Tracking Rydberg atoms with Bose-Einstein condensates

Abstract

We propose to track position and velocity of mobile Rydberg excited impurity atoms through the elastic interactions of the Rydberg electron with a host condensate. Tracks first occur in the condensate phase, but are then naturally converted to features in the condensate density or momentum distribution. The condensate thus acts analogous to the cloud or bubble chambers in the early days of elementary particle physics. The technique will be useful for exploring Rydberg-Rydberg scattering, rare inelastic processes involving the Rydberg impurities, coherence in Rydberg motion and forces exerted by the condensate on the impurities. Our simulations show that resolvable tracks can be generated within the immersed Rydberg life time and condensate heating is under control. Finally we demonstrate the utility of this Rydberg tracking technique to study ionizing Rydberg collisions or angular momentum changing interactions with the condensate.

Dynamics of atoms within atoms

“…Also the highly oscillatory character that is inherited from the radial part of the Rydberg wavefunction poses numerical challenges. This can be partly alleviated by replacing the Rydberg-electron wavefunction with a classical approximation [30], as discussed in [16]. To this end, we consider a third potential, referred to as "classical approximation of s-wave" (CASW), in which we replace (1) for ion at the origin by…”

“…where ρ Q (R) = |ψ(R)| 2 and ρ cl (R) (see Appendix B) are the quantum and classical electron probability densities respectively, as used in Ref. [16], R ct is the outer classical turning point and R min ≈ 0.1µm or ≈ 1900a 0 . The latter is the distance of the Rydberg nucleus from the shape resonance in electron-87 Rb scattering for the | νl = | 133s Rydberg state, as indicated in figure 1(c).…”

“…In the Raman-Nath approximation, the initial effect of the Rydberg impurity is then to imprint a phase ϕ(R) = −V ryd (R)∆t/ within a short time ∆t [37,15] while leaving the density relatively unaffected. Only with some delay will phase gradients, corresponding to initially imparted momentum, be converted into variations of condensate density through motion of the groundstate atoms [16]. For a numerically and conceptually tractable model, we ignore the backaction on the Rydberg impurity in the present study.…”

“…The Rydberg electron affects the Bose-Einstein condensate by imprinting a phase on its mean field wave function at short times, which evolves into density waves at later times. It has been suggested to use these features for tracking the motion, detecting the position and deducing or decohering the quantum state of isolated Rydberg impurities [15,16,17,18,19]. However, for these proposals a detailed understanding of the joint BEC and Rydberg impurity dynamics is required.…”

“…Earlier studies have shown that a Rydberg impurity excited in a BEC will result in condensate heating [9,17,16] that increases with the number of repeated excitations. Since the Rydberg electron interacts only with the condensate atoms present in its orbit, this effect is, on short time-scales, localized within the orbit, and, as we show here, not strong enough to invalidate mean-field theory.…”