Dipole operator and correlations

[Niles]

Hi

I am reading a paper (http://arxiv.org/abs/0901.3105), where they after eq. (3) mention something I can't understand. First of all, (3) comes from the master equation of a collection of N atoms in a cavity. They say that (page 2, right after (3)):

The last term describes the coupling of the atom-field coherence to the collective spin-spin correlations which locks the relative phase between atoms and field to the phase of the macroscopic atomic dipole.

I don't see why the term $\left\langle {\sigma _1^ + \sigma _2^ - } \right\rangle$ constitutes the dipole correlations between atoms. σ^± is a simple transition operator, and I have never heard that it is related to the dipole of a transition.

I would be grateful to get some help with this.


Niles.

 

[DrDu]

I have no idea of laser theory, but I find the last term in eq.3 not too strange. Obviously the expectation of $\sigma_1^-$ will change when a spin is shifted from 2 to 1 which is described by the last term.