Two photons spontaneous emission (2s->1s)

[leviadam]

Hi all,

I'm doing a project that includes an hydrogen 2s->1s decay and I need the full derivation of this process, so if anyone can recommend about a book it would be great.
I first thought it should be easy to find but to tell you the truth I have looked and found scratch.

10x a lot,
Adam

 

[conway]

I'd also like to know how this works. There ought to be a mechanism that describes it. Some transitions have a strong oscillating dipole moment, but this one doesn't. Not even a quadrupole or higher moment. So what explains the transition process?

 

[leviadam]

It comes from the A² operator in the Hamiltonian, all the dipole and quadrupole etc comes from A*P, when A*p is possible A² is neglected.
In 2s->1s A*p is impossible so there has to be a two photons emission.

Adam.

 

[conway]

You say "it" comes from the A-sqaured operator, but what is "it"?

You say "the dipole moment" comes from A*P.

I know what "the dipole moment" is but I don't know what your "it" is. It is not helpful to say "it" comes from A-squared because I don't know what "it" is.

 

[leviadam]

This is a quantum field of course, and is represented with ladder operators , so when you have A² you get a product of two ladder operators that creates two photons.

Adam.

 

[alxm]

In the words of Marvin Gaye: "It takes two, baby."
You get a zero transition probability with a single photon, no matter what order you expand A.p to (dipole, quadrupole, etc). 2s->1s is completely forbidden. So if there's a transition (which there is), it's from taking into account a two-photon (A.A) term, that is, two photons are emitted.

What this corresponds to 'physically', if you like, is a decay to and then from a virtual level. 2s->virtual->1s.

And it's not terribly spontaneous.. IIRC, the lifetime of 2s is on the order of seconds.

 

[leviadam]

alxm, you seem to know the phenomena, can you think of a book that has the full derivation?

 

[alxm]

alxm, you seem to know the phenomena, can you think of a book that has the full derivation?

I can't seem to find one, but "Atomic and laser spectroscopy" by Alan Corney has some of it in section 7.4, but it's mostly geared towards experiment.
Poking around with Google turned up http://calima.univalle.edu.co/revista/vol38_1/articulos/pdf/3801365.pdf" [Broken] which does a pretty good job.

 

[Cthugha]

I have recently been to a conference, where some guy talked about two photon emission in semiconductors. In his papers he also refers to two photon emission in atomic optics and hydrogen and usually refers to the following papers:

Goldman, S. P. & Drake, G. W. F. "Relativistic two-photon decay rates of 2s1/2 hydrogenic ions", Phys. Rev. A 24, 183–191 (1981).

and

Shapiro, J. & Breit, G. "Metastability of 2s states of hydrogenic atoms", Phys. Rev. 113, 179–181 (1959).

I am no expert on that field, but maybe these papers contain what you are looking for.

 

[conway]

What this corresponds to 'physically', if you like, is a decay to and then from a virtual level. 2s->virtual->1s.

And it's not terribly spontaneous.. IIRC, the lifetime of 2s is on the order of seconds.

Any idea what the virtual level looks like? And is the decay process sequential (first one photon, then another photon a second later) or simultaneous?

 

[alxm]

Any idea what the virtual level looks like? And is the decay process sequential (first one photon, then another photon a second later) or simultaneous?

Well, it looks like an energy level in your calculations. In reality it looks like nothing since it doesn't actually exist outside of that - both photons are emitted simultaneously.

You could compare to virtual energy levels in Raman scattering.

 

[conway]

You could compare to virtual energy levels in Raman scattering.

OK. What do they look like physically?