Topological Zak Phase in Strongly-Coupled LC Circuits

Abstract

We show the emergence of topological Bogoliubov bosonic excitations in the relatively strong coupling limit of an LC (inductance-capacitance) one-dimensional quantum circuit. This dimerized chain model reveals a ${\mathcal{Z}}_2$ local symmetry as a result of the counter-rotating wave (pairing) terms. The topology is protected by the sub-lattice symmetry, represented by an anti-unitary transformation. We present a methos to measure the winding of the topological Zak phase across the Brillouin zone by a reflection measurement of (microwave) light. Our method probes bulk quantities and can be implemented even in small systems. We study the robustness of edge modes towards disorder.

arXiv comment4 figures

References in corpus (30)

• Topological Insulators
• Topological Photonics
• Quantized Electric Multipole Insulators
• Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Lasing in topological edge states of a 1D lattice
• Topological Semimetals
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Observation of the topological soliton state in the Su-Schrieffer-Heeger model
• Topological chiral magnonic edge mode in a magnonic crystal
• Time-reversal symmetry breaking in circuit-QED based photon lattices
• Time Reversal Invariant Topologically Insulating Circuits
• Topological properties of linear circuit lattices
• Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons
• Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
• Observation of topological transitions in interacting quantum circuits
• Quantum Non-Demolition Detection of Strongly Correlated Systems
• Measurement of the Zak phase of photonic bands through the interface states of metasurface/photonic crystal
• Chiral Bogoliubons in Nonlinear Bosonic Systems
• On the phase transition of light in cavity QED lattices
• Many-Body Quantum Electrodynamics Networks: Non-Equilibrium Condensed Matter Physics with Light
• A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions
• Measuring topological invariants from generalized edge states in polaritonic quasicrystals
• Anomalous Hall Effects of Light and Chiral Edge Modes on the Kagome Lattice
• Kerr coefficients of plasma resonances in Josephson junction chains
• A two-leg Su-Schrieffer-Heeger chain with glide reflection symmetry
• Topological nodal points in two coupled SSH chains
• Topological Bogoliubov excitations in inversion-symmetric systems of interacting bosons
• Direct cavity detection of Majorana pairs
• Topologically-enforced bifurcations in superconducting circuits

Cited by in corpus (31)

• Topological Photonics
• Higher-Order Topological Insulator in Twisted Bilayer Graphene
• Unconventional quantum optics in topological waveguide QED
• Quantum electrodynamics in a topological waveguide
• Gain and loss induced topological insulating phase in a non Hermitian electrical circuit
• Topologically Enhanced Harmonic Generation in a Nonlinear Transmission Line Metamaterial
• Topolectric circuits: Theory and construction
• 4D spinless topological insulator in a periodic electric circuit
• Topological nodal states in circuit lattice
• Topological circuits of inductors and capacitors
• Observation of Antichiral Edge States in a Circuit Lattice
• Topology and retardation effect of a giant atom in a topological waveguide
• Boundary states of 4D topological matter: Emergence and full 3D-imaging of nodal Seifert surfaces
• Topology-dependent quantum dynamics and entanglement-dependent topological pumping in superconducting qubit chains
• Strongly Nonlinear Topological Phases of Cascaded Topoelectrical Circuits
• Fluxon-Based Quantum Simulation in Circuit QED
• Entangling two giant atoms via a topological waveguide
• Wavefront dislocations reveal the topology of quasi-1D photonic insulators
• A controllable two-qubit swapping gate using superconducting circuits
• Two-point spectroscopy of Fibonacci topoelectrical circuits
• Direct measurement of topological invariants through temporal adiabatic evolution of bulk states in the synthetic Brillouin zone
• Observation of dynamical topology in 1D
• Valley-Chern Effect with LC-Resonators: A Modular Platform
• Soliton metacrystals: topology and chirality
• Light-matter correlations in Quantum Floquet engineering of cavity quantum materials
• Spectroscopy and topological properties of a Haldane light system
• Non-Hermitian Topoelectrical Circuits: Expedient Tools for Topological State Engineering with Gain-Loss Modulation
• Topological bosonic Bogoliubov excitations with sublattice symmetry
• Pancharatnam-Zak phase
• Screened topological plasmons in graphene plasmonic crystals
• Nonlinearity-driven Topology via Spontaneous Symmetry Breaking