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Experimental distinction between states with one and two photons

  1. Feb 4, 2008 #1
    Hi All,

    Does anybody know if there is an experimental setup which is able to distinguish between a state of light with one photon and state with n = 2 ?

    This is about the bosonic behavior of light, according to which two photons may be in the same physical state - and in stimulated emission is what seems to happen.

    Thank you in advance,

  2. jcsd
  3. Feb 5, 2008 #2


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    In all generality, it is difficult. But coincidence counting comes to mind of course. Although one has to be careful with the statistical analysis of this kind of things, and it depends of course on which kind of 2-photon state we have.
  4. Feb 6, 2008 #3
    The two photon state I have in mind is (apart from global and local phase) two photons in the same channel (kind of wave train that is generated by one stimulated emission)

    Possibly we could discuss in this same post how this bosonic feature does appear. In stimulated emission, does the second photon occupy the same sate of the "stimulator"?

    I know that the more stimulated dacays happen the longer is the coherence length of the output radiation, which suggests that upon stimulated emission, the second photon is generated in sequence, coming right behind the stimulator, making the package longer.

    Should I remember that the post is mainly about detection of such two photon states of light.

    I have this doubt since long.

    Best wishes

  5. Feb 6, 2008 #4
    Logically no two photon correlation test can be done on a system generating one photon. Thus the test to be comparable would require testing two sets of single photons that as alike as possible. With one set generating at its source two photons, of some known multi photon state shared between them, but with the second photon going completely unused in the testing.
    Every definition I’ve seen requires the two photons both be used to see the n=2 state.

    The only experiment I know of that requires seeing the n=2 state without using correlations, except maybe in setting up the experiment, is “Backward Causality” by John Cramer at U of Washington. Progress on that test is slow and few think it will work, even Cramer says the odds of success are small. See thread “Cramer's Backward Causality Experiment”.
  6. Feb 6, 2008 #5


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    So all the HBT-measurements of photon antibunching in the emission of single photon sources are just nonsense from your point of view?

    Well, they usually have the same energy, phase and go in the same direction, if that is what you mean.

    Could you tell us, what exactly your goal is?
    Do you really have Fock states with n=1 and n=2 or do you just want to characterize some coherent/thermal/other typical light source, where stimulated emission occurs?

    If you just want to monitor the process of stimulated emission from a single emitter, you do not necessarily need to classify the field in the sense those guys doing quantum optics would do. In this case a simple TRDT measurement (time resolved differential transmission) might be enough.

    If you want to have a look at the emission from an ensemble of emitters, the case would be of course different. Second order intensity correlation measurements are regularly used to classify such emission.
  7. Feb 6, 2008 #6
    What is your referance or example on your point.
  8. Feb 7, 2008 #7


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    Maybe I was a bit unclear.

    I was just wondering, whether you think of coincidence count measurements of single photon source emission like http://www.iop.org/EJ/article/1367-2630/9/12/434/njp7_12_434.html" [Broken] as not being sensible or whether you do not consider single photon sources as systems, which generate just 1 photon.
    Last edited by a moderator: May 3, 2017
  9. Feb 7, 2008 #8
    Hi Cthugha,

    Let me put here the elements of knowledge I have and what is the distinction I would like to make.

    Suppose one photon state enter a gain medium and stimulates only one emission. After thismission, the state of this channel will be n = 2 (Hip: T = 0).
    Now the first doubt arises:
    We know that the same direction, phase and spectrum is shared, but what about

    If this wave train enters a beam splitter, could we have both detectors (x and y) click ?

    Will they click at the same time?

    I am talking about stimulated emission for it is possibly one way to build a two photon state. Down conversion in the main channel is also a possibility.

    I hope I have offered some useful considerations to this debate.

    Best wishes

  10. Feb 7, 2008 #9


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    Well, let's start with time. Last week I saw a presentation on pump probe experiments on single quantum dots. One example, which was given was, that stimulated emission could be monitored and the two photons arrived simultaneously. The temporal resolution of the setup used was in the femtosecond regime, which is better than most detectors you could use will have. So they will click at the same time, if the photons get there.

    What happens when the photons enter a beam splitter is a bit more complicated. If you assume a symmetric bs with two input ports and two output ports, the expectation value of a correlation count (both detectors click) depends on the states of the photon field at the input ports.
    If there are one photon Fock states at each of the input ports, there will not be any correlation counts due to interference. If there is a two photon state at one input and just the vacuum field at the other, there will be a correlation count in 1/8 of the measurements, if I remember correctly. To make sure I would have to look it up in the famous book of Mandel and Wolf (optical coherence and quantum optics), which gives a good QM treatment of beam splitters and photon correlation. I am sorry, that I do not have it at hand right now, but I will look it up.
  11. Feb 7, 2008 #10
    Those are not examples of " two photon correlation tests ".
    They are making coincidence counts off a single photon against other time phase shifted single photons.
    That is not the same as measuring the "two photon" state in an individual photon it might have when generated as one of a pair of photons.
    As far as I know that two photon state aka “entanglement” can only be tested for by using the matching correlated twin, and even then requires testing a reasonable sized sample of several such twin generated correlated pairs to confirm the entanglement.

    The Cramer Experiment I referred to depends an being able to gain information from the two photon state in a group of individual photons without using (or at least before using) any correlation measurements against the other half of the two photon pairs. His objective is to demonstrate the possibility of “Backwards Causality” and as I said most, myself included, have no doubt he will receive a null result.
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  12. Feb 7, 2008 #11


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    Well, doing coincidence counting with time shifted photons is a very time saving way to normalize the second order intensity correlation function, but it is not necessary. It would be fully sufficient to test the equal time intensity correlation of an ensemble of emission cycles, which is the correlation of the photon number of the fields at two detectors. I can't see, why these are not two photon correlation tests, especially as the second order intensity correlation function in this case clearly distinguishes between n=1 and n=2 Fock states.

    Of course thereby I assume that the OP can create these states in a reproducible manner. He has to be able to prepare the same state repeatedly and test it. This method as used today will not work if he prepares the photon field in a n=1 state part of the time and a n=2 state the rest of the time and wants to know, which occurs when. However QND measurements should in principle be able to repeat the measurement on a given photon state, so in principle it should be possible to find out, whether you have a state with n=1 or a state with n=2 on a single emitted photon/photon pair. But that is just a thought experiment.
    Last edited: Feb 8, 2008
  13. Feb 8, 2008 #12
    Just to be clear the testing, even in a thought experiment, on single emitted photons vs. single emitted photon pairs must be done only on individual photons.
    That is when checking for that n=2 state there can be no use of any information from the potential paired second photon that might exist if it is part of a pair. Under those conditions I don't see any principle to apply, even in a thought experiment, that can allow measurement to separate individual photons into two separate groups of n=1 & n=2.
  14. Feb 8, 2008 #13


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    No it isn't. A pair of entangled photons can also be tested by observing that they can beat the diffration limit if they were single photons. And in this case, they don't just test each photon separately.

    P. Walther et al., Nature 429, 158 (2004).
    M.W. Mitchel et al., Nature 429, 161 (2004).

    Last edited: Feb 8, 2008
  15. Feb 8, 2008 #14


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    Well, I agree to the part, that you cannot find out, whether a single photon is indeed a single photon or just one half of a photon pair without testing for the second photon, but I do not understand why you insist on just testing individual photons in the case the OP mentioned.

    The absence of any two photon detection events after repeatedly doing coincidence counting after preparing the same state or after doing several QND measurements on one prepared state shows, that the probability for having a n=1 state is very high. This probability can be made arbitrarily large by repeating (at least in thought experiments). The occurence of any two photon coincidence counts will show, that there is a n=2 state.
    Last edited: Feb 8, 2008
  16. Feb 8, 2008 #15
    These appear to me to be testing for single pairs of entangled photons to eliminate any single non entangled photons. Meaning they are allowing for both individuals of each pair into the experiment and not testing just one of those individuals.

    From one of them:

    “… by using two-photon interference to suppress unwanted single-photon contributions”

    Let me know if you think I miss read them.

    However, I also see no effort to be sure single photons are created using similar near field vs. far field source affects (also known as ‘walk off’) from their source as are expected from the source used for the entangled photon pairs.
    This simple and basic effect is being accounted for by John Cramer in his work.

    Ok I see your point,
    I assumed the OP was speaking of entangled photons separated into two separate beams and looking at only one of the beams to test for n=2.
    Yes I agree when the pairs are contained in a single beam going with both individuals of the pair into the test system distinguishing those pairs from non-entangled individuals (including entangled individuals where for some reason the entangled partner failed to follow along for some reason) should be trivial.

    Separating out those ‘unwanted single-photon contributions’ in that manner is the point of the Walther test.
  17. Feb 8, 2008 #16


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    But the fact remains that you do not get to beat the diffraction limit with single photons. Only a "macro particle" consisting of an "object" tied together having double the energy (and thus, half of the wavelength) of a single photon would produce that same diffraction effect. You send 2 single photons through the setup, you do not get the same thing.

  18. Feb 9, 2008 #17
    I already agreed with that at the end of the prior post.
  19. Feb 9, 2008 #18
    both photons are in the same channel, and as close as possible (exagerated bosonic behavior).

    The question: how to experimentally verify that the wave train corresponds to two photons?
  20. Feb 10, 2008 #19
    I'm not sure even in theory if the case in question gives rise to a "pure" state of n=2. The e-m field states you get from a laser are analogous to the coherent states of a harmonic oscillator, which are different from the pure number states.

    I wonder if it is helpful to mention that the tendency of an oscillator to radiate more strongly into an existing beam is a feature of classical antenna theory.

  21. Feb 10, 2008 #20
    Ok, let's examine further this.

    Weisskopf-Wigner theory for spontaneous emission seems not to be useful in the context of stimulated emission.
    If the direction of the first photon is given (if this first photon is one of a pair created in a down conversion process inside a non linear cristal, detection of one is certainty about the existence of the other), and (gedanken) an atom emits according to Einsteins description of stimulated process, then the second photon must be travelling in the same channel, with the same phase and spectral properties of the incidence.
    Given the bosonic nature of photons, one is tempted to imagine that the second photon is invited to occupy the same quantum state of the incident photon. But due to an argument of causality, one may argue that the second photon should present at least half wavelength delay relatively to the first one.

    Corroborating this idea is the fact that stimulated emission works increasing the coherence length of the radiation.

    It seems unnatural to conceive an stimulated photon appearing in the first one's channel only long after the passing of the first. Note however that this situation would give rise to a possibility of photo-detection presenting double click and evidencing the two photon structure.

    best wishes

    Last edited: Feb 10, 2008
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