Stimulated emission Vs Absorption and an atom in an excited state?

Kohl

Is it possible to fire a photon at an atom in an excited state, and to have equal chance of the atom absorbing the photon and moving to a higher state of energy AND the atom undergoing stimulated emission and dropping to a lower state of energy?

Could you point me in the direction of research that shows this if it is possible.

ApeXaviour

Fascinating, I'm not a laser guy but I've a bit of experience with absorption. For an atom to absorb again when it's already in an excited state is a good question as binding energies would presumably be different in that state. It would have to be in a doubly excited state which I'd never thought about, but it apparently does exist, 2. The only thing I can think of that's related is two-photon absorption which is a non-linear optical process.

That stimulated emission might have an equal chance would certainly be something difficult to engineer. Not only that there is always a preferred route and there is no reason for it to be 50/50... but they presumably would have very different wavelength requirements to occur... stimulated emission and doubly excited states that is. The doubly excited state I'm guessing requires very energetic (singly ionised?) where as stimulated emission would (I assume, again not a laser guy) require the incident photon to be somewhat resonant with the energy of the excited state minus the ground state.

Professor_Fink

Kohl wrote: »

Is it possible to fire a photon at an atom in an excited state, and to have equal chance of the atom absorbing the photon and moving to a higher state of energy AND the atom undergoing stimulated emission and dropping to a lower state of energy?

Could you point me in the direction of research that shows this if it is possible.

Yes, it's entirely possible, and in fact can pretty much be read straight off the Jaynes-Cummings Hamiltonian (see the Wikipedia entry for details). You just need a chain of two transitions A->B->C, such that the corresponding energy levels satisfy $E_A - E_B = E_B - E_C$. In this case, if the state atom is prepared in the state B, it will have an equal chance of absorbing or emiting.

This is a somewhat artificial setup, however, since B is a rather weird state for the system to be in naturally (since it is neither a thermal state, nor a maxima or minima of energy (by the assumptions made about E_A and E_C relative to E_B). Thus you would need to deliberately prepare the system in that state, but it can certainly be done.

Kohl

Professor_Fink wrote: »

Yes, it's entirely possible, and in fact can pretty much be read straight off the Jaynes-Cummings Hamiltonian (see the Wikipedia entry for details). You just need a chain of two transitions A->B->C, such that the corresponding energy levels satisfy $E_A - E_B = E_B - E_C$. In this case, if the state atom is prepared in the state B, it will have an equal chance of absorbing or emiting.

This is a somewhat artificial setup, however, since B is a rather weird state for the system to be in naturally (since it is neither a thermal state, nor a maxima or minima of energy (by the assumptions made about E_A and E_C relative to E_B). Thus you would need to deliberately prepare the system in that state, but it can certainly be done.

Thank you both for your replies.

Ok, so let's say I prepare the system in this state. Is it possible to measure the atom after the absorption or stimulated emission occurs. For instance, I want to be able to detect the atom after the process occurs and tell whether it was absorption or stimulated emission that occured. Is there any experimental technique that would permit me to do that?

Thanks again.

ApeXaviour

Kohl wrote: »

Ok, so let's say I prepare the system in this state. Is it possible to measure the atom after the absorption or stimulated emission occurs.

Experimentally one would almost never measure a single atom, rather a bulk sample.

For instance, I want to be able to detect the atom after the process occurs and tell whether it was absorption or stimulated emission that occured.

You need something to detect. The difference between the two processes is going to be photons released in stimulated emission, or whatever the process of decay is from your doubly excited state. For the latter it can be by release of a photo-electron, an augier electron, phonon, photon (i.e. spontaneous emission / fluorescence) etc. it really depends at what energy you're exciting to, whether it's the IR/UV/x-ray etc regime.

Also your atoms don't remain in the excited state for very long. For visible fluorescence the lifetime is of the order of nanosecods. For x-rays (so core hole decay) it's of the order of femtoseconds. Once it's relaxed back to the ground state there's no way of telling what went on.

Is there any experimental technique that would permit me to do that?

Let's say for a moment that your doubly excited state decays spontaneously by emission of a more energetic photon, there are a number of ways you could measure this. A spectrometer for example could easily discern the difference between a stimulated emission photon and a spontaneously emitted photon from a higher state (as they'd have different wavelengths).

Another way would be to put any kind of photodetector at an angle away from the direction of your stimulated photons. Presumably then any photons detected would be from spontaneous emission from the higher state.

In both of the above methods you'd have to remember you're only detecting a small solid-angle of the photons you get from spontaneous emission (it can emit in mostly any direction), thus a direct comparison to the stimulated photons (which emit in the direction you decide... hence lasers) isn't possible.

Possibly the easiest method, if the excited state decayed photoelectrically, would be to measure the net electrical current to the sample (from ground). Again you'd only get a relative measure... unless you had a similar sample for comparison that only absorbed or only underwent stimulated emission.

Professor_Fink

Kohl wrote: »

For instance, I want to be able to detect the atom after the process occurs and tell whether it was absorption or stimulated emission that occured. Is there any experimental technique that would permit me to do that?

It is certainly possible in principle, but in practice it will depend on exactly what experimental system you have in mind. I'm not an experimentalist, so I'm really not the best person to ask about this kind of thing. That said, the way that seems most obvious to me for a single atom would be to look for a specific transition from one of the states to the other (for example a transition from the the highest of the three levels to some 4th level, which cannot transition to the other two levels due to selection rules. If you have such a transition, you could simply drive it and look for flourescence. Or you could try StiRAP or similar. Either way, I suspect you will need to be in the strong coupling regime for a single atom to produce any decent results, which means you need a cavity.