Understanding Quantum Circuit Jaynes-Cummings Model

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Hello... I am trying to study "Quantum Circuit based on Jaynes_Cummings model " . I guess you are familiar with this method..i mean introducing the cavity with a resonator and the atom as a set of LC circuits..Please be gentle and tell me what is the main purpose of this experiment and what results it gives . Actually i can understand the theory until it comes handling with the artificial atom and 1D resonator..And the theory starts to calculate some hamiltonians for the sets of circuits ,but i can actually understand very little things . Please help me!
 
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I think you have to be a bit more specific about what you are asking.
Have you read any "review-type" papers, e.g. the paper by Blais et al(think it was a PRA or PRB 2004) or the article by Lindstrom et al in Superconducting science and technology (easier to understand than Blais work, although it deals with flux qubits)?

It might also be a good idea to find a book about quantum optics and read about cavity-QED, the basic ideas and most of the formulas of circuit-QED are identical to that of cavity-QED but the latter has been around for much longer.

Also, the copper pair box is more or less irrelevant, it was used in the early experiments but ANY type of qubit can be used; so don't spend too much time on it if the goal is to understand cQED (J-C Hamiltonians etc)