Topologically-enforced bifurcations in superconducting circuits

Abstract

The relation of topological insulators and superconductors and the field of nonlinear dynamics is widely unexplored. To address this subject, we adopt the linear coupling geometry of the Su-Schrieffer-Heeger model, a paradigmatic example for a topological insulator, and render it nonlinearly in the context of superconducting circuits. As a consequence, the system exhibits topologically-enforced bifurcations as a function of the topological control parameter, which finally gives rise to chaotic dynamics, separating phases which exhibit clear topological features.

5 pages, 3 figures, supplementary information; comments are welcome

References in corpus (3)

• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Topological Bogoliubov excitations in inversion-symmetric systems of interacting bosons

Cited by in corpus (15)

• Observation and control of nonlinear electromagnetic topological edge states
• Topological Zak Phase in Strongly-Coupled LC Circuits
• Stability of topological edge states under strong nonlinear effects
• Topological phases of polaritons in a cavity waveguide
• Engineering of topological state transfer and topological beam splitter in an even-size Su-Schrieffer-Heeger chain
• Signatures of a 4$\pi$-periodic supercurrent in the voltage response of capacitively shunted topological Josephson junctions
• Dynamical symmetries of periodically-driven quantum systems and their spectroscopic signatures
• Topological synchronization of quantum van der Pol oscillators
• Discontinuities in driven spin-boson systems due to coherent destruction of tunneling: breakdown of the Floquet-Gibbs distribution
• Transition from topological to chaos in the nonlinear Su-Schrieffer-Heeger model
• Topological edge solitons and their stability in a nonlinear Su-Schrieffer-Heeger model
• Topological inheritance in half-SSH Hubbard models
• Generalized Su-Schrieffer-Heeger model in one dimensional optomechanical arrays
• Random-walk topological transition revealed via electron counting
• Topological interface states mediated by spontaneous symmetry breaking