Lattices in Circuit Quantum Electrodynamics: A Platform for Nonequilibrium Quantum Simulation

Devin Underwood, Will Shanks, Andy C. Y. Li +4 more

Guillermo Romero, E. Solano, Lucas Lamata

James J. Raftery

Alicia J. Kollár, Mattias Fitzpatrick, Andrew Houck

Oliver Viehmann, Jan von Delft, Florian Marquardt

Abstract We study several dynamical properties of a recently proposed implementation of the quantum transverse-field Ising chain in the framework of circuit quantum electrodynamics (QED). Particular emphasis is placed on the effects of disorder on the nonequilibrium behavior of the system. We show that small amounts of fabrication-induced disorder in the system parameters do not jeopardize the observation of previously predicted phenomena. Based on a numerical extraction of the mean free path of a wave packet in the system, we also provide a simple quantitative estimate for certain disorder effects on the nonequilibrium dynamics of the circuit QED quantum simulator. We discuss the transition from weak to strong disorder, characterized by the onset of Anderson localization of the system's wave functions, and the qualitatively different dynamics it leads to.

Alicia J. Kollár, Mattias Fitzpatrick, Andrew Houck

Abstract After two decades of development, cavity quantum electrodynamics with superconducting circuits has emerged as a rich platform for quantum computation and simulation. Lattices of coplanar waveguide resonators constitute artificial materials for microwave photons, in which interactions between photons can be incorporateded either through the use of nonlinear resonator materials or through coupling between qubits and resonators. Here we make use of the previously overlooked property that these lattice sites are deformable and permit tight-binding lattices that are unattainable even in solid-state systems. We show that networks of coplanar waveguide resonators can create a class of materials that constitute lattices in an effective hyperbolic space with constant negative curvature. We present numerical simulations of hyperbolic analogues of the kagome lattice that show unusual densities of states in which a macroscopic number of degenerate eigenstates comprise a spectrally isolated flat band. We present a proof-of-principle experimental realization of one such lattice. This paper represents a step towards on-chip quantum simulation of materials science and interacting particles in curved space.