# Pseudospin operator

1. Nov 2, 2012

### Niles

Hi

Often in the context of multi-atom systems, such as in cavity QED, it is customary to introduce a so-called "collective pseudospin operator". An example of this is for the inversion for some atom j, $\sigma_{j, z}$, which becomes
$\sum_{j} \sigma_{z, j} = \sigma_z$
To me this seems very reasonable, we just try to describe the collectice behavior via a single operator. But what makes is "pseudospin"?

Best,
Niles.

2. Nov 5, 2012

### Cthugha

From the historical point of view, the first detailed study of a two-level system has been given by Bloch (F. Bloch, "Nuclear Induction", Phys. Rev. 70, 460–474 (1946)). This was a study of a spin 1/2 NMR system. In this paper the famous Bloch equations were presented first. Afterwards it could be shown that any ensemble of noninteracting two-level sytems subject to external perturbation behaves similarly and follows equations having the same structure as the Bloch equations (I think it was shown in J. Appl. Phys. 28, 49 (1957) by Feynman et al. first, but I am not sure about that).

So as these two-level systems behave in the same manner as the spin systems which were well known at that time, but obviously are not necessarily spin systems, they were termed pseudospin systems.

3. Nov 5, 2012

### Niles

Ah, I see, that makes good sense actually. Thanks for taking the time to write all that and also for the links!

Best,
Niles.

Last edited: Nov 5, 2012