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arXiv:1510.07003 · Physical Review Letters

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

Michael Schlagmüller, Tara Cubel Liebisch, Huan Nguyen, G. Lochead, Felix Engel, Fabian Böttcher, Karl M. Westphal, K. S. Kleinbach, Robert Löw, Sebastian Hofferberth, Tilman Pfau, Jesús Pérez‐Ríos, Chris H. Greene

Published Feb 1, 2016• 70 citations
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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, 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^{-}-Rb(5S) scattering, which significantly modifies the interaction potential. With a peak density of 5.5×10^{14} cm^{-3}, and therefore an interparticle 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, pointlike particles, with binding energies associated with their ion-neutral separation, and good agreement is found.

DOI
10.1103/physrevlett.116.053001

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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^{-}-Rb(5S) scattering, which significantly modifies the interaction potential. With a peak density of 5.5×10^{14} cm^{-3}, and therefore an interparticle 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, pointlike particles, with binding energies associated with their ion-neutral separation, and good agreement is found.
A single Rydberg atom impurity excited in a BEC is a system that can be utilized to measure the quantum mechanical properties of electron - neutral scattering andthe electron probability density of a Rydberg atom. The Rydberg electron – neutral atom scattering process, is a fundamental scattering process, which can be described via Fermi’s pseudopotential as V{vec{r},vec{R} )=2pi textit{a}[k(R)]delta^{(3)}(vec{r}-vec{R}). The scattering length is dependent on the momentum of the Rydberg electron, and therefore is dependent on the separation of the Rydberg electron from the ion core. At the classical outermost turning point of the electron, it has the slowest momentum leading to s-wave dominated scattering potentials 10’s of MHz in depth for n<40 (Greene et al. PRL 85 2458 (2000), Bendkowsky et al. PRL 105 163201 (2010)). In alkali atoms there is a shape resonance for p-wave scattering, which becomes relevant at ion-neutral separations of ~75nm (I.I. Fabrikant J.Phys B 19, 1527 (1985)). This shape resonance potential is several GHz deep, spanning the energy level spacing between n and n-1 principal quantum numbers. At high BEC densities of 5x10^14cm-3 the nearest neighbor spacing is less than 70nm. A Rydberg atom excited within a BEC, is an excitation of the Rydberg atom and all N neutral atoms located within the Rydberg orbit, described as nS+N x 5S. The nS+N x 5S state is density shifted from the Rydberg resonance. Not only does the distribution of atoms within the Rydberg orbit lead to a density shift, but, at these high densities, atoms excited in the nS+N x 5S state near the shape resonance potential cause large perturbations to the density shift, leading to a line broadening. Therefore the spectroscopic line shape of a Rydberg atom in a BEC allows us to probe the theoretically calculated p-wave shape resonance potential. Furthermore, we can observe and measure the dynamics of neutrals excited in the nS+N x 5S state. In the ultracold regime of a BEC, the background neutral atoms within the Rydberg orbit have kinetic energies of a few kHz, and experience large forces due to the GHz-deep shape resonance potentials. An atom dragged into this deep potential leads to an exothermic state-changing collision. We measure the timescale of this state-changing collision and compare to semi-classical calculations of the neutral atoms evolving in the potential of the two-particle nS+ 5S system. We also measure the change in energy from the original nS state to the product state, (n-4)L (L<3). On time scales shorter than the state-changing collisions, which for n<100 is on the order of 10 microseconds, the neutral atoms will evolve and collect in the shallower electron-neutral potentials, which mimic the electron probability density of the Rydberg atom.With n<100, the Rydberg atom has a diameter greater than 2 micrometers. With an imaging system with <1 micrometer resolution, we expect to observe a macroscopic change in the density profile of the BEC indicating an nS versus nD Rydberg state. The BEC would serve as a contrast agent for observing textbook atomic wavefunctions (Karpiuk et al. New Journal of Physics 17, 053046 (2015)).
A single Rydberg excitation in the high-density and low-temperature environment of a Bose-Einstein condensate (BEC) leads to a fascinating testbed of low-energy electron-neutral and ion-neutral scattering. In particular the small interparticle spacing in a BEC makes it possible to study the role of ion-neutral interactions in l-changing collisions on time scales much shorter than the Rydberg lifetime. We take advantage of the mean field density shift, caused by elastic electron-neutral collisions, to probe density dependent shells of the 87^{87}87Rb BEC and thereby measure the l-changing collision time versus density and principal quantum number. We report on l-changing collisions due to inelastic scattering of the Rydberg electron with a neutral atom located near the Rydberg ionic core. We measure timescales of both the l-changing collision and the Rb2_{2}2​ molecule formation of less than one microsecond for n <<< 100 at the highest BEC densities. We extract a change in kinetic energy of the Rydberg atoms that matches well with the energy gap to the next-lowest manifold. We measure Rb2_{2}2​ signal that decreases with increasing principal quantum number. The mechanism and timescales of the l-changing collision are compared with simulations including the motion of the ionic core and neutral atoms, as well as the Rydberg electron.
We present a novel spectroscopic method for probing the \insitu~density of quantum gases. We exploit the density-dependent energy shift of highly excited {Rydberg} states, which is of the order 101010\MHz\,/\,1E14\,cm-3^{\text{-3}}-3 for \rubidium~for triplet s-wave scattering. The energy shift combined with a density gradient can be used to localize Rydberg atoms in density shells with a spatial resolution less than optical wavelengths, as demonstrated by scanning the excitation laser spatially across the density distribution. We use this Rydberg spectroscopy to measure the mean density addressed by the Rydberg excitation lasers, and to monitor the phase transition from a thermal gas to a Bose-Einstein condensate (BEC).
The level structure of negative-ions near the electron detachment limit dictates the low-energy scattering of an electron with the parent neutral atom. We demonstrate that a single ultracold atom bound inside a Rydberg orbit forming an ultralong-range Rydberg molecule provides an atomic-scale system which is highly sensitive to electron-neutral scattering and thus allows for detailed insights into the underlying near-threshold anion states. Our measurements reveal the so far unobserved fine structure of the 3PJ^3P_J3PJ​ triplet of Rb−^-− and allow us to extract parameters of the associated ppp-wave scattering resonances which deviate from previous theoretical estimates. Moreover, we observe a novel alignment mechanism for Rydberg molecules mediated by spin-orbit coupling in the negative ion.
Abstract We discuss the density shift and broadening of Rydberg spectra measured in cold, dense atom clouds in the context of Rydberg atom spectroscopy done at room temperature, dating back to the experiments of Amaldi and Segrè in 1934. We discuss the theory first developed in 1934 by Fermi to model the mean-field density shift and subsequent developments of the theoretical understanding since then. In particular, we present a model whereby the density shift is calculated using a microscopic model in which the configurations of the perturber atoms within the Rydberg orbit are considered. We present spectroscopic measurements of a Rydberg atom, taken in a Bose–Einstein condensate and thermal clouds with densities varying from 5 × 10 14 to 9 × 10 12 cm −3 . The density shift measured via the spectrum’s center of gravity is compared with the mean-field energy shift expected for the effective atom cloud density determined via a time of flight image. Lastly, we present calculations and data demonstrating the ability of localizing the Rydberg excitation via the density shift within a particular density shell for high principal quantum numbers.
Rydberg atoms immersed in a Bose-Einstein condensate interact with the quantum gas via electron-atom and ion-atom interaction. To suppress the typically dominant electron-neutral interaction, Rydberg states with a principal quantum number up to n=190 are excited from a dense and tightly trapped micron-sized condensate. This allows us to explore a regime where the Rydberg orbit exceeds the size of the atomic sample by far. In this case, a detailed line shape analysis of the Rydberg excitation spectrum provides clear evidence for ion-atom interaction at temperatures well below a microkelvin. Our results may open up ways to enter the quantum regime of ion-atom scattering for the exploration of charged quantum impurities and associated polaron physics.