h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Why, if you hit an exited atom with a photon of the right frequency, will it emit another photon of the same frequency, phase, polarization, and direction?

* Why does frequency matter? (only certain frequencys will stimulate emission)
* Why isn't the first photon affected? (is it?)
* Are the emitted photons of exactly the same frequency as the first photon befor it hit the atom? (doppler broadening in lasers)

All processes are theoretically reversible as far as I know and so the same mechanism that allows induced absorption is likely to be simply the reverse of stimulated emission I guess.

For each spectroscopic transition there is only *one* frequency that will stimulate emission because the two energy states have a discrete energy gap which equated to the frequency of the photon either inducing absoporption or released by SE.

>>Why isn't the first photon affected?<<

Don't follow the question Can you explain that question a bit more?

If the process truly *is* stimulated emission then yes the emitted photon must by definition be the same freqency as the incident photon.
You mention doppler broadening in lasers - dunno about that sorry.

I do know that you can't have stimulated emission without induced absorption (and usually a bit of spontaneous emission thrown in). In most spectra you see both processes but because there is a population difference you see net absorption because the lower energy state has the higher population and so absoprtion predominates. Only when you can achieve a population inversion does stimulated emission become the dominant process.

Damn, and I was thinking this was about....

Oh. Never mind. I'll get my coat.

B

When I was lectured on this stuff as an undergraduate the guy who did the lectures illustrated stimulated emission (and the others) by use of cartoons of Snoopy in various er... lude acts shall we say

Doppler broadening. Just looked it up.

It's due to thermal motion and depends on temperature. I guess a molecule emitting whilst it travels away from you will emit at a fractionally different wavelength as one travelling towards you because of the doppler effect. This will broaden the spectral line. As temperature increases this motion will increase in velocity and so the broadening will increase.

"Why does frequency matter? (only certain frequencys will stimulate emission)"

Now I'm sure I don't really know enough about this to be answering, so take this with a pinch of sodium choloride, but...

Higher frequency/shorter wavelength light (the two are effectively the same with a wave of constant speed, which is light) has higher energy photons. So what is important is probably that you get exactly the right energy to jump 1 or more shells (possibly it could also eject an electron completely). I guess the electron could jump back down, which should certainly produce a photon of exactly the same energy as the first, but I don't know about the rest.

I *think* this absorbtion and re-emision process is what slows down light in a medium, as the retransmission is not instant, and light certainly actually only propagates at C.

Incidentally, when we shoot particles at each other and excite them or knock bits out, the energy doesn't have to match precisely because the particle can just bounce off. Light can't do this for some reason, probably momentum conservation won't allow it.

>>Higher frequency/shorter wavelength light (the two are effectively the same with a wave of constant speed, which is light) has higher energy photons. So what is important is probably that you get exactly the right energy to jump 1 or more shells (possibly it could also eject an electron completely). I guess the electron could jump back down, which should certainly produce a photon of exactly the same energy as the first, but I don't know about the rest.<<

Exactamundo

>>Incidentally, when we shoot particles at each other and excite them or knock bits out, the energy doesn't have to match precisely because the particle can just bounce off. Light can't do this for some reason, probably momentum conservation won't allow it.<<

Well yes, but then these processes are not the process called stimulated emission. If a particle is excited, it can relax in many ways, vibrational and rotational motion can dissipate the excitation energy and that then ends up with thermal motion - ultimately heat. but these are specifically different processes to stimulated emission which is in essence a resonance effect. If you have an excited population of species, when one relaxes, releasing a photon exactly equal in energy to the energy gap then this stimulated the emission of a second photon which then stimulates others in a cascade.

If the top energy level is more highly populated that the bottom (quite difficult to achieve -but possible in some special systems) then the overall emission is amplified by the first photon to many and one gets Light Amplification by the Stimulated Emission of Radiation (LASER)

"Why isn't the first photon affected? (is it?)"

do you mean the photon that excites S --> S* ? (which then goes on to stimulated emission: S* +hv --> S + 2hv) if so, it is affected, as with all absorption, the intensity of the electromagnetic radiation is lost as the absorbing species gains energy (note it is the intensity that is reduced, the wavelength is not changed, so the same radiation which excites S-->S* can stimulate the emission).

Probably.

Good answer, like that.

I suspect the answer is that intensity is changed when there is a barrage of many photons. But I suspect the quesioner is asking to the specific photon that is absorbed.

I guess the answer is that it's 'being' becomes part of the electron that is excited with all the appropriate changes in quantum number needed to conserve everything.
*how* this happens is way too deep for me

1st off, let's start with the 2 level model of the atom, as described previously on this thread. You've got a "ground" state and an excited state. The excited state is higher in energy.

Now let's add another piece of quantum mechanics. In general, there can be more than one ground state. There can also be more than one excited state *with the same energy*. If this happens, the state is said to be "degenerate" (maybe this is the part B was looking for? ) The number of ground states is known as the "degeneracy" of the ground state. The number of excited states with the same energy is the "degeneracy" of that excited state.


OK, so now that we have the definition of degeneracy, we can explain stimulated emmission. We start with an atom which has 2 levels - neither of which are degenerate. A photon comes in. The photon can also be described as an electromagnetic wave. The electric field of this wave greatly perturbs the structure of the atom. If the frequency (=energy) of the photon/wave matches up with the original energy gap between the levels, then the ground and excited state are now degenerate with each other! Now, if 2 states are degenerate, there is no barrier to switching between them - and if you do some complicated quantum maths, you see that the atom is now oscillating between the 2 degenerate states. Now as the initial photon leaves, then the atom maybe in the original ground state, and a new photon has been created.

The fact that the new photon has the same frequency is a result of the requirement that the above process works extremely well when the frequencies are matched, and very poorly for small differences in the frequencies.

The same polarization is a result of the physical process which causes the electromagnetic wave to perturb the atom, causing the 2 levels to be degenerate. Atoms are (roughly speaking) spherically symmetric, and thus you would expect any perturbation of the atom to occur in the exact same direction as the perturbing field.

Direction is the same because propagation must occur perpendicular to the electric field oscillation (polarization). It could actually be going exactly the opposite direction, I think.

Frequency matters because of the underlying physics which determines how the 2 levels of the atom become degenerate. This depends on the atom/transition heavily, and is the weak point of my whole explanation. I'll try to look something up.

Why the first photon isn't affected - perhaps an analogy. imagine a magnet held in place. You bring a wrench near it, and it is pulled towards the magnet. Well, the magnet (the source of the field) isn't affected by the wrench, even though it is affecting the wrench.

Doppler broadening in lasers - not sure exactly how this works. I would imagine it has to do with the distribution of velocities of the atoms within the laser cavity. A very slight change in the frequency of absorption/emmision occurs because of this. The lasing still works, but instead of being infinitely sharp, it is now slightly broadened.

Interesting, thanks for that Dealer
I like the idea of the two energy levels becoming degenerate

So how does spontaneous emission occur then?

On another thread I was mentioning that I'd heard in a lecture on metrology that the most modern atomic clocks cool their Cesium atom source down to around 0.0001 K and they said that this narrowed the spectral line increasing the precision in time measurement.
From what I read on doppler broadening earlier, I guess this means that they are minimising this effect

Glad you understood that Orcus! I'm really glad that the question was asked, it's really made me dust off my old books and clean the cobwebs out of my head.


A key difference of spontaneous emission is the fact that there are few requirements on the created photon. It can be travelling in any direction with any polarization.

So what we do now is instead of taking the system as being composed of the atom, and that being perturbed by the electromagnetic wave, we describe the system as being the atom + electromagnetic wave.

In the beginning we have just an excited atom - there are no photons present, no electromagnetic waves. At the end we have a ground state atom and a photon/electromagnetic wave. There is only 1 initial state. But because of the degrees of freedom for the photon/electromagnetic wave, there are an *infinite* number of final states. The final state is infinitely degenerate.

Now comes the statistical mechanics/entropy part. It may take some random internal oscillation or event which causes the switch from the initial state (excited atom) to the final state (ground state atom + photon), but once that switch has occured, it is irreversible - effectively because of the large change in entropy associated with the infinite degeneracy of the final state.

You can't put the genie back in the bottle.

ps. I think you're absolutely right about the temperature reducing the doppler broadening of the cesium, and that increasing the precision of the time measurement.

I wonder if they've tried it with Bose-Einstein condensates (which are at billionths of a degree kelvin in temperature). The atoms in those condensates are all in the exact same quantum state, so I would imagine that would give a near infinitely sharp peak in the emmision.

Hmmm, now there be the next level of precision...

To be fair though, I might have overestimated the temperature at which they get the atoms down to. That figure I put in was pulled out of the air, I suspect it was lower.

Back to spontaneous emission. I got what you were saying there and again it rings true. I see no reason in there though why spontaneous emission probablility drops with increasing wavelength.

In NMR there is effectively no spontaneous emission leading to other relaxation modes that are utilised in many ways.

I guess it's all in the maths. I do remember that the rate of spontaneous emission was inversly proportional to wavelength but I can't remember if they told us why...

great points Orcus

OK, digging deeper into spontaneous emission. Remember the basic treatment of the quantum mechanical harmonic oscillator? In all of the states of the harmonic oscillator, the average value of the position is exactly equal to zero. However, the average value of the position squared is *not* zero.

Now, you can apply the exact same mathematics to the electromagnetic field. This is where quantum electrodynamics comes from, and a rigorous treatment of photons. Now, if you have no electromagnetic field (no photons) this is mathematically equivalent to being in the ground state of the harmonic oscillator described above.

Hence on average there is no electric field present, but there are random oscillations present which mean that the average of the *square of the electric field* is non-zero. These fluctuations are called "vacuum fluctuations".

So, according to my text book*, the random event which causes spontaneous emission is a "vacuum fluctuation" in the background electric field. So another name for spontaneous emission would be "stimulated emission induced by the vacuum fluctuations".

This then gives us the dependence on wavelength - same as stimulated emission, and a fairly strict requirement. There is no spontaneous absorption from the vacuum fluctuations because that would violate energy conservation.

Regarding NMR, I don't really know. Are you saying that neither the T1 nor T2 relaxation times are spontaneous?

* the text book is Quantum Mechanics, volume 1, by Cohen-Tannoudji, Diu, Laloe. not recommended for the faint of heart/maths. It's taken me *years* to understand it.

Thanks, that answers my question pretty thoroughly.

To nitpick, are you sure about the fixed magnet being unaffected by the wrench? Equal and opposite forces and all that.

bad analogy...How about the field created by the wrench? The total field changes when you bring the wrench in, but the field from the magnet is unchanged.

that should be "How about the field created by the *magnet*" not *wrench*.