Optimal excitation transfer in two-dimensional lattices of Rydberg atoms

Abstract: We investigate perfect transfer of an excitation in networks of 4 to 8 Rydberg atoms via dipole-dipole interaction. We demand that the excitation is transferred between a given pair of an input and an output site with the highest possible efficiency and as fast as possible. Existing experiments motivate a restriction to networks with atoms located on a two-dimensional lattice. We start with an analysis of all possible configurations on lattice sizes accessible with our computational power. In this framework, we do not find any configurations that exhibit 100\% transport efficiency. In a second step, we therefore remove the lattice condition and allow the atoms to be placed continuously in two-dimensional space. Indeed, a discrete and finite set of "perfect" configurations, i.e. ones which provide 100\% efficiency on short timescales, is found.\\
As a consequence of this, we ask the question why our numerical optimization results in a set of single perfect configurations, but not in continuous, parameterized families of such configurations. To tackle this problem, we derive a simple formula which predicts the dimension of the space of solutions in our problem. It states that for two dimensions, i.e. if we place the atoms in two-dimensional space, only a discrete set of solutions exists, whereas it yields a certain number of free parameters in three dimensions. These predictions are reproduced with an analysis of the Hessian that describes the infinitesimal neighborhood of a perfect configuration

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch
• Notes: Albert-Ludwigs-Universität Freiburg, Bachelorarbeit, 2017

Classification and Topics

• Classification: Physik
• Keyword: Rydberg-Zustand ; Atom

Contributors, Places and Time

• Event: Veröffentlichung
• (where): Freiburg
• (who): Universität
• (when): 2018
• Creator: Bäuerle, Dominik
• Contributor: Albert-Ludwigs-Universität Freiburg. Fakultät für Mathematik und Physik ; Albert-Ludwigs-Universität Freiburg

Further information

• DOI: 10.6094/UNIFR/14600
• URN: urn:nbn:de:bsz:25-freidok-146003
• Rights: Kein Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 14.08.2025, 10:57 AM CEST