Fig. 3: LZSM interference patterns.

a–c (red) Analysis of the N = 10 device, with input power P_in = −138.8 dBm, ensuring that we are in the qubit regime. b The transmission coefficient ∣S₂₁∣ as a function of the detuning Δ and the modulation strength ζ, for fixed modulation frequency Ω/2π = 30 MHz [see Eq. (1)]. a Comparison of the experimental and theoretical data for ∣S₂₁∣. Solid lines represent the results of the numerical simulations of the full quantum model obtained at Δ = 0, Δ = −Ω, and Δ = −2Ω (see Supplementary Information). The circles are the experimental data obtained from panel (b), in which Δ is slightly re-scaled to account for the nonlinear flux-dependency of the resonator frequency (see Supplementary Information). c ∣S₂₁∣ as a function of Δ and Ω. d–f (blue) As in (a–c), but for the N = 32 device, with P_in = −133.3 dBm to ensure that the system is in the linear regime. From these plots, the two regimes appear almost indistinguishable. g The photon number vs Δ and ζ is obtained from a simulation using the effective model of Eq. (3) that reproduces the interference pattern in (b, e). h–j Depiction of the time evolution of the energy level \(\left\vert 1\right\rangle\), in the frame rotating at the drive frequency ω_d, if F = 0. A finite drive F opens gaps at each crossing between \(\left\vert 0\right\rangle\) and \(\left\vert 1\right\rangle\), allowing a non-adiabatic passage between the two. The parameters Δ and ζ are indicated by green markers in (g). h At Δ = 0, the level \(\left\vert 1\right\rangle\) becomes resonant with \(\left\vert 0\right\rangle\) (they form a level crossing, see the inset). The values of ζ, F, and κ then determine the probability of transitioning out of the vacuum. i For non-zero detuning (e.g., ∣Δ∣ = Ω) and small modulation (ζ ≪ Ω), the level \(\left\vert 1\right\rangle\) is never resonant with \(\left\vert 0\right\rangle\) and it cannot be populated. j For strong enough modulation ζ > ∣Δ∣, the level \(\left\vert 1\right\rangle\) can form again an avoided level crossing, and constructive interference is possible again.