Modeling many-particle mechanical effects of an interacting Rydberg gas

In a recent work [Phys. Rev. Lett. 98, 023004 (2007)], we investigated the influence of the attractive van der Waals interaction on the pair distribution and Penning ionization dynamics of ultracold Rydberg gases. Here we extend this description to atoms initially prepared in Rydberg states exhibiting repulsive interaction. We present calculations based on a Monte Carlo algorithm to simulate the dynamics of many atoms under the influence of both repulsive and attractive long-range interatomic forces. Redistribution to nearby states induced by blackbody radiation is taken into account, changing the effective interaction potentials. The model agrees with experimental observations, where the ionization rate is found to increase when the excitation laser is blue detuned from the atomic resonance.

Figure 1

(Color online) (a) Rydberg atoms excited in a repulsive potential. Blackbody photons can transfer one atom to a dipole-coupled state, allowing for attractive interaction. (b) One-dimensional calculation of particle trajectories to illustrate the idea of many-particle repulsive interaction. When all particles have the same (large) initial distance from their neighbors, they will be only slightly repelled (left graph). When some close pairs exist in the beginning, there will repeatedly be atoms coming close to each other over a long time scale (right graph). Here an average initial distance of $8\mu \text{m}$ and a van der Waals potential with $C_6=-{10}^{21}\text{a}\text{.u}\text{.}$ are assumed.

Figure 2

(Color online) Expected collisional ionization when exciting in a repulsive potential. The upper graphs show the Rydberg signal directly after excitation, including a Lorentz fit to determine the excitation fraction and saturation to be used in the model. The other graphs show the ion signal detected after various delays. The corresponding simulated signals are plotted as bold (blue) lines. $n=\left(\text{a}\right)40$, (b) $60$, and (c) $82$.