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This parameter was then plotted in Fig. 9 for Ne = 2 and the detunings δ = 0, δ = 2J , and δ = 3J . In all three cases the nonlinearity goes rapidly to zero for g J . Although these results are correct, the plot shows only the nonlinearity parameters for the mostly photonlike states with δ = 2J and δ = 3J , instead of the more relevant cases of the fully hybridized state at the band edge with δ = −2J or the atomlike state inside the band gap with δ = −3J . In Fig. 1 we show again the same plot of the nonlinearity parameter, but now including the cases δ = −2J and δ = −3J (we recall that in Fig. 9 we focus on the lowest dressed state). It can be seen that although for δ = −2J the nonlinearity (compared to the Jaynes-Cummings nonlinearity) vanishes at small g, it is still much stronger than for the resonant case δ = 0. This is consistent with the observation that for δ = −2J the wavelength of the second photon, λ2, can be much larger than the wavelength of the first bound photon, λ1 (see discussion in Sec. V C in the original paper). In contrast, for δ = 0 one finds λ1 ≈ λ2. Note that the approximate scaling of the nonlinearity parameter for g → 0 can be understood from the simplified assumption

Erratum: Atom-field dressed states in slow-light waveguide QED [Phys. Rev. A93, 033833 (2016)]