Driving protocol for a Floquet topological phase without static counterpart
arXiv:1704.00306 · doi:10.1088/1367-2630/aa8646
Abstract
Periodically driven systems play a prominent role in optical lattices. In these ultracold atomic systems, driving is used to create a variety of interesting behaviours, of which an important example is provided by topological states of matter. Such Floquet topological phases have a richer classification that their equilibrium counterparts. Although analogues of the equilibrium topological phases exist, which are characterised by a Chern number, the corresponding Hall conductivity, and protected edge states, there is an additional possibility. This is a phase that has vanishing Chern number and no Hall conductivity, but nevertheless hosts anomalous topological edge states. Due to experimental difficulties associated with the observation of such a phase, it has not been experimentally realised so far. In this paper, we show that optical lattices prove to be a good candidate for both its realisation and subsequent observation, because they can be driven in a controlled manner. Specifically, we present a simple shaking protocol that serves to realise this special Floquet phase, discuss the specific properties that it has, and propose a method to experimentally detect this fascinating topological phase that has no counterpart in equilibrium systems.
arXiv comment14 pages, 4 figures
References in corpus (44)
- Topological Insulators
- Many-Body Physics with Ultracold Gases
- Quantum Spin Hall Insulator State in HgTe Quantum Wells
- Experimental realisation of the topological Haldane model
- Floquet Topological Insulator in Semiconductor Quantum Wells
- Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
- Observation of Floquet-Bloch states on the surface of a topological insulator
- Topological characterization of periodically-driven quantum systems
- Atomic quantum gases in periodically driven optical lattices
- The quantum spin Hall effect and topological insulators
- Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
- Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
- Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms
- Realization of Two-Dimensional Spin-orbit Coupling for Bose-Einstein Condensates
- Observation of chiral edge states with neutral fermions in synthetic Hall ribbons
- Topological Quantum Matter with Ultracold Gases in Optical Lattices
- Quantum simulation of frustrated magnetism in triangular optical lattices
- Dynamical control of matter-wave tunneling in periodic potentials
- Visualizing edge states with an atomic Bose gas in the quantum Hall regime
- Tunable gauge potential for neutral and spinless particles in driven lattices
- Observation of photonic anomalous Floquet Topological Insulators
- Photo-Induced Topological Phase Transition and a Single Dirac-Cone State in Silicene
- Superfluid-insulator transition in a periodically driven optical lattice
- Observation of the Meissner effect with ultracold atoms in bosonic ladders
- Experimental reconstruction of the Berry curvature in a topological Bloch band
- Experimental observation of anomalous topological edge modes in a slowly-driven photonic lattice
- Topological singularities and the general classification of Floquet-Bloch systems
- Simulation and detection of Dirac fermions with cold atoms in an optical lattice
- Microscopy of the interacting Harper-Hofstadter model in the few-body limit
- The anomalous Floquet-Anderson insulator as a non-adiabatic quantized charge pump
- In situ observation of strongly interacting ferromagnetic domains in a shaken optical lattice
- Effective Theory of Floquet Topological Transitions
- Direct imaging of topological edge states in cold-atom systems
- Topological index for periodically driven time-reversal invariant 2D systems
- Detecting Chiral Edge States in the Hofstadter Optical Lattice
- Real-space imaging of a topological protected edge state with ultracold atoms in an amplitude-chirped optical lattice
- Driven Electronic States at the Surface of a Topological Insulator
- Floquet Edge States with Ultracold Atoms
- Scattering matrix invariants of Floquet topological insulators
- Effective time-independent description of optical lattices with periodic driving
- Merging and alignment of Dirac points in a shaken honeycomb optical lattice
- Tight binding models for ultracold atoms in honeycomb optical lattices
- Creating topological interfaces and detecting chiral edge modes in a 2D optical lattice
- Dynamical competition between Quantum Hall and Quantum Spin Hall effects
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- Topological Photonics
- Realization of an anomalous Floquet topological system with ultracold atoms
- Measuring topology by dynamics: Chern number from linking number
- Tailoring quantum gases by Floquet engineering
- Anomalous Floquet Insulators
- Hopf characterization of two-dimensional Floquet topological insulators
- Thermalization and Prethermalization in Periodically Kicked Quantum Spin Chains
- Quantized large-bias current in the anomalous Floquet-Anderson insulator
- Prethermalization and Thermalization in Periodically-Driven Many-Body Systems away from the High-Frequency Limit
- Discrete time crystals enforced by Floquet-Bloch scars
- The Floquet Engineer's Handbook
- Strongly Disordered Floquet Topological Systems
- Chiral 1D Floquet topological insulators beyond rotating wave approximation
- Localization counteracts decoherence in noisy Floquet topological chains
- Genesis of the Floquet Hofstadter butterfly
- Counterdiabatic Driving for Periodically Driven Systems
- Hierarchy of many-body invariants and quantized magnetization in anomalous Floquet insulators
- Towards Topological Protection based millimetre wave devices
- Chiral Flow in One-dimensional Floquet Topological Insulators
- Effective vacua for Floquet topological phases: A numerical perspective on switch-function formalism
- Electronic transport in one-dimensional Floquet topological insulators via topological and nontopological edge states
- Anomalous Floquet topological crystalline insulators
- Unconventional Floquet topological phases from quantum engineering of band inversion surfaces
- High-frequency Expansion for Floquet Prethermal Phases with Emergent Symmetries: Application to Time Crystals and Floquet Engineering
- Anomalous topological edge modes in a periodically-driven trimer lattice
- Floquet band engineering with Bloch oscillations
- Wave packet dynamics and edge transport in anomalous Floquet topological phases
- Geometric Floquet theory
- Floquet topological insulators: from band structure engineering to novel non-equilibrium quantum phenomena
- Enhanced repulsively bound atom pairs in topological optical lattice ladders
- Anomalous levitation and annihilation in Floquet topological insulators
- Topological phonons in arrays of ultracold dipolar particles
- Nonlinear signatures of Floquet band topology
- Light-matter correlations in Quantum Floquet engineering of cavity quantum materials
- Topological reflection matrix
- Dissipative preparation of a Floquet topological insulator in an optical lattice via bath engineering
- Dynamical preparation of an atomic condensate in a Hofstadter band
- Floquet topological properties in the Non-Hermitian long-range system with complex hopping amplitudes
- Ultracold atomic lattice systems for simulating topological phases: A review
- Localization and topological signatures under periodic twisting
- Liouvillian topology and nonreciprocal dynamics in open Floquet chains