Quantum Simulation of Hyperbolic Space with Circuit Quantum Electrodynamics: From Graphs to Geometry

by Dr Igor Boettcher (University of Maryland)

Wednesday 30 Oct 2019, 16:15 → 17:45 Europe/Berlin

Looking for some fresh bathroom tiles? Why don't you try regular 7-gons this time, it looks really cool! Only requirement: You'd need to live in hyperbolic space of constant negative curvature. To see how this would be like, let me take you onto a journey into hyperbolic space through recent breakthrough experiments in circuit quantum electrodynamics, where such tilings are realized with superconducting resonators and photons are tricked into believing that space is hyperbolic. I will show how these
finite lattice geometries can be mapped onto quantum field theories in continuous negatively curved space. We use this as a computational tool to quantitatively reproduce ground state energy, spectral gap, and correlation functions of the noninteracting lattice system by means of analytic formulas on the Poincare disk, and show how conformal symmetry emerges for large lattices. This sets the stage for studying interactions and disorder on hyperbolic graphs, and to resolve fundamental open problems at the interface of interacting many-body systems, quantum field theory in curved space, and quantum gravity using tabletop experiments.