Direct measurement of topological invariants in optical lattices

Abstract

We propose an experimental technique for classifying the topology of band structures realized in optical lattices, based on a generalization of topological charge pumping in quantum Hall systems to cold atom in optical lattices. Time-of-flight measurement along one spatial direction combined with in situ detection along the transverse direction provide a direct measure of the system's Chern number, as we illustrate by calculations for the Hofstadter lattice. Based on an analogy with Wannier functions techniques of topological band theory, the method is very general and also allows the measurement of other topological invariants, such as the $Z_2$ topological invariant of time-reversal symmetric insulators.

4.5 pages, 5 figures

References in corpus (10)

• Spin-Injection Spectroscopy of a Spin-Orbit Coupled Fermi Gas
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Tunable gauge potential for neutral and spinless particles in driven lattices
• Computing topological invariants without inversion symmetry
• Robustness of the Spin-Chern number
• Detecting Chiral Edge States in the Hofstadter Optical Lattice
• Expansion of a quantum gas released from an optical lattice
• Electric polarization in a Chern insulator
• Effects of Smooth Boundaries on Topological Edge Modes in Optical Lattices

Cited by in corpus (11)

• Z2Pack: Numerical Implementation of Hybrid Wannier Centers for Identifying Topological Materials
• Floquet Edge States with Ultracold Atoms
• Topological insulator and particle pumping in a one-dimensional shaken optical lattice
• Emergent pseudospin-1 Maxwell fermions with a threefold degeneracy in optical lattices
• Constructing a Weyl semimetal by stacking one dimensional topological phases
• Quantum simulation of non-trivial topology
• Phase spectroscopy of topological invariants in photonic crystals
• Direct Probe of Topological Order for Cold Atoms
• Fractional charge pumping of interacting bosons in one-dimensional superlattice
• Exploring topological double-Weyl semimetals with cold atoms in optical lattices
• Propagation in media as a probe for topological properties