Cesium Atom quantum mechanical description

[TheDestroyer]

Hello guys,

I need the quantum mechanical description of the Cesium atom/gas with its hyperfine states, and preferably with some density matrix.

I don't really know where to start my search. I googled a lot, and looked for articles and books, but failed.

Any help is highly appreciated. Thank you for any efforts.

 

[TheDestroyer]

OK... let me rephrase the question...

Has anyone in the history of physics solved the Schrödinger equation of a Cesium Atom? Why can't I find anything about that?

Any references would help. Thanks!

 

[f95toli]

There should be a lot of stuff available for Cs. Have you tried looking at review articles/books on Cs clocks?

 

[TheDestroyer]

I didn't find any particular thing available for the wave-function of the Cesium atom... that's why I'm surprised.

If you know any reference that would help, please let me know.

 

[f95toli]

What do you mean by "the wave function"?
I doubt anyone ever solves the full SE for the Cs atom, that would be incredibly computationally intensive.

 

[TheDestroyer]

Well that's my question. What are the available methods for obtaining the wave-function of Cs?

I have a problem where I have a Cs gas in a chamber under a magnetic field and pumped by a laser beam. I need at least some wave function to put it in my density matrix to start doing this. But this information is NEVER available anywhere...

How can I solve such a problem? any idea?

 

[torquil]

Well that's my question. What are the available methods for obtaining the wave-function of Cs?

I have a problem where I have a Cs gas in a chamber under a magnetic field and pumped by a laser beam. I need at least some wave function to put it in my density matrix to start doing this. But this information is NEVER available anywhere...

How can I solve such a problem? any idea?

The Cs atom contains too many eletrons to solve the Schrödinger equation in the same manner as one usually does for the Hydrogen atom to find the wavefunction. However, if you know that only a limited number of energy eigenstates are participating in the physical phenomenon under study, you can try to make an effective Hamiltonian for only those states.

 

[cgk]

Well that's my question. What are the available methods for obtaining the wave-function of Cs?

I have a problem where I have a Cs gas in a chamber under a magnetic field and pumped by a laser beam. I need at least some wave function to put it in my density matrix to start doing this. But this information is NEVER available anywhere...

How can I solve such a problem? any idea?

The standard approach would be to enter something like "geometry={Cs}; mcscf; {mrci; ..}" into your favorite quantum chemistry program and ask it to make those wave functions (and matrix elements) for you.

 

[TheDestroyer]

Has anyone made such a Hamiltonian and solved it? I would like to see previous contributions to this field, so that I could start working. I found nothing so far, and that's why I'm asking for help!

 

[f95toli]

Which transitions are you probing?
If it is any of the hyperfine transitions used for clocks you should -as pointed out above- be able to find a LOT of information.

I suspect part of the problem is that you are a bit too vauge, calculations like this are usually done with respect to some specific transition, and even then with numerical methods. You are not going to find a "full" description as for e.g. H or He.
Hence. look for papers relevant for what you are doing.

 

[TheDestroyer]

Thank you again for your replies.

We're doing a very specific research about Cesium magnetometers. The transitions I'm looking for are depicted in the attachment please take a look at it.

We're currently solving the Bloch's equation numerically to simulate the responce of the gas to the magnetic field. But this isn't sufficient, and the damping profile of the gas isn't exactly exponential like the Bloch's equation predicts. It's somehow a complicated exponential with quadratic stuff... we don't know. So we'd like to find the equation that governs the transitions so that we could resume with this.

In the picture attached, we used a right-circularly polarised light to induce the transition of the atoms to the upper states, and then we apply an RF field to get some resonance with the magnetisation of the system. The frequency, with which the system responces, is proportional to the magnetic field.

I couldn't find anything about those transitions. If you know any articles/books/references can you please point them out?