Ionization spectra of highly Stark-shifted rubidium Rydberg states

We report on the observation and numerical calculation of ionization spectra of highly Stark-shifted Rydberg states of rubidium beyond the classical ionization threshold. In the numerical calculations, a complex absorbing potential (CAP) allows us to predict the energy levels and ionization rates of Rydberg states in this regime. Our approach of adjusting the CAP to the external electric field reduces the number of free parameters from one per resonance to a single one. Furthermore, we have measured the ionization spectra of magneto-optically trapped rubidium atoms which are excited to principal quantum numbers of 43 and 70 at various electric fields. The emerging ions are detected using an ion optics. We find good agreement between the numerically and experimentally obtained spectra.

Figure 1

Illustration of the complex absorbing potential (CAP). The parameter $r_{\mathrm{c}}$ is determined according to Eq. (6) which places it at the radius of the saddle point of the potential $V_{\mathrm{C},\mathrm{E}}$ [see Eq. (4)]. Note that in this 1D graph along the $z$ axis, the saddle point appears as a local maximum. This choice of $r_{\mathrm{c}}$ creates a potential $W$ that resembles the shape of $r^6$ but is spherically shifted by $r_{\mathrm{c}}$.

Figure 2

Schematic diagram of the experimental setup. Rubidium atoms are trapped at the intersection of the MOT beams (red). Atoms from the MOT are continuously excited to Rydberg states by the coupling laser (blue) at various electric fields, which are applied via the extractor electrodes. The field is also used to guide the ions (green) to the ion optics.

Figure 3

Ionization Stark spectrum near $43S_{1/2}$. (a) Detected ion signal from the experiment. (b) Results from the numerical calculations for $\eta =1\times {10}^6$. The detuning is given relative to the unperturbed state. We have applied a linear scaling to match the electric field from the experiment to the theoretical results. The classical ionization threshold is located at $\approx 127\mathrm{V}/\mathrm{cm}$.

Figure 4

Ionization Stark spectrum near $70S_{1/2}$. (a) Detected ion signal from the experiment. (b) Results from the numerical calculations for $\eta =2\times {10}^5$. The detuning is given relative to the unperturbed state. We have applied a linear scaling to match the electric field from the experiment to the theoretical results. The classical ionization threshold is located at $\approx 16.1\mathrm{V}/\mathrm{cm}$. The white dashed lines mark the cut that is shown in more detail in Fig. 8.

Figure 5

Ionization Stark spectrum near $70S_{1/2}$. Continuation from Fig. 4. The white dashed lines mark the cut that is shown in more detail in Fig. 8.

Figure 6

Ionization Stark spectrum near $70S_{1/2}$. Continuation from Fig. 5.

Figure 7

Ionization Stark spectrum near $70S_{1/2}$. Continuation from Fig. 6.

Figure 8

Ionization Stark spectra from the experiment (blue solid lines) and the numerical calculations (red dashed lines) near $70S_{1/2}$ at (a) $16.53\mathrm{V}/\mathrm{cm}$ (see Fig. 4) and (b) $24.10\mathrm{V}/\mathrm{cm}$ (see Fig. 5). While we find agreement within our experimental resolution of $25\mathrm{MHz}$ in (a), some small deviations can be seen in (b). The two highest peaks from the experimental data in (b) have a slightly asymmetric line shape, which may indicate possible Fano resonances. Furthermore, we find discrepancies around 1.3–2 GHz, which we attribute to drifts of the voltage source that was used in the experiment and the high sensitivity of these resonances to the electric field.