# Identical atoms in the Dicke model...

by lfqm
Tags: atoms, dicke, identical, model
 P: 10 Hey guys, I've recently read about the Tavis-Cummings and Dicke models and I got a little bit confused about them. They are suppoused to model N identical atoms interacting with a one-mode EM field, however the atomic operators are defined in the basis (for the case of two atoms): $$\left\{{|e_{1},e_{2}>, |e_{1},g_{2}>, |g_{1},e_{2}>, |g_{1},g_{2}>}\right\}$$ which obviously makes a distinction between the atoms. Then it gets even more confusing, as they start working in a spin basis $$\left\{{|j,m>}\right\}$$ which makes the atoms identical for the case j=N/2... I don't even undestand why they fix j=N/2 Concretely, my question is: What is the basis of the hilbert space the Dicke hamiltonian is acting on (the atomic part)? The $$2^N$$ elements basis (distinguishable atoms), the $$\displaystyle\sum_{j=0}^{N/2}(2j+1)$$ elements basis (considering all spin values) or the $$N+1$$ elements basis (fixing j=N/2). And what is the form of the atomic operators in this basis? Thanks