Role of Coulomb antiblockade in the photoassociation of long-range Rydberg molecules

We present a mechanism contributing to the detection of photoassociated long-range Rydberg molecules via pulsed-field ionization: ionic products, created by the decay of a long-range Rydberg molecule, modify the excitation spectrum of surrounding ground-state atoms and facilitate the excitation of further atoms into Rydberg states by the photoassociation light. Such an ion-mediated excitation mechanism has been previously called a Coulomb antiblockade. Pulsed-field ionization typically does not discriminate between the ionization of a long-range Rydberg molecule and an isolated Rydberg atom, and thus the number of atomic ions detected by this mechanism is not proportional to the number of long-range Rydberg molecules present in the probe volume. By combining high-resolution UV and rf spectroscopy of a dense, ultracold gas of cesium atoms, theoretical modeling of the molecular-level structures of long-range Rydberg molecules bound below $n{}^{2}P_{3/2}$ Rydberg states of cesium, and a rate model of the photoassociation and decay processes, we unambiguously identify the signatures of this detection mechanism in the photoassociation of long-range Rydberg molecules bound below atomic asymptotes with negative Stark shifts.

Figure 1

Left column: Schematic depiction of the three mechanisms by which long-range Rydberg molecules are detected in this work (filled circle: atom; overlapping circles: molecule; blue symbol: excited atom/molecule; red symbol: ionized atom/molecule; PFI: pulsed-field ionization; AI: molecular autoionization; Fac.: ion-facilitated excitation), for details see text. Right-hand column: Illustration of the corresponding time-vs-charge traces recorded in the experiments ($I$: detector current, $t$: time of flight of the ion).

Figure 2

Stark shift of the $40{}^{2}P_{3/2}$ Rydberg state (black: $\mathrm{\Omega }=1/2$; red: $\mathrm{\Omega }=3/2$) in the spherical Coulomb potential of an ion at distance $R$, calculated following Refs. [16, 17]. The opaque bands illustrate the effect of an (exaggerated) excitation bandwidth of $4\mathrm{M}\mathrm{Hz}$. Inset: Artistic impression of the facilitation shell with radius $R_{\mathrm{fac}}$ and thickness $\mathrm{\Delta }{R}_{\mathrm{fac}}$ surrounding an ion (red ball) in a gas of ground-state atoms (gray balls).

Figure 3

Ion signals detected after a photoassociation pulse with a length of $6.5\mu \mathrm{s}$ [(a) and (c)] and $27\mu \mathrm{s}$ [(b) and (d)], respectively, with frequencies below the atomic transition $40{}^{2}P_{3/2}\leftarrow 6{}^{2}S_{1/2}(F=3)$. (a, b) (black line) Signal detected in the time-of-flight window for ${\mathrm{Cs}}^{+}$ ions created by pulsed-field ionization as function of the detuning of the UV-laser frequency from the atomic transition. (gray line) Gaussian line profiles fitted to the experimental spectrum, see Sec. 4 for details. (dashed-red line) Sum of all Gaussian line profiles. (c, d) (black line) Signal detected in the time-of-flight window for $\mathrm{Cs}{{}_2}^{+}$ ions created by autoionization, other lines as in (a). Black and red-dashed curves have been vertically offset for clarity.

Figure 4

Fractional population in the $39{}^{2}D_{5/2}$ state after 15 $\mu \mathrm{s}$ of photoassociation followed by $2\mu \mathrm{s}$ of rf transfer (blue: zero transfer; yellow: maximal transfer) as a function of the detuning of the UV laser from the atomic transition $40{}^{2}P_{3/2}\leftarrow 6{}^{2}S_{1/2}(F=3)$ and the detuning of the rf field from the atomic transition $39{}^{2}D_{5/2}\leftarrow 40{}^{2}P_{3/2}$. Dashed line: Transition frequencies for dissociation of LRMs. Dotted line: Transition frequencies for transfer of isolated Rydberg atoms.

Figure 5

Left panel: (thick lines) Calculated potential-energy curves (PECs) correlated to the asymptote $40{}^{2}P_{3/2}\text{−}6{}^{2}S_{1/2}(F=3)$. (Filled curves) Vibrational wave functions of selected levels with normalized peak heights, scaled by a global factor to be displayed on the same scale as the PECs and offset by the binding energy of the level. (Horizontal, thin lines): Binding energies of all vibrational levels. Right-hand side panel: (black line) Expected experimental spectrum, simulated as described in the text. (Horizontal, thin lines): Binding energy of all vibrational levels.

Figure 6

Experimentally detected ion signals in the time-of-flight windows set for detection of ions produced by PFI (blue dots) and autoionization (orange dots) vs time of the PFI pulse (with respect to the beginning of the photoassociation pulse) for two selected resonances at the indicated detuning from the atomic transition $40{}^{2}P_{3/2}\leftarrow 6{}^{2}S_{1/2}(F=3)$. The data is compiled from two experimental sequences: In sequence 1 the length of the photoassociation pulse was varied up to $5\mu \mathrm{s}$, followed directly by the PFI pulse, while in sequence 2 the length of the photoassociation pulse was kept fixed at $5\mu \mathrm{s}$ and an additional delay was inserted before PFI. Solid lines are results of weighted fits of the rate model (3) to the combined data set: (blue) $N_{\mathrm{LRM}}\left(t\right)+N_{\mathrm{Fac}}\left(t\right)$, (orange) $N_{{\mathrm{Cs}}_2^{+}}\left(t\right)$, (green) only $N_{\mathrm{LRM}}\left(t\right)$.

Figure 7

Extracted facilitation rates for photoassociation resonances below $31{}^{2}P_{3/2}$ (blue) and $40{}^{2}P_{3/2}$ (orange) as a function of the effective detuning from the atomic resonance (see text for details). The gray line is a fit of the analytical model described in the text, and the gray band indicates the $95\%$ confidence interval.