A topological charge pump

Yoshiro Takahashi

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.

Hsin I Lu, Max Schemmer, Lauren Aycock +3 more

We realized a quantum geometric "charge" pump for a Bose-Einstein condensate (BEC) in the lowest Bloch band of a novel bipartite magnetic lattice. Topological charge pumps in filled bands yield quantized pumping set by the global-topological-properties of the bands. In contrast, our geometric charge pump for a BEC occupying just a single crystal momentum state exhibits nonquantized charge pumping set by local-geometrical-properties of the band structure. Like topological charge pumps, for each pump cycle we observed an overall displacement (here, not quantized) and a temporal modulation of the atomic wave packet's position in each unit cell, i.e., the polarization.

Victor Victorovich Kotlyar, A. A. Kovalev, Anton Gennadyevich Nalimov

Qian Niu

Andrew L. C. Hayward, C. Schweizer, Michael Lohse +2 more

We investigate topological charge pumping in a system of interacting bosons in the tight-binding limit, described by the Rice-Mele model. An appropriate topological invariant for the many-body case is the change of polarization per pump cycle, which we compute for various interaction strengths from infinite-size matrix-product-state simulations. We verify that the charge pumping remains quantized as long as the pump cycle avoids the superfluid phase. In the limit of hardcore bosons, the quantized pumped charge can be understood from single-particle properties such as the integrated Berry curvature constructed from Bloch states, while this picture breaks down at finite interaction strengths. These two properties---robust quantized charge transport in an interacting system of bosons and the breakdown of a single-particle invariant---could both be measured with ultracold quantum gases extending a previous experiment [Lohse et al., Nat. Phys. 12, 350 (2016)]. Furthermore, we investigate the entanglement spectrum of the Rice-Mele model and argue that the quantized charge pumping is encoded in a winding of the spectral flow in the entanglement spectrum over a pump cycle.