New publications

Modeling Rydberg Gases using Random Sequential Adsorption on Random Graphs

We have submitted Modeling Rydberg Gases using Random Sequential Adsorption on Random Graphs, and it is currently under review. This is joint work between Daan Rutten and myself. A preprint is available on arXiv.

Abstract

The statistics of strongly interacting, ultracold Rydberg gases are governed by the interplay of two factors: geometrical restrictions induced by blockade effects, and quantum mechanical effcts. To shed light on their relative roles in the statistics of Rydberg gases, we compare three models in this paper: a quantum mechanical model describing the excitation dynamics within a Rydberg gas, a Random Sequential Adsorption (RSA) process on a Random Geometric Graph (RGG), and a RSA process on a Decomposed Random Intersection Graph (DRIG). The latter model is new, and refers to choosing a particular subgraph of a mixture of two other random graphs. Contrary to the former two models, it lends itself for a rigorous mathematical analysis; and it is built speciffcally to have particular structural properties of a RGG. We establish for it a fluid limit describing the time-evolution of number of Rydberg atoms, and show numerically that the expression remains accurate across a wider range of particle densities than an earlier approach based on an RSA process on an Erdos-Renyi Random Graph (ERRG). Finally, we also come up with a new heuristic using random graphs that gives a recursion to describe a normalized pair-correlation function of a Rydberg gas. Our results suggest that even without dissipation, on long time scales the statistics are affected most by the geometrical restrictions induced by blockade effects, while on short time scales the statistics are affected most by quantum mechanical effects.

Preprint

Loader Loading...
EAD Logo Taking too long?

Reload Reload document
| Open Open in new tab

Download

Curious for more?

Head on over to My Articles for more of my work, and check out My Research for a peek into upcoming themes. You can also find out who is on our team right here: Academic Supervision.

Jaron
Jaron
Jaron Sanders received in 2012 M.Sc. degrees in Mathematics and Physics from the Eindhoven University of Technology, The Netherlands, as well as a PhD degree in Mathematics in 2016. After he obtained his PhD degree, he worked as a post-doctoral researcher at the KTH Royal Institute of Technology in Stockholm, Sweden. Jaron Sanders then worked as an assistant professor at the Delft University of Technology, and now works as an assistant professor at the Eindhoven University of Technology. His research interests are applied probability, queueing theory, stochastic optimization, stochastic networks, wireless networks, and interacting (particle) systems.
https://www.jaronsanders.nl