Sometimes, researchers report results that are absolutely astounding and I don't report them here because I can't find a way to convey the significance of what they have achieved. On other occasions, the press hypes the research to such an extent that I feel the only objective thing to do is to balance that with a view of why the research isn't such a huge step or is, in fact, complete rubbish. Now I find myself in unfamiliar territory, where the reported research is very interesting but there is a fatal flaw in their description of it and I am not sure if that invalidates all of the research, or just a part of their conclusions, or is completely irrelevant.
The researchers claim to have demonstrated some noncommuting operations on light that had been predicted, but not previously observed. A noncommuting set of operations is one that gives different results depending on the order in which they are performed. A perfect example is rotation: hold your left hand in front of you with the palm away from you, fingers up, and the thumb as horizontal as you can. Now rotate about the thumb 90 degrees forward (your palm should now be facing the floor). Now rotate about the fingers 90 degrees anticlockwise (your thumb should be pointing upwards). Now re-do the rotations in the opposite order. The second rotation was a rotation about the axis pointing outwards from your body, so that one should leave you with the palm still facing forwards and the thumb point upwards. The first rotation was about the axis running parallel to the front of the body and the correct rotation should leave you with your thumb pointing away from your body and your wrist feeling like it is dislocated. The differences between the results are an indication that the actions are noncommuting.
A particularly weird example of noncommuting behavior is the relationship between the creation and annihilation operators of light. Basically, destroying a photon and then creating a photon does not give the same result as creating a photon and then destroying a photon. A team of researchers, mostly based in Florence, have elegantly demonstrated this. Controlled photon subtraction is achieved by a very low reflecting mirror and a detector in the path of the reflected photon. Statistically speaking, when the detector goes bing, a single photon has been removed from the light.
A single photon can be added back using a particular form of amplifier. A high energy photon can be split into two low energy photons. By choosing the high energy photon correctly, the generated photons are exactly the same color as those of the beam we want to add a photon to. Performing the addition in a specific crystal medium allows one photon to be added to the light while the second goes in a different direction and can be detected by a light detector—a bing from this detector means a photon has been added. After that, a second very low reflectance mirror can be used to perform a subtraction, which is detected by a third detector. Finally, the number of photons in the beam is measured.
When the light source is switched on and off rapidly, there are a number of possible results. Sometimes a photon is subtracted and nothing else occurs. Sometimes a photon is added and nothing else occurs. Occasionally a photon is added and then another photon is subtracted. Occasionally a photon is subtracted and then another photon is added. Finally all three operations may occur: a photon is subtracted, a photon is added, and another photon is subtracted. If photon creation and annihilation were commutative, then both subtraction and addition and addition and subtraction should result in the same number of photons. However, the researchers showed that they do not.
A very elegant experiment and case closed, right? Well no, I have a problem. The annihilation and creation operators are only noncommuting when applied to an incoherent light source. Think of it like this: light from a laser has phase coherence—that is, the photons have a strict spatial and temporal relationship to one another (called a mode). To add a photon to this beam, it must be in the same mode. When I subtract a photon, it can only be subtracted from the photons in the mode, because there are no other modes available. Under these circumstances, it doesn't matter which order I do addition and subtraction. However, with an incoherent light source, the photons have no fixed spatial and temporal relationship to each other (e.g., they are spread across many modes), so the adder can place a photon in any mode, provided one other photon is in that mode. In this way, the order of addition and subtraction can produce different results.
So, to do this experiment properly the source of light must be incoherent; instead, the researchers used a pulsed laser. To make the light incoherent, they used ground glass to mess up the laser light. They refer to this as thermal light, but, it ain't thermal light. After light goes through something like ground glass, it is spatially incoherent, but still temporally coherent. We have seen this previously by looking at how laser light can be sent through an opaque substance. Furthermore, the light from the ground glass is then coupled into a single mode optical fiber. This means that the researchers are selecting a single spatial mode from the scattered light—that their light is coherent in every respect.
The only loophole that I can see is that the ground glass rotates so that they obtain a different scattered mode from one laser pulse to the next (the laser pulses are very short, so the glass doesn't rotate during a pulse). They don't tell us how fast their glass sample rotates or how long they average for, which means we are not in a position to say that there are statistical errors in there (e.g., the beat frequency between the rotating ground glass and the pulse repetition frequency).
This is the second time I have seen results like this, and the researcher involved in the first case did not really answer this question, either. However, given that the session chair had just abused his power by giving an impromptu talk of his own to the effect that the results were rubbish (for different reasons), before calling for questions, I can forgive the less than coherent response to the questions that focused on coherence issues. Given this publication, however, it is time for us to see proper data that clearly demonstrates that the light is truly identical to thermal light.
Science, 2007, DOI: 10.1126/science.1148947