Spontaneous Absorption of Photons in Two State Quantum System

[Smalde]

Let's consider a two state quantum system in which an electron is either in the ground state or in the excited state with the energy difference E.

We know that if we put this system in a monochromatic electromagnetic field (with frequency E/h) the electron can become excited by means of stimulated absorption of a photon. We know that if the electron is in the excited state it can "fall" to the ground state by emitting a photon either by means of the stimulated emission in which a photon of the electromagnetic field stimulates the electron and two photons gets emitted or by spontaneous emission (which in turn is stimulated too, because it is stimulated by the vacuum field fluctuations of QED).

My question is the following. Since we know that spontaneous emission is not spontaneous at all but has its origins in the stimulation due to the vacuum field fluctuations, what hinders spontaneous absorption of a photon of this fluctuating field?

I don't really see why this in fact wouldn't be possible. I do know that spontaneous absorption is not something that one talks about when for instance calculating Einstein's A and B coefficients, neither when calculating Rabi oscillations. This makes me thing that if spontaneous absorption is possible, it should be far less probable. If this is the case, what makes it so improbable?

 

[goodphy]

I'm not expert at all about Quantum Mechanics but I have to ask what spontaneous absorption means? The term "spontaneous" is used typically to indicate some event which occurs without external induction. I also heard that the spontanoue emission is yes, induced by vacuum field fluctuation fundmentally so name of this phenomena actually do not reflect ture nature of this. It is what I can agree with you.

However, technically, the spontaneous emission is the photon emission (by excited state decay into lower energy state) without external electromagnetic field (no external photons). In this sense, the spontanous absorption may mean the absorption without external electromagnetic field (external photons). However, It doesn't make sense as there is no photon to be absorbed. The absorption of vacuum energy is not really likely to be happen i guess.

 

[vanhees71]

I've also no clue what "spontaneous absorption" should mean. If you want to absorb something it must be present to be absorbed. So there's no sense in something called "spontaneous absorption".

Spontaneous emission is when you have an excited state (say of an atom) and then it emits a photon. This spontaneous emission is indeed due to the coupling of the electron to the quantized radiation field and is missing in the semiclassical description. It is an example for a vacuum polarization process (in the true sense of the word, i.e., you have not simply the vacuum state of photons and nothing else but you probe this vacuum with the presence of the excited atom). Semiclassical here means the approximation, where you treat the electrons quantum mechanically but the electromagnetic field as a classical field.

Induced emission is if you have an excited state in an electromagnetic wave field (which can often treated classically). The interaction of the electron with this electromagnetic field triggers the emission of a photon and the deexcitation of the atom.

The total deexcitation rate is thus proportional to (1+<n>), where <n> is the average photon number in the (maybe semiclassical) em. field. The additional 1 describes the spontaneous emission, which was predicted by Einstein making use of old-fashioned quantum mechanics and comparison with the Planck-radiation law describing photons in thermal equilibrium ("black-body radiation").

 

[Smalde]

I know that spontaneous emission happens in the absence of external fields.

What I mean is that, due to the fact that the vacuum field fluctuations can stimulated an emission, why can they not stimulate an absorption in the same sense?

You need (if I am not wrong) your electromagnetic field to have the transition frequency in order to stimulate emission. This means that the vacuum field can have the same energy, because else it would not be in the condition of "stimulating" spontaneous emission. Thus the field could in an analogous way stimulate an absorption (meaning absorb a photon of this field). Where is my logic wrong?

I suppose I will have to wait until next semester, when I am finally going to have a QFT lecture to know the answer.

 

[vanhees71]

What do you want to absorb, if there's nothing present to be absorbed. "Spontaneous absorption" is just a non-sensical expression!

 

[Andy Resnick]

My question is the following. Since we know that spontaneous emission is not spontaneous at all but has its origins in the stimulation due to the vacuum field fluctuations, what hinders spontaneous absorption of a photon of this fluctuating field?

It seems like you are asking about the Jaynes-Cumming model:
https://en.wikipedia.org/wiki/Jaynes–Cummings_model

 

[Paul Colby]

A QED model of an atom interacting with the radiation field would have vacuum bubbles corresponding to spontaneous absorption followed by emission. I would assume (as apposed to actually knowing, which I don't) that these would be renormalized or appear as vacuum polarization effects.