Detecting topological transitions in two dimensions by Hamiltonian evolution

Abstract

We show that the evolution of two-component particles governed by a two-dimensional spin-orbit lattice Hamiltonian can reveal transitions between topological phases. A kink in the mean width of the particle distribution signals the closing of the band gap, a prerequisite for a quantum phase transition between topological phases. Furthermore, for realistic and experimentally motivated Hamiltonians the density profile in topologically non-trivial phases displays characteristic rings in the vicinity of the origin that are absent in trivial phases. The results are expected to have immediate application to systems of ultracold atoms and photonic lattices.

Ref. [12] fixed; updates in response to referee comments

References in corpus (12)

• Topological Photonics
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Exploring Topological Phases With Quantum Walks
• Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms
• Realistic Time-Reversal Invariant Topological Insulators With Neutral Atoms
• An Aharonov-Bohm interferometer for determining Bloch band topology
• Symmetries, Topological Phases and Bound States in the One-Dimensional Quantum Walk
• Topological invariants for gauge theories and symmetry-protected topological phases
• Limit distributions of two-dimensional quantum walks
• Edge-state enhanced transport in a 2-dimensional quantum walk
• Focus on topological quantum computation