time dependence. The transition rate and, therefore, the population transfer, at each n-photon resonance is related to the matrix element squared, $\Delta_n^2$. At specific amplitudes, despite driving the system resonantly, no net transition occurs due to a complete destructive Mach-Zehnder interference corresponding to the zeros of $J_n(\lambda)$; this is the coherent destruction of tunneling [@Grossmann91a; @Llorente92a; @Kayanuma08a] condition for driven n-photon transitions [@Oliver05a; @Berns06a]. More generally, as a function of the driving amplitude, we have observed the continuous evolution between regions of enhanced and suppressed tunneling as dictated by $J_n(\lambda)$ over several Bessel-function lobes (Fig. \[fig:3\]A).

In the discrete resonance limit, n-photon resonances are distinguishable, because the coherence time of the qubit is sufficiently longer than the driving period. By reducing the frequency to $\nu = 90$ MHz (Fig. \[fig:3\]A, right panel), we effectively made the drive period comparable with the linewidth, $\nu T_2^* \sim 1$ (Fig. \[fig:3\]B). In this spectroscopy plot, the individual n-photon resonances are no longer resolvable. However, the Mach-Zehnder interference fringes (vertical slice, Fig. \[fig:3\]C) are clearly visible, because the qubit remains coherent during the critical fraction of the drive period during which the phase $\Delta \theta_{12}$ accumulates and the Mach-Zehnder interference occurs. Intuitively, provided $\nu 