Time fractals and discrete scale invariance with trapped ions
Abstract
We show that a one-dimensional chain of trapped ions can be engineered to produce a quantum mechanical system with discrete scale invariance and fractal-like time dependence. By discrete scale invariance we mean a system that replicates itself under a rescaling of distance for some scale factor, and a time fractal is a signal that is invariant under the rescaling of time. These features are reminiscent of the Efimov effect, which has been predicted and observed in bound states of three-body systems. We demonstrate that discrete scale invariance in the trapped ion system can be controlled with two independently tunable parameters. We also discuss the extension to n-body states where the discrete scaling symmetry has an exotic heterogeneous structure. The results we present can be realized using currently available technologies developed for trapped ion quantum systems.
Keywords
Cite
@article{arxiv.1901.01661,
title = {Time fractals and discrete scale invariance with trapped ions},
author = {Dean Lee and Jacob Watkins and Dillon Frame and Gabriel Given and Rongzheng He and Ning Li and Bing-Nan Lu and Avik Sarkar},
journal= {arXiv preprint arXiv:1901.01661},
year = {2019}
}
Comments
4 + 5 pages (main + supplemental materials), 2 + 3 figures (main + supplemental materials), version to appear in Physical Review A Rapid Communications