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

Abstract

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 [1], but a line shape which 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 --Rb(5S) scattering, which significantly modifies the interaction potential. With a peak density of 5.5×10 14 cm -3 , and therefore an inter-particle spacing of 1300 a 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, point-like particles, with binding energies associated with their ion-neutral separation, and good agreement is found.A Rydberg atom excited in a dense background gas of atoms provides a testbed of Rydberg electron-neutral atom collisions. Spectroscopy has always been a sensitive technique for studying these collisions and in particular spectroscopy performed in a cold, dense atom sample eliminates most other line broadening mechanisms, thereby isolating the effects of elastic and inelastic electron-neutral atom collisions on the line shape. The realization of ultralong-range Rydberg molecules via elastic electronneutral collisions [2] relies on cold, dense atom samples. Since the first observation [3], Rydberg molecules continue to be realized with increasing experimental control in various potential energy landscapes and atomic species [3][4][5][6][7][8][9][10], where the neutral atom ground state wavefunction is typically bound in the outer one or two potential wells of the electron-atom potential energy curves (PECs). By applying an electric field [11] or by exciting nS states with nearly integer quantum defects, as in Cs [12], more deeply bound trilobite Rydberg molecules [2] are realized. With higher densities of cold atom samples, many neutral atoms overlap with the Rydberg orbit and the bound states become unresolvable [13,14]. By utilizing the high densities of a Bose-Einstein condensate (BEC), the neutral atoms within the Rydberg orbit provide a probe of elastic and inelastic electron-neutral collisions for a large range of ion-neutral separations. We show in this paper that Rydberg spectroscopy in a BEC allows us to probe, with high resolution, the scattering resonance directly for the first time in this temperature regime.In a completely different temperature regime (> 400 K) than the work presented here (< 1 µK), Rydberg spectroscopy done during the 1980s in unpolarized thermal vapors investigated the line shift and line broadening of Rydberg atoms excited in a background gas of the same species atoms at similar densities [15,16]. Subsequent theory work [17][18][19][20] modeled the line shapes b...

Controlling Rydberg atom excitations in dense background gases

“…The scattering potential is affected in the range of approximately 10 meV around the resonance [17,21,59]. Evidence of the p-wave shape resonance was recently observed and modeled via Rydberg spectroscopy in a BEC [34]. The p-wave shape resonance also plays a role in changing the binding energy of longrange Rydberg molecules.…”

“…With such a representation it is straightforward to denote the total energy shift, δ i , of each possible Rydberg excitation within the atomic sample located at r i , [34] as,…”

Theory of excitation of Rydberg polarons in an atomic quantum gas

“…Hence we can neglect the Bose-Bose interactions and Eq. (5) reduces to the simplified, extended Fröhlich model [11]:…”

“…9, we show the experimental spectrum obtained for n = 60 in comparison with the prediction from the FDA (dashed red line) and a classical statistical approach (solid black). In the latter approach, using a classical Monte Carlo (CMC) algorithm [11], we randomly distribute atoms in three-dimensional space around the Rydberg ion such that the correct density profile is obtained. Due to statistical fluctuations in the random sampling of coordinates (sampled from a uniform distribution), the local density within the Rydberg-electron radius fluctuates.…”

“…In the frequency domain, the FDA predicts a Gaussian shape for the intrinsic spectrum, which is a hallmark of Rydberg polarons. A classical Monte Carlo simulation [11] which reproduces the background spectral shape is shown to miss spectral features arising from quantization of bound states. Agreement between * richard.schmidt@cfa.harvard.edu experimental results and FDA theory for both the observed few-body molecular spectra and the many-body polaronic states is excellent.…”