# How to calculate the dielectric constant of an media from its microscopic structure?

wdlang
assume that i have a cloud of cold dilute Rubidium atoms

i know the atomic levels of the Rubidium atom

How to calculate the dielectric constant of this gas?

Which book can i consult?

Homework Helper

I think that in Feynman's lectures there is a calculation of dielectric constant for a gas.
I am not sure, I don't have the books now.
May be a good start.

wdlang

I think that in Feynman's lectures there is a calculation of dielectric constant for a gas.
I am not sure, I don't have the books now.
May be a good start.

Thanks a lot. But i am afraid that his book is a bit not to details

Is there any book suitable for guys on cold atom experiments?

Gold Member

I don't think there is a "general" answer to how you calculate something as complicated as the dielectric constant, the latter is -in general- frequency and temperature dependent and what model you use will depends on which processes are involved for that particular frequency/temperature.
Rememeber that all absorbtion processes will also give rise to a change in the dielectric constant, so it is probably a good idea to first think about absorbtion and then worry about the dielectric constant.
It is fairly straightforward to e.g. calculate the change (and in some cases even the absolute value) if you can model your system as an uncoupled ensemble to two-level systems. The way to do this is to first calculate the absorbtion via the Bloch equations (textbook stuff if you are dealing with an ensemble of spin 1/2 systems) and then use the Kramer-Kronig relations to get the permittivity.
I don't know much about cold atoms, but presumably it should be possible to use a relatively simple model (maybe even just the Bloch equations) for the absorbtion and still get a reasonable answer, right?

wdlang

I don't think there is a "general" answer to how you calculate something as complicated as the dielectric constant, the latter is -in general- frequency and temperature dependent and what model you use will depends on which processes are involved for that particular frequency/temperature.
Rememeber that all absorbtion processes will also give rise to a change in the dielectric constant, so it is probably a good idea to first think about absorbtion and then worry about the dielectric constant.
It is fairly straightforward to e.g. calculate the change (and in some cases even the absolute value) if you can model your system as an uncoupled ensemble to two-level systems. The way to do this is to first calculate the absorbtion via the Bloch equations (textbook stuff if you are dealing with an ensemble of spin 1/2 systems) and then use the Kramer-Kronig relations to get the permittivity.
I don't know much about cold atoms, but presumably it should be possible to use a relatively simple model (maybe even just the Bloch equations) for the absorbtion and still get a reasonable answer, right?

Thanks a lot for the reply.

i find a book on the topic

"Electric-Dipole Polarizabilities of Atoms, Molecules and Clusters"

Alkali atoms are simple but not so simple as a two-level system. In many cases, you have to take the hyperfine structures into account. There are many stuffs like CG coefficients to care.