Proceedings Article | 3 August 2016
Tara Liebisch, Michael Schlagmüller, Felix Engel, Karl Westphal, Kathrin Kleinbach, Fabian Böttcher, Robert Loew, Sebastian Hofferberth, Tilman Pfau, Jesus Perez-Rios, Chris Greene
KEYWORDS: Chemical species, Scattering, Ions, Spectroscopy, Imaging systems, Image resolution, Neodymium, Physics, Quantum optics, Current controlled current source
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)).
