Making waves

Well, there's always the wave-particle duality. The electric field between the positively charged nucleus of an atom and the cloud of electrons orbiting it is pretty intense, so you may not need much length to get adequate radiation effectiveness.

Efficiency is always a comparison between what actually happens and some hypothetical ideal, so to talk about radiation efficiency implies a hypothetical ideal radiator which you haven't specified.

You can also get efficient coupling by having a sufficiently high Q resonator, which is more the QM situation.

Cheers

Phil Hobbs

So here's an interesting piece of data. We take a cell filled with Rb atoms. You can change the density by changing the temperature. You then shine resonant light through the cell. (Light resonant with some atomic transition.) And measure how much is absorbed as a function of temperature... density. From this you can get a measure of the cross section of the atoms. (How many atoms do you need such that light has a 50% chance of making it through the cell.) It turns out the cross section is close to (lamda/(2*pi))^2, where lamda is the wavelength of the light. And this is much bigger than the "electronic" size of the atom.

George H.

(It might be (lamda/pi)^2.)

The etendue of a single electromagnetic degree of freedom is lambda**2/2, so since a dipole radiates into 2 pi steradians, I think the cross-section ought to be lambda**2/ 4 pi if the oscillator strength were unity. (I last took QM 30 years ago.) You get another factor of 2 by adding the orthogonal polarization, e.g. in a single-mode optical fibre.

Cheers

Phil Hobbs

Hmm... I was looking at the (very) old data.. and I might have to walk some of what I said back. For the 795 nm transiton in Rb I got x-sec = 1.5E-15 m^2 lamda^2 = 6.4E-13?

I then went looking on the web for help. This seems to agree with what I said... but not what I measured.

George (color me confused) Herold

OK (note mostly to myself) the discrepancy has to do with the ratio of the doppler broadened absorption profile and the life time of the excited state. (Doppler width to the "real" width of the atomic transition.) The real width is ~10 MHz, and the Doppler width is ~1GHz... so something on the order of 100... which is what I see.

Good I'm glad we cleared that up. :^)

George H.

Interesting paper, thanks. There are all sorts of other things that go into a cross-section besides the etendue. Since I mostly think of that stuff from an astronomer's point of view, I use oscillator strengths as my mental model when thinking about atomic transitions, which I don't need to do very often. ;)

Cheers

Phil Hobbs

All that QM stuff is hard to visualize. Consider a microwave-range maser/laser. An centimetres-long photon passes over an excited molecule. The multi-atom molecule is spinning and wiggling and moving and the photon comes in at an unexpected time and direction. The molecule thinks about things as the giant photon oozes past and, at some point, decides to add another gigantic photon to the incoming one at the same wavelength and time and direction. It has to reach out, at superluminal speed, in all directions, to both measure the incoming photon and to donate that second coherent photon.

Einstein's paper on A&B coefficients (spontaneous and stimulated emission/absorption) is a nice read. (Well in english) This was the first copy I could find.

George H.

It's easier if you think of it as resonator with a negative resistance across.

Jeroen --it's waves all the way down-- Belleman

Thanks guys, interesting discussion.

Even the resonator model has problems. If the Q of the resonator is n, then it surely ought to take of order n 'pings' from an incoming source to build up enough amplitude before it can release the energy as another photon.

And I very much distrust QM type 'explanations'. QM is so counter-intuitive that explanations in ordinary language usually fail, only maths works there.

QM makes no sense. And since human brains are quantum computers, we don't make sense either.

Huh.. AFAICT QM is the "law of the land". there are classical approximations, which work sometimes, but not always. You're stuck in this universe, learn QM, or go do something else... (There are lots of QM things I don't really understand... (CPT for one*.) That's a challange for me... not a reason to dismiss QM.

George H.

It is not possible to "explain" QM in terms of your intuition. Why should it be? It has been trained by the behaviour of macroscopic objects.

It is the other way around. QM is what is used to "explain" both macroscopic *and* microscopic behaviour. Which it does extremely well.

There is a great Feynman interview which I have linked to before that does a good job of highlighting this and the limits of "explanation".

(transcription for those who don't like videos)

I'm not dismissing QM. It works. It's just that it doesn't help understanding. It's a bit like epicycles of old. Those worked too, but didn't help understanding. We need another Newton to make sense of it all.

Jeroen Belleman

Grin, We've had this conversation before. For me, I don't see any hope of a new Newton explaining it classically to you. There are lots of things that just have no classical analog. I don't have any problem with using QM to help with understanding. It's weird, but you accept the weirdness and move on. CPT (coherent population trapping) is the weirdest QM thing I've done recently. (I don't have a good theory paper... They are too simplistic, or over the top. This wiki is on the simplistic side,

Anyway the combination of a field driving two transitions, and interference between the transistions, leads to this dark state. Which doesn't interact with the field! Weird, but real!

There are lots of other examples. (The Lamb shift comes immediately to mind.)

George H.

cy.

"Superluminal speed"?

In reality, either the molecule is in a vibrational and rotational state an d orientation which matches it with the passing photon, and you get stimula ted emission, or it isn't and you don't.

There are a lot of molecules in a maser cavity - Avogadro's number is remar

olecule in just the right state isn't all that improbable

Nothing is "measuring" anything. Either the electromagnetic fields line up or they don't. Maxwell's Demon is an imagined character in a thought experi ment.