Autoionization of very-high-$n$ strontium Rydberg states

We study, using a combination of experiment and theory, the excitation and decay of very-high-$n(n\sim 280\text{–}430)$ strontium autoionizing Rydberg states formed by near-resonant driving of the $5s{}^{2}S_{1/2}\to 5p{}^{2}P_{1/2}$ core-ion transition. The branching ratio between decay through radiative transitions and through autoionization is explored. Autoionization rates are measured as a function of both the $n$ and $\ell$ quantum numbers of the Rydberg electron. The nonstationary decay dynamics is studied by creating and manipulating Rydberg wave packets and by varying the laser pulse that drives the core excitation.

Figure 1

Energy-level diagram for autoionization and radiative decay of doubly excited Rydberg states of strontium. Initially, the ground-state atom is excited to a singly excited Rydberg state, $5sn\ell {}^{1}L_J$, in the singlet sector by three-photon excitation (indicated by a sequence of three arrows). The subsequent core excitation of the other valence electron yields doubly excited states, $5p_{1/2}n{\ell }_j$ (a single solid arrow). They autoionize (open arrows) or decay radiatively (dashed arrows) to singly excited states, $5sn\ell {}^{2S+1}L_J$, or to doubly excited states, $4d_{3/2}n{\ell }_j$. Each shaded area represents the continuum states associated with an ionization threshold corresponding to the indicated energy level of the ${\mathrm{Sr}}^{+}$ core ion. The subspace spanning the basis of the master equation [Eq. (6)] is indicated by the light-blue box.

Figure 2

Schematic diagram of the apparatus. The inset shows the three-photon excitation scheme employed.

Figure 3

(a) Calculated complex eigenenergies between the $4d{}^{2}D$ and the $5p{}^{2}P$ ionization thresholds. Yellow (light gray) dots: extended continuum states; green (gray) dots: $5p_{j_1}n{p}_{j_2}$ autoionizing resonances; red (black) dots: $5p_{j_1}n{f}_{j_2}$ autoionizing resonances. The top frame shows a blow-up of the region near the $5p{}^{2}P$ threshold. (b) Autoionization lifetimes of the $5p_{1/2}n{\ell }_j$ eigenstates as a function of effective quantum number $n_{\mathrm{eff}}$.

Figure 4

Measured (dots) and calculated (line) Rydberg atom loss spectra for (a) the $387{}^{1}P_1$ and (b) $384{}^{1}F_3$ states as the 422 nm autoionizing laser is scanned across the $5s{}^{2}S_{1/2}\to 5p{}^{2}P_{1/2}$ core-ion transition. The duration of the 422 nm laser pulse is 140 ns. The calculated excitation spectra at the end of the core-excitation pulse starting from (c) the $5s5p{}^{1}P_1$ state and (d) the $5s5f{}^{1}F_3$ state. While the excitation spectra [(c),(d)] are time dependent, the surviving Rydberg populations [(a),(b)] are evaluated in the stationary limit after all doubly excited states have decayed radiatively or via autoionization.

Figure 5

Measured (filled symbols) and calculated (open symbols) widths of (a) $5p_{1/2}n{p}_j$ and (b) $5p_{1/2}n{f}_j$ autoionization features as a function of $1/n_{\mathrm{eff}}^3$. For $5snp{}^{1}P$, the data are fitted separately for the measured (solid line) and the simulated (dashed line) results, while a single linear fit is performed for $5snf{}^{1}F$. The extrapolation $n_{\mathrm{eff}}^{-3}\to 0$ provides an estimate for the radiative decay rate of the isolated core ion.

Figure 6

Measured (filled symbols) and calculated (open symbols) detuning of the $5s{}^{2}S_{1/2}\to 5p{}^2{P}_{3/2}$ core-ion transition as a function of $1/n_{\mathrm{eff}}^3$. The dashed lines show linear fits to the data.

Figure 7

Rydberg atom loss spectrum for the $5s320p{}^{1}P_1$ state obtained using a high 422 nm (core-exciting) laser power ($\sim 8$ mW) and a 500-ns-long excitation pulse. For reference, the upper scale indicates the positions of neighboring $nP$ states.

Figure 8

Number of surviving Rydberg atoms as a function of the duration of the 422 nm core-exciting laser pulse for the (average) laser powers indicated. The symbols and the lines are the measured data and the simulated results, respectively. The initial state is $5s320p{}^{1}P_1$.

Figure 9

(a) Calculated $L$ distribution as a function of pump-pulse duration $T_p$ when the initial $5s320p{}^{1}P_1(M_J=1)$ state is subject to a pump pulse with a field strength of $1.8\mathrm{mV}{\mathrm{cm}}^{-1}$ (see text). (b) Measured fraction of $5s320p{}^{1}P_1$ Rydberg atoms that survives as a function of the duration of the pump pulse (see text) for the 422 nm core-excitation laser powers indicated. The 422 nm laser pulse is 100 ns long. (c) Calculated autoionization rates for $L=1$, $L=3$, and $L>3$ weighted by the $L$-state population in (a) as a function of pump-pulse duration $T_p$.

Figure 10

Left column: Excitation spectra for “$5s310f{}^{1}F_3$” initial states recorded using identical laser powers in the presence of the dc fields indicated (note the change in scale of the vertical axis). The positions of the vertical lines represent the energy of the field-dressed “$5s310f{}^{1}F_3$” state and its height represents the overlap between the field-dressed and the field-free $5s310f{}^{1}F_3$ states. Right column: Rydberg atom autoionization loss spectra recorded with the Rydberg excitation lasers tuned to the points indicated by the lines in the corresponding excitation spectra.