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SYQC: Symposium Quantum Cooperativity of Light and Matter

SYQC 2: Quantum Cooperativity of Light and Matter - Session 2

SYQC 2.6: Invited Talk

Thursday, March 17, 2022, 15:30–16:00, Audimax

Quantum Fractals — •Cristiane Morais-Smith — Institute for Theoretical Physics, University of Utrecht, The Netherlands

The human fascination for fractals dates back to the time of Christ, when structures known nowadays as a Sierpinski gasket were used in decorative art in churches. Nonetheless, it was only in the last century that mathematicians faced the difficult task of classifying these structures. In the 80’s and 90’s, the foundational work of Mandelbrot triggered enormous activity in the field. The focus was on understanding how a particle diffuses in a fractal structure. However, those were classical fractals. This century, the task is to understand quantum fractals. In 2019, in collaboration with experimental colleagues from the Debye Institute, we realized a Sierpinski gasket using a scanning tunneling microscope to pattern adsorbates on top of Cu(111) and showed that the wavefunction describing electrons in a Sierpinski gasket fractal has the Hausdorff dimension d = 1.58 [1,2]. However, STM techniques can only describe equilibrium properties. Now, we went a step beyond and using state-of-the-art photonics experiments in collaboration with colleagues at Jiao-Tong University in Shanghai, we unveiled the quantum dynamics in fractals. By injecting photons in waveguide arrays arranged in a fractal shape, we were able to follow their motion and understand their quantum dynamics with unprecedented detail. We built and investigated 3 types of fractal structures to reveal not only the influence of different Hausdorff dimension, but also of geometry [3].

[1] S.N. Kempkes, M.R. Slot, S.E. Freeney, S.J.M. Zevenhuizen, D. Vanmaekelbergh, I. Swart, and C. Morais Smith, Design and characterization of electronic fractals, Nature Physics 15, 127 (2019).

[2] Physics Today 72, 1, 14 (2019) https://physicstoday.scitation.org/ doi/full/10.1063/PT.3.4105

[3] X.-Y. Xu, X.-W. Wang, D.-Y. Chen, C. Morais Smith, and X.-M. Jin, Shining light on quantum transport in fractal networks, Nature Photonics 15, 703 (2021).