Figure 1

Dashed line: experimental ionization probability of $n_0=37$ hydrogen Rydberg atoms exposed to $\approx 300$ cycles of a linearly polarized microwave field of frequency $9.92\mathrm{GHz}$ as a function of field strength $\mathcal{E}$. Solid line: field-averaged ionization probability $\overline{P}\left(\mathcal{E}\right)$ computed on the basis of the one-dimensional SSE model as discussed in the text.Reuse & Permissions

Figure 2

Experimental ionization probabilities $P\left(\mathcal{E}\right)$ [6, 16] as a function of microwave field amplitude $\mathcal{E}$ at $9.92\mathrm{GHz}$. The curves are labeled by their initial principal quantum numbers $n_0$. (a) $n_0=32,\dots ,38$, (b) $n_0=39,\dots ,44$, and (c) $n_0=45,\dots ,50$. Prethreshold structures are marked with arrows and labeled with their corresponding multiphoton orders $\nu$. The multiphoton order $\nu =13$ in (c) is marked by a star since it corresponds to a transition from $n_0=45$ to $n=47$.Reuse & Permissions

Figure 3

False-color and gray-scale plot (see intensity scale to the right of the panel) of the ionization probability after 50 cycles as a function of frequency and field strength for $n_0=37$.Reuse & Permissions

Figure 4

Area $P_{<}$ under the ionization curve below the linear fit to the 10% ionization threshold as a function of frequency for $n_0=37$. The vertical dashed lines indicate the positions of multiphoton transitions from $n_0=37$ to $n=38$, shifted $0.45\mathrm{GHz}$ to the left. Selected peaks are labeled with their respective multiphoton orders.Reuse & Permissions

Figure 5

Eigenphases $\alpha$ of the one-cycle propagator $\widehat{U}\left(T\right)$ as a function of microwave field strength at $f=9.92\mathrm{GHz}$. Shown are the eigenphases ${\alpha }_{37}$ and ${\alpha }_{38}$ whose corresponding eigenstates $\mid {\alpha }_{37}⟩$ and $\mid {\alpha }_{38}⟩$ have the largest overlap with the unperturbed SSE states $\mid n=37⟩$ and $\mid n=38⟩$. The position of the prethreshold structure in the $n=37$ experimental ionization curve is marked by an arrow. The position of the onset of the main rise of the experimental ionization signal is marked by the vertical dashed line. (a) Solid lines: the numerically computed eigenphases ${\alpha }_{37}$ and ${\alpha }_{38}$. They show an anticrossing at the position of the prethreshold structure. Dashed lines: the results for ${\alpha }_{37}$ and ${\alpha }_{38}$ obtained from second-order quasienergy perturbation theory. (b) Magnification of (a). The field mesh points do no longer blend into a continuous line and the corresponding results for $\alpha$ are shown as bullets $\left({\alpha }_{37}\right)$ and crosses $\left({\alpha }_{38}\right)$. For clarity of presentation only every third point is marked. Dashed lines: the results for ${\alpha }_{37}$ and ${\alpha }_{38}$ obtained from fourth-order quasienergy perturbation theory.Reuse & Permissions

Figure 6

Area $P_{<}$ under the ionization curve below the linear fit to the 10% ionization threshold as a function of frequency for $n_0=10$. Overlaid are the positions of multiphoton transitions from $n_0=10$ to $n=11$ shifted $0.45\mathrm{GHz}$ to the left. The photon order is noted above selected peaks.Reuse & Permissions