Dynamical Fractal in Quantum Gases with Discrete Scaling Symmetry

Chao Gao, Hui Zhai, and Zhe-Yu Shi
Phys. Rev. Lett. 122, 230402 – Published 12 June 2019

Abstract

Inspired by the similarity between the fractal Weierstrass function and quantum systems with discrete scaling symmetry, we establish general conditions under which the dynamics of a quantum system will exhibit fractal structure in the time domain. As an example, we discuss the dynamics of the Loschmidt amplitude and the zero-momentum occupation of a single particle moving in a scale invariant 1/r2 potential. In order to show these conditions can be realized in ultracold atomic gases, we perform numerical simulations with practical experimental parameters, which shows that the dynamical fractal can be observed in realistic timescales. The predication can be directly verified in current cold atom experiments.

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  • Received 31 January 2019

DOI:https://doi.org/10.1103/PhysRevLett.122.230402

© 2019 American Physical Society

Physics Subject Headings (PhySH)

  1. Physical Systems
General Physics

Authors & Affiliations

Chao Gao1,*, Hui Zhai2, and Zhe-Yu Shi3,†

  • 1Department of Physics, Zhejiang Normal University, Jinhua, 321004, China
  • 2Institute for Advanced Study, Tsinghua University, Beijing, 100084, China
  • 3School of Physics and Astronomy, Monash University, Victoria 3800, Australia

  • *gaochao@zjnu.edu.cn
  • zheyu.shi@monash.edu

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Issue

Vol. 122, Iss. 23 — 14 June 2019

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