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note
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If the higher lying junction states m=2,3,. are not initially occupied and the resonator also starts in the ground state, only the qubit states m=0,1 are coupled by "energy-conserving" terms. Therefore, the higher-lying junction states m=2,3,. can be treated with ordinary perturbation theory in g.
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σ (t) by a series or cumulant expansion in V leads to a result that is valid only for short times.
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