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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 [itex]\left\langle {\sigma _1^ + \sigma _2^ - } \right\rangle[/itex] 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.

Best,

Niles.