Fig. 4: LZSM interferometry for the N = 10 device, in the Kerr regime and strongly-modulated case Ω ≫ ∣χ∣.

a–c The magnitude of S₂₁ is measured vs Δ and ζ for fixed modulation frequency Ω/2π = 150 MHz. As the drive power P_in is increased, Kerr multiphoton resonances from \(\left\vert 0\right\rangle\) to \(\left\vert n\right\rangle\) appear detuned by (n − 1)χ on the left of bare LZSM resonances. For large ζ, notice the shift of the pattern to negative detuning, due to the nonlinear dependence of the SQUID array frequency on the flux, as explained in the Supplementary Information. d Photon-number simulation using the effective model of Eq. (3) for the same parameters as in (b), recovering the same interference pattern. e–g In the drive frame, energy vs time for different values of ζ and Δ including the first three levels of an undriven Kerr resonator (F = 0). Green markers indicate the corresponding value of Δ and ζ in (d). e For Δ = 0, although multiple levels cross with \(\left\vert 0\right\rangle\), only the level \(\left\vert 1\right\rangle\) forms a constructive interference. f For Δ = χ, the second level \(\left\vert 2\right\rangle\) crosses \(\left\vert 0\right\rangle\), and an appropriate choice of parameters leads to constructive interference. g For Δ = χ + Ω, similar LZSM interference can be constructive again and the level \(\left\vert 2\right\rangle\) can be populated. We verified that both the data and full numerical simulations recover that the interference patterns are fully constructive at Δ = Ω and ζ ≈ 1.84Ω, where the Bessel function J₁(ζ/Ω) is at a maximum, confirming the prediction of the effective model in Eq. (3).