Topological Charge Pumping with Cold Atoms

R. Citro

Lei Wang, Matthias Troyer, Xi Dai

A topological charge pump transfers charge in a quantized fashion. The quantization is stable against the detailed form of the pumping protocols and external noises and shares the same topological origin as the quantum Hall effect. We propose an experimental setup to realize topological charge pumping of cold fermionic atoms in a one-dimensional optical lattice. The quantization of the pumped charge is confirmed by first-principles simulations of the dynamics of uniform and trapped systems. Quantum effects are shown to be crucial for the topological protection of the charge quantization. Finite-temperature and nonadiabatic effects on the experimental observables are discussed. The realization of such a topological charge pump serves as a firm step toward exploring topological states and nonequilibrium dynamics using cold atoms.

Stephen Inglis, Roger G. Melko

Ran Wei, Erich J. Mueller

We model atomic motion in a sliding superlattice potential to explore ``topological charge pumping'' and to find optimal parameters for experimental observation of this phenomenon. We analytically study the band structure, finding how the Wannier states evolve as two sinusoidal lattices are moved relative to one another, and relate this evolution to the center-of-mass motion of an atomic cloud. We pay particular attention to counterintuitive or anomalous regimes, such as when the atomic motion is opposite to that of the lattice. We propose a practical cold-atom experiment to detect this anomalous behavior. Through numerical simulations, we find that a negative adiabatic current and a nontrivial Chern number $\mathcal{C}=\ensuremath{-}1$ are readily measured.

Peter P. Orth, Stephan Rachel, Karyn Le Hur

Lei Wang, Alexey A. Soluyanov, Matthias Troyer

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 atoms in optical lattices. Time-of-flight measurement along one spatial direction combined with in situ detection along the transverse direction provides a direct measure of the system's Chern number, as we illustrate by calculations for the Hofstadter lattice. Based on an analogy with Wannier function 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.