Dispersive shift χ = g²/Δ for two-level limit; χ = g² α/(Δ(Δ+α)) for transmon

Blais-Huang-Wallraff-Girvin-Schoelkopf 2004 dispersive shift for circuit-QED. In the two-level (σ_z) truncation of the Jaynes-Cummings model, perturbation theory in g/Δ yields an effective Hamiltonian whose σ_z a†a coefficient — the…