Atomic photon versus cavity photon

[DaTario]

Hi all

My question arises in the context of a photon which is emitted by an atom located inside a cavity. From quantum mechanics, a photon is a quantum of an electromagnetic mode, but we also use the definition which says that the photon is what is released by an atomic system when its electronic state suffers a decay in energy. So, my question is the following: when an atom suffers a decay inside a cavity would it be correct to think of this as an atomic photon being generated and after a small time interval (time for the radiation to complete a complete turn inside the cavity) there appears a cavity photon?

Best Wishes

DaTario

 

[Meir Achuz]

The wavelength of an atomic photon is much smaller than a reasonable cavity size, so the photon would not excite a cavity mode. The photon would just bounce around the cavity like a billiard ball.

 

[DaTario]

Ok,

But I mention here the case of some microwave cavities where the atomic photon is in resonance with the cavity mode.

 

[Rach3]

Ok,

But I mention here the case of some microwave cavities where the atomic photon is in resonance with the cavity mode.

There do exist optical cavities like this - in resonsance with atomic transitions - but they are not microwave cavities by far. Atomic transitions are usually in the visible or infrared range - photons tens of thousands times more energetic than microwave photons. (see http://en.wikipedia.org/wiki/Electromagnetic_spectrum)

In answer to your question: a two-level atom in resonance with an optical cavity will not merely decay, but rather oscillate between absorbing and emitting the photon! The model used for this is the Jaynes-Cummings Hamiltonian for the combined atom+cavity system (defined here: http://qwiki.caltech.edu/index.php/Jaynes-Cummings_Hamiltonian ). It turns out that the eigenstates of this hamiltonian (the stationary states) are superpositions of the states in which the photon is in the cavity, and in which it is absorbed in the atom; so an initial system of an excited atom will be in a non-eigenstate and thus must oscillate; the photon will "oscillate between the atom and the field". These are atomic Rabi oscillations, a consequence of the number operators not commuting with the Hamiltonian. The frequency is determined by how close to resonance your atom-cavity system is.

In practice these photonic cavities are being built (http://ab-initio.mit.edu/photons/resonant-cavities.html, from google search). Of course the cavities aren't perfect resonators, the Rabi oscillations will decay away, though they're good enough to still get - I believe hundreds? - of Rabi oscillations - I was at a talk about this in APS March meeting '06, I'll try to hunt down the paper for you if I can.

Unfortunately I don't know any half-decent online resources for cavity QED, hence the paucity of good hyperlinks.
(late edit, removed typo)

 

[DaTario]

There do exist optical cavities like this - in resonsance with atomic transitions - but they are not microwave cavities by far. Atomic transitions are usually in the visible or infrared range - photons tens of thousands times more energetic than microwave photons. (see http://en.wikipedia.org/wiki/Electromagnetic_spectrum)

In answer to your question: a two-level atom in resonance with an optical cavity will not merely decay, but rather oscillate between absorbing and emitting the photon! The model used for this is the Jaynes-Cummings Hamiltonian for the combined atom+cavity system (defined here: http://qwiki.caltech.edu/index.php/Jaynes-Cummings_Hamiltonian ). It turns out that the eigenstates of this hamiltonian (the stationary states) are superpositions of the states in which the photon is in the cavity, and in which it is absorbed in the atom; so an initial system of an excited atom will be in a non-eigenstate and thus must oscillate; the photon will "oscillate between the atom and the field". These are atomic Rabi oscillations, a consequence of the number operators not commuting with the Hamiltonian. The frequency is determined by how close to resonance your atom-cavity system is.

In practice these photonic cavities are being built (http://ab-initio.mit.edu/photons/resonant-cavities.html, from google search). Of course the cavities aren't perfect resonators, the Rabi oscillations will decay away, though they're good enough to still get - I believe hundreds? - of Rabi oscillations - I was at a talk about this in APS March meeting '06, I'll try to hunt down the paper for you if I can.

Unfortunately I don't know any half-decent online resources for cavity QED, hence the paucity of good hyperlinks.



(late edit, removed typo)

I know how to derive Rabi oscillations from JC model. But what I have in mind is another issue. I was wondering if the difference between atomic and cavity photon play some role in such formalism. My guess is that these formalism skip all this subtleties and assume simply that an atomic photon is equal to a cavity photon.

Best Wishes

DaTario