Probing an Electron Scattering Resonance using Rydberg Molecules within a Dense and Ultracold Gas

We present spectroscopy of a single Rydberg atom excited within a Bose-Einstein condensate. We not only observe the density shift as discovered by Amaldi and Segrè in 1934, but a line shape that changes with the principal quantum number $n$. The line broadening depends precisely on the interaction potential energy curves of the Rydberg electron with the neutral atom perturbers. In particular, we show the relevance of the triplet $p$-wave shape resonance in the $e^{-}\text{−}\mathrm{Rb}(5S)$ scattering, which significantly modifies the interaction potential. With a peak density of $5.5\times {10}^{14}{\mathrm{cm}}^{-3}$, and therefore an interparticle spacing of $1300a_0$ within a Bose-Einstein condensate, the potential energy curves can be probed at these Rydberg ion-neutral atom separations. We present a simple microscopic model for the spectroscopic line shape by treating the atoms overlapped with the Rydberg orbit as zero-velocity, uncorrelated, pointlike particles, with binding energies associated with their ion-neutral separation, and good agreement is found.

Figure 1

Potential energy curves around the $40S+5S$ state. The red color indicates the $S$ character of the state and, therefore, the probability to excite into this state due to the selection rules. The butterfly shape resonance [15] has an anticrossing with the $40S+5S$ at around $1200a_0$. Neutral perturbers inside this region can shift the resonance frequency tens of MHz or more, therefore causing significant spectral broadening. The left inset shows a 2D cut through the electron density of a butterfly state at $1175a_0$. The right inset is a zoom in on the crossing of the shape resonance and the $40S+5S$ state.

Figure 2

Simplified schematic of a localized Rydberg excitation in our BEC drawn to scale. A focused infrared laser along the $z$ axis excites Rydberg atoms and determines the excitation volume inside the BEC together with a 420 nm collimated beam along the $y$ axis. The extent of the classical Rydberg electron orbital for the highest Rydberg state under investigation ($111S$) is shown as a tiny solid sphere (cyan) at the very center (closed circle on projection). A simplified level scheme of our two-photon excitation is illustrated in the upper right corner.

Figure 3

Rydberg spectra in the BEC for different principal quantum numbers. The average ion count (black dots) is plotted versus the theory with $s$-wave scattering components only (dashed blue) and the accurate PEC including also $p$-wave components (red) of the $nS+5S$ system, which includes the shape resonance. The zero detuning point is set by measuring the spectral position of the atomic line in a low density of ${10}^{12}{\mathrm{cm}}^{-3}$ and $20\mu K$ thermal cloud, where density and interaction effects can be neglected. The long tail to far red detuning and the signal at positive detuning taken at $40S$ can only be explained by taking the $p$-momentum components into account and therefore the shape resonance.

Figure 4

Potential energy curves of the $40S+5S$ with $s$-wave (blue) momentum components of the Rydberg electron only and including $p$-wave scattering (red). As an example, particles (dots) are placed according to a Poissonian density distribution corresponding to a density of $5\times {10}^{14}{\mathrm{cm}}^{-3}$, resulting in a shift of the resonance of $-25.5\mathrm{MHz}$ for $s$-wave scattering only (blue dots) and $-64.2\mathrm{MHz}$ including also $p$-wave scattering (red dots). The mean interparticle separation at this density is $1300\pm 500a_0$, which corresponds to the mean distance between the Rydberg atom and the nearest neighbor particle.