Built on Facts

Grad school and a major (good) event in my personal life have been gobbling huge swaths of time, hence the comparative silence around here. I’m afraid we may be down to a few times a week for the next few months. I hope y’all’ll bear with me. (“Y’all’ll” is of course the standard contraction for “you all will”, is it not?)

Still, there’s always time for some physics now and then. Say you’re presented with a box with two holes in the side. From one opening, a laser beam – say, HeNe red – from a laser in the box emerges. From the other, the light from a red hot object in the box emerges. But there’s a filter in front of the hot object, so it only lets red light at the HeNe wavelength emerge from the hot object.

Assuming you don’t know which light comes from which opening, is there any way to distinguish the two? Just to make our life a little harder, let’s say the thermal light is appropriately focused and collimated so that the actual beam profile is indistinguishable from the profile of the laser beam. In other words, what we’re asking is if there’s some difference between laser light and ordinary light of the same frequency.

We might be tempted to see which light source is coherent, but classically speaking monochromatic light is also coherent. If both the laser and the thermal light span the same narrow frequency range, we’re probably stuck here. Coherence is, of course, the property a light wave has when it maintains a regular constant phase. Light from a thermal source like a light bulb hasn’t got it unless it’s filtered:

The image is from a great site at Ryerson University; I’m pretty sure using it here is educational fair use, but to be safe I’m thumbnailing it with a link to the great full image and explanation at their site.

Anyway, checking for classical coherence is out. Can we distinguish the beams by other methods? We can. We can stick a photon counter in front of each beam as look at the rate at which they hit the detector. For the coherent laser source, the photons are emitted randomly in a way that obeys Poisson statistics – these are the statistics followed by events which are unrelated to one another. The events consisting of a car passing a particular interstate mile marker on an interstate with very light traffic is pretty much Poissonian, for instance. But the light from the thermal source exhibits different statistics – in particular, the photons tend to come in clusters. To demonstrate this mathematically is much more difficult than is realistic here, as it requires some rather serious quantum mechanics. The American physicist Roy Glauber got a Nobel Prize for doing it, after all.

If you were to measure the photons with your detector, you could see which beam exhibited the most photon bunching and distinguish between the light in that way. This is more dramatic than it sounds, because this effect is entirely non-classical. Classical or semi-classical theories treating light only as a wave would leave you stuck.

Comments

#1 John
February 19, 2010

“Y’all’ll” works great everywhere except in Pittsburgh, where the accepted contraction is “Yinz’ll.”
#2 Jr
February 19, 2010

Congratulations on your major personal event! (I am guessing marriage, by the way.)
#3 Uncle Al
February 19, 2010

Hmmm… feedback. Reflect the beam back to its source. The thermal source won’t care. The lasing medium can care re mode locking and such.
#4 Anonymous
February 19, 2010

I believe you may be obfuscating in your post. I don’t think physically one can really distinguish coherence (which adopts a wave point of view) from photon statistics (which adopts a particle point of view). I think mathematically both points of view must come down to the same thing. Random photon statistics IMPLY wave decoherence.

To measure coherence, sample the wave over some suitably long interval of time and then Fourier transform it. Surely the peak widths can then be related to the photon statistics. (Perhaps there’s no UNIQUE relation between the two, but I suspect they’re connected.)

I’m open to correction if I’m way off base. But surely coherence IS the answer from a wave point of view. Carl
#5 Anonymous Coward
February 19, 2010

I apologize for the overzealous nit-picking, but the differences between “coherent states of light” (the thing that’s produced by a laser or a microwave generator) and “chaotic” or “thermal” states of light (the thing that’s produced by a blackbody source) can be described perfectly well by classical E&M without resorting to photons or photon counting.

You can describe first-order correlations (what you call classical coherence) and second-order correlations (what you call photon bunching) with classical electrodynamics for both a coherent state and a thermal state. The first is described by temporal correlations of the electric field, the second is described by temporal correlations of the intensity. See Chapter 3 of Loudon’s “The quantum theory of light” if you want more.

That being said, photons are a convenient way to look at this (now that everyone and their brother owns a single-photon counting device). And photons and quantum mechanics ARE absolutely necessary for describing the coherence properties of certain states of light that CANNOT be described by classical E&M in any limit (say, a Fock state, or maybe a state with anti-correlated photons?). But to get the correlation properties of the “coherent state” and the “thermal state” right, you don’t actually need photons.
#6 Anonymous Coward
February 19, 2010

I just want to amend my last comment to make it clear I’m not coming down on most of what you wrote: I liked your post (except maybe for some weird terminology).

The only part I object to the final two sentences.
#7 Carl Brannen
February 19, 2010

Congratulations! Hopefully the personal news has something to with assuring me that there will be tax payer available to pay into my social security when I retire about 25 years from now.
#8 ColonelFazackerly
February 20, 2010

Would it not be incredibly hard to get the same intensity of light from the hot source? Once it is collimated and filtered, there will not be many photons left.
#9 wichitarick
February 20, 2010

Hello sir
We uze yewl as our standard speak round here.

If I understand at least part of your writing correctly I believe I own a meter that will distinguish the type of light almost every time.
Even a short term exposure to a laser light will put my by brain into a tonic clonic (gran mal) seizure .
My brain changed recently and every type of exposure to these sources has had an effect on me.
Although a strobe effect does not seem to have any effect on me.
Forgive me if I am off base here but at least I am trying to comprehend the information and maybe a solution and that is what education is about. Rick
#10 Robert P.
February 22, 2010

Matt, you really need to correct this. As “anonymous coward” pointed out on Feb. 19, Comment 6, the statistics associated with “photon bunching” are entirely compatible with a classical description of the electromagnetic field. In fact, its experimental consequences (intensity correlations, as exemplified in the Hanbury-Brown-Twiss effect) were originally derived from purely classical electrodynamics – and the initial response of many experts in QED was that their analysis had to be wrong. Glauber’s reformulation of quantum optics in terms of coherent states cleared things up, by showing that the classical treatment – which predicts the HBT intensity correlations – was also correct in quantum mechanics. Photon “bunching” is entirely compatible with classical electrodynamics. It’s photon _antibunching_ that requires a quantum treatment of the electromagnetic field.