by the em-field. In nonclassical optics, this is not that trivial as the wave function of a single photon is not too well defined. Equivalently you could say that a correct formulation of the em-field of single photons or other nonclassical states of light is nontrivial.

Essentially (in my opinion) many concepts in optics are easier to grasp when you keep in mind that the em-field and the photon are not the same thing and attribute interference to the fields and not to the photons.

23. Jul 15, 2010

### unusualname

In the case of electrons moving non-relativistically the probabilty amplitudes for location are given by the Schrodinger eqn.

For photons there isn't a such a simple interpretation in terms of location, usually you talk about energy density or photon number probabilities, for a comprehensive review (52 pages) see:

Photon wave function
Iwo Bialynicki-Birula
Progress in Optics, Vol. 36, E. Wolf, Editor, Elsevier, Amsterdam, 1996
http://arxiv.org/abs/quant-ph/0508202

24. Jul 15, 2010

### Galap

I don't know about the previously mentioned one, but here's an experiment with two lasers where you DEFINATELY should get interference:

Two lasers, close in wavelength like stated before. Instead of slits, combine the beams. Along the beam itself you should get alternating regions of high and low intensity due to constructive and destructive interference of the two waves of slightly differing frequency.

Now here it gets interesting: Make it so each laser only fires one photon at a time. Have two detectors, one which is frequency sensitive and another which is frequency blind. The frequency blind detector should detect the photons with higher or lower intenisty at distances from the combined beam source according to the constructive and destructive sine wave envolope. The frequency sensitive one, which can measure which laser the photon came from, should detect the same intensity throughout.

Am I right?

25. Jul 16, 2010

### Edgardo

http://www.its.caltech.edu/~qoptics/Presentations/MandelOSA-web.pdf [Broken]
See slide 7, "Early experiments on interference between indpendent lasers",
slide 9, "Interference between independent lasers at low light levels - Do photons interfere with each other or only themselves"

2) A discussion on physicsforums
"Do 2 laser beams interfere?"

3) Google books search: Interference between Independent lasers: Magyar-Mandel and Pfleegor-Mandel Experiments

4) "Interference between different photons from two incoherent sources"
Takasi Endo and Kouichi Toyoshima
Optics Communications
Volume 90, Issues 4-6, 15 June 1992, Pages 197-200
Abstract
Intensity interference fringes are observed by using two incoherent light-emitting diodes. It is verified that even an incoherent light interferes with another one.

5) "Quantum interference between two single photons emitted by independently trapped atoms"
J. Beugnon1, M. P. A. Jones1, J. Dingjan1, B. Darquié1, G. Messin1, A. Browaeys1 and P. Grangier1
Nature 440, 779-782 (6 April 2006)
Abstract
When two indistinguishable single photons are fed into the two input ports of a beam splitter, the photons will coalesce and leave together from the same output port. This is a quantum interference effect, which occurs because two possible paths—in which the photons leave by different output ports—interfere destructively. This effect was first observed in parametric downconversion1...

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