How Can Two Qubits Interacting with Photons Be Simplified Using Pauli Operators?

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xlh
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please see the following Hamiltonian mode.
two two-level atoms(or two qubits) interact with photon.
á、à are the creation and annihilation operators of photon
please rewriting H in the way of pauli operators , will looks very simple

H = E1 ( |e1><e1| －|g1><g1| ) + E2 ( |e2><e2| －|g2><g2| ) + hωáà

+ g (á + à ) ( |g1><e1|.|g2><e2| + |g1><e1|.|e2><g2| + |e1><g1|.|g2><e2| +|e1><g1|.|e2><g2|)

considering the case of resonant interaction and Rotating Wave Approximation , only two interaction terms exist

I have no ideas to make use of the H.
I want to cite some ideas from Quantum Optics or other areas.( besides entanglement of two atoms)

Would you please tell me the documents If someone have seen the mode?
Would you please tell me some ideas?

thanks very much!

Xiaoling He
xlhfudan@yahoo.com
 
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See Mandel and Wolf, Optical Coherrence and Quantum Optics, Chap. 15, all about photons and 2 level atoms (Bloch and Rabi were key players in the development of this now mature field. Also, Cohen-Tannoudji et all cover the subject in their Atom-Photon Interactions -- Basic Processes and Applications. There's also newer work, based on work by Jaynes dealing with exact solutions, which can be found via Google.

Regards,
Reilly Atkinson