Topological bound states of a quantum walk with cold atoms

Abstract

We suggest a method for engineering a quantum walk, with cold atoms as walkers, which presents topologically non-trivial properties. We derive the phase diagram, and show that we are able to produce a boundary between topologically distinct phases using the finite beam width of the applied lasers. A topologically protected bound state can then be observed, which is pinned to the interface and is robust to perturbations. We show that it is possible to identify this bound state by averaging over spin sensitive measures of the atom's position, based on the spin distribution that these states display. Interestingly, there exists a parameter regime in which our system maps on to the Creutz ladder.

arXiv comment17 pages, 16 figures

References in corpus (41)

• Topological characterization of periodically-driven quantum systems
• Quantum walks of correlated particles
• Exponential algorithmic speedup by quantum walk
• Entanglement of atoms via cold controlled collisions
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• Observation of chiral edge states with neutral fermions in synthetic Hall ribbons
• A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical Superlattice
• Quantum Walk in Position Space with Single Optically Trapped Atoms
• Topological Thouless Pumping of Ultracold Fermions
• Visualizing edge states with an atomic Bose gas in the quantum Hall regime
• Synthetic gauge fields in synthetic dimensions
• Observation of topologically protected bound states in a one dimensional photonic system
• Exploring Topological Phases With Quantum Walks
• Realization of a quantum walk with one and two trapped ions
• Topological Transition in a Non-Hermitian Quantum Walk
• Anderson localization of entangled photons in an integrated quantum walk
• Quantum walk of a trapped ion in phase space
• Strongly Correlated Quantum Walks in Optical Lattices
• A 2D Quantum Walk Simulation of Two-Particle Dynamics
• Decoherence and disorder in quantum walks: From ballistic spread to localization
• Topological creation and destruction of edge states in photonic graphene
• Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
• Bulk--Boundary Correspondence for Chiral Symmetric Quantum Walks
• Quantum-state control in optical lattices
• Quantum walks and wavepacket dynamics on a lattice with twisted photons
• Photonic quantum walk in a single beam with twisted light
• End states, ladder compounds, and domain wall fermions
• Ideal negative measurements in quantum walks disprove theories based on classical trajectories
• Electric quantum walks with individual atoms
• Topology induced anomalous defect production by crossing a quantum critical point
• Dynamical moments reveal a topological quantum transition in a photonic quantum walk
• Real-space imaging of a topological protected edge state with ultracold atoms in an amplitude-chirped optical lattice
• Relativistic quantum walks
• Breakdown of an Electric-Field Driven System: a Mapping to a Quantum Walk
• Atom-optics simulator of lattice transport phenomena
• From fractionally charged solitons to Majorana bound states in a one-dimensional interacting model
• Robustness of topologically protected edge states in quantum walk experiments with neutral atoms
• Bulk-edge correspondence of one-dimensional quantum walks
• Manipulating atoms in an optical lattice: Fractional fermion number and its optical quantum measurement
• Direct Observation and Analysis of Spin Dependent Transport of Single Atoms in a 1D Optical Lattice
• Interaction-induced decoherence in non-Hermitian quantum walks of ultracold Bosons

Cited by in corpus (20)

• Topological quantum matter with cold atoms
• Effective theory and emergent $SU(2)$ symmetry in the flat bands of attractive Hubbard models
• Topological edge states with ultracold atoms carrying orbital angular momentum in a diamond chain
• Playing a true Parrondo's game with a three state coin on a quantum walk
• Topological edge states and Aharanov-Bohm caging with ultracold atoms carrying orbital angular momentum
• Synthetic dimensions for topological and quantum phases: Perspective
• Majorana Spin Liquids, Topology and Superconductivity in Ladders
• A Comparison of Quantum Walk Implementations on NISQ Computers
• Measuring Chern numbers in Hofstadter strips
• Universal and optimal coin sequences for high entanglement generation in 1D discrete time quantum walks
• Topological quantum walks: theory and experiments
• Different models of gravitating Dirac fermions in optical lattices
• Bipartite charge fluctuations in one-dimensional ${\mathbb{Z}}_2$ superconductors and insulators
• Boltzmann-Gibbs states in topological quantum walks and associated many-body systems: Fidelity and Uhlmann parallel transport analysis of Phase Transitions
• Enhanced repulsively bound atom pairs in topological optical lattice ladders
• Simulating artificial one-dimensional physics with ultra-cold fermionic atoms: three exemplary themes
• Proposal of a quantum version of active particles via a nonunitary quantum walk
• Real-space effects of a quench in the Su-Schrieffer-Heeger model and elusive dynamical appearance of the topological edge states
• History states of one-dimensional quantum walks
• Investigating the quench dynamics of the bound states in a spin-orbital coupling system using a trapped ion