What happens if we use two lasers for interference?

[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?

 

[Creator]

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?

What is the distance from slit to the screen?

 

[mgb_phys]

What is the distance from slit to the screen?

Does that matter?

hint - what does interference mean?

 

[Glen Bartusch]

Does that matter?

hint - what does interference mean?

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?
thanks in advance...

 

[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

 

[jVincent]

You can calculate this just using regular electromagnetism, and I believe 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 separate InAs quantum dots where brought to interfere at a beamsplitter interface.

 

[Antiphon]

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

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.

 

[Andy Resnick]

Consider the following:
Two point-sources of lased light, one 600nm and the other 602nm.

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

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:

http://ieeexplore.ieee.org/Xplore/login.jsp?url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F4378109%2F4378110%2F04378178.pdf%3Farnumber%3D4378178&authDecision=-203

 

[Andy Resnick]

You can calculate this just using regular electromagnetism, and I believe 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.

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

 

[Creator]

To get an interference pattern you need the same photon to pass though both slits -...

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

 

[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 )

Suppose I had created double slit experiment with light successfully. I would then change the set up as follows. I would replace one light source with two, and place a wall between the two slits so that light from one source reaches only the one slit, and from the other source the other slit. Question is then, do I still have interference pattern?

I think I've read about experiments in which two separate light sources have been made to interfere, but they're difficult to do.

But I just happened to hit into this quote else where in these forums

The quote is due to Paul Dirac (The Principles of Quantum Mechanics, 1930):

"Each photon then interferes only with itself. Interference between two different photons never occurs."

But different radio transmitters and lasers do interfere...

If you have two coherent sources of light, and a photon strikes a screen, you really can't tell which source the photon came from. Regardless of whether the sources are just separate slits or completely separate emitters, the two "paths that the one photon may have taken" interfere and Dirac's statement is justified

Hanbury Brown-Twiss (HBT) intensity interferometer. R. Hanbury Brown and R.Q. Twiss, Nature,177, 27 (1956).

There are a few experiments where photons coming from different sources have been shown to interfere.
See e.g,. Kaltenback et al PRL 96, pp 240502 (2006) which also gives are good background to the topics.

The conditions are essentially that the two sources are well synchronized and that the photons are indistinguishable when they arrive at the detector.

They use two sources. The paper is freely available on the arXiv
http://www.arxiv.org/abs/quant-ph/0603048

If this is reality, then I can accept it, but how is this not in contradiction with what Dirac is saying? Different photons don't interfere!

Jostpuur, have you ever heard of indentical particles ? If you could tell "where a photon comes from" this would amount to stamping labels on them (e.g. the labels "A" and "B" or say ... a grin on the face). But, according to quantum mechanics this is not possible.

So when source A and source B both create one photon, the Bose statistics forces these photons to get in superposition, so that each of the photons immediately has amplitude for starting at both sources?

If this is the explanation for the interference of independently emitted photons, that certainly is a convincing proof for the Bose statistics.

My final word on this is, that merely saying "you cannot know where the photon came from" doesn't make the whole point clear, pedagogically. As I said in my original response to the cesiumfrog, there can be several reasons for why we don't know something, and they are not always related to the quantum mechanics itself. I understood originally that we cannot know from which source the photon comes from, but so what, I don't know what you are doing behind your computer either, and that doesn't mean that you are in superposition of doing several things. The symmetry of the wave function, according to the Bose statistics, makes the explanation complete.

 

[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.

 

[jostpuur]

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

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

Here's a blog with a discussion:

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

From the blog:

"each photon then interferes only with itself. Interference between different photons never occurs.”

This statement is bold and unambiguous: in Dirac’s view, a photon only creates interference patterns by virtue of its own wave function, and wave functions of different photons do not interact.

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

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

So when source A and source B both create one photon, the Bose statistics forces these photons to get in superposition, so that each of the photons immediately has amplitude for starting at both sources?

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

 

[unusualname]

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

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

Over the last few decades our understanding of inter-
ference, one of the most important concepts of physics,
has advanced considerably since the days that Dirac
said [34],“Each photon then interferes only with itself.
Interference between two different photons can never oc-
cur.” The statement provoked widespread debate and led
to a surge of experimental tests as well as philosophical
argument. It is now generally agreed that Dirac’s state-
ment should be viewed in its historical content when the
resolution time of photon detectors was still limited

 

[|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.

 

[Cthugha]

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

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:

Every photon then interferes only with itself. Interference between two different
photons never occurs.

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

Now that simple statement, which has been treated as scripture, is absolute nonsense.

(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.

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

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"

 

[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.

 

[Cthugha]

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.

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.

 

[unusualname]

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.

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?

 

[Cthugha]

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

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.

 

[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 possesses them as well as photons, they must not necessarily travel at c, correct?
Just asking...

 

[Cthugha]

What's a probability amplitude?

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.

 

[unusualname]

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 possesses them as well as photons, they must not necessarily travel at c, correct?
Just asking...

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

 

[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?

 

[Edgardo]

More links:

http://www.its.caltech.edu/~qoptics/Presentations/MandelOSA-web.pdf
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"

https://www.physicsforums.com/showthread.php?t=218827
"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...

 

[unusualname]

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?

I would think so. Interference can only be observed between indistinguishable photons, so if you are able to distinguish between them you shouldn't get any interference.

I think the argument for/against Dirac's statement depends on how you interpret indistinguishable photons, and whether you see that as photons interfering with only themselves.