Transitions on resonance with a cavity.

[wotanub]

I'm not exactly sure what I'm trying to ask, and I'm not very keen on laser physics, so bear with me.

If I have a system in an excited state that can decay by spontaneous emission with a certain lifetime, what is the effect of placing it in a cavity with a mode resonant with this transition?

Does it increase or decrease the likelihood of decay into the lower energy state? If the cavity is isolated and the photon that is emitted into the cavity has to stay, does the energy "flip" back and forth between the system and the cavity producing something like a superposition of the excited and excited state?

If it is evident that I have some misconception about what a cavity or spontaneous emission is, please enlighten me. As I said, I'm not sure if I'm asking the right thing.

 

[Jolb]

In a conventional laser, the gain medium (usually a tube of gas in a population-inverted state) is placed in between two parallel mirrors, and this system of mirrors is usually called a "cavity" or an "optical feedback system." The purpose of this is to encourage stimulated emission--when a photon passes nearby a gain medium atom in the excited state, it can induce a transition in the gain medium atom, provided the atom's emission occurs at the same frequency as the incident photon. The mirrors send the photons coming out of the gain medium back and forth between the mirrors, repeatedly passing near the excited gain medium atoms in order to cause stimulated emission.

The reason the cavity must be "tuned" (i.e., designed with the correct length) to the emission frequency of the gain medium is because otherwise standing-mode EM waves cannot form between the mirrors, and if a standing wave doesn't form, then the EM wave interferes with its reflection, decreasing the number of photons traversing the gain medium, thus reducing the stimulated emission. When the emission of the gain medium occurs at a frequency which coincides with a standing-wave mode of the cavity, this EM wave gets bigger and bigger with more stimulated emission--there is no destructive interference between the EM wave and its reflection off the mirrors capping the cavity. The latter case is what you want to make a bright laser.

Let me know if this resolves your question.

 

[Cthugha]

Does it increase or decrease the likelihood of decay into the lower energy state? If the cavity is isolated and the photon that is emitted into the cavity has to stay, does the energy "flip" back and forth between the system and the cavity producing something like a superposition of the excited and excited state?

If it is evident that I have some misconception about what a cavity or spontaneous emission is, please enlighten me. As I said, I'm not sure if I'm asking the right thing.

No, these are actually very good questions. In addition to what has already been pointed out, a cavity can also have an effect in the spontaneous emission regime way below the lasing regime. You can loosely interpret spontaneous emission as stimulated emission stimulated by the vacuum state (which is never truly empty). Therefore, spontaneous emission must depend on the density of final states to emit to. The presence of a cavity can alter the density of states and correspondingly also the spontaneous emission rate (for a resonant cavity the rate usually increases). This is known as the Purcell effect (http://en.wikipedia.org/wiki/Purcell_effect). The Wikipedia article is not comprehensive, but a good starting point giving some good references. The Purcell effect is most prominent for very good cavities or for cavities with very small mode volume. Therefore it is most easily seen in small semiconductor microcavities or photonic crystal cavities.

Regarding your other question: Yes, in a good cavity, the energy can go back and forth between the cavity and the system. If the lifetime of the photon inside the cavity is so long that at least one reabsorption event by the system is likely to happen (sometimes termed reversible spontaneous emission), the characteristics of the system change drastically. This is the so-called strong coupling regime. In the simplest approximation you can consider the cavity mode and the atom as two harmonic oscillators effectively interchanging energy. As a consequence, the energy of the two modes will change. You get one mode of higher and one of lower energy than the original one, which effectively correspond to in-phase and out-of-phase energy exchange. This is in principle very similar to coupling to spring pendulums via another spring which will also cause normal modes to occur. As a consequence, the new modes do not represent the atom or the cavity mode, but a mixed mode describing the permanent energy exchange between both. In atomic physics, these are called dressed photons. In semiconductor physics, these modes are called polaritons. This regime allows to observe interesting phenomena like coherence revivals and Rabi oscillations. The basic model treating that problem is the Jaynes-Cummings model (http://en.wikipedia.org/wiki/Jaynes–Cummings_model).

 

[wotanub]

Thanks, you guys answered my questions and gave me more to think about.