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.
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.
A topological charge pump is a one-dimensional, dynamical analogue of a quantum Hall system that is particularly well suited for studying topology, both theoretically and experimentally, since no synthetic gauge fields are required and efficient numerical algorithms exist to treat one-dimensional interacting systems in the form of matrix-product state methods. Instead of a robustly quantized Hall conductivity, a topological charge pump pumps a quantized amount of charge in each cycle of a parameter modulation that is given by the same topological invariant as in the quantum Hall effect. The goal of this thesis is to understand the stability of quantized transport in various contexts that are relevant in ultracold quantum gases, such as disordered systems, quantum systems where energy can be exchanged with a bath and in the presence of genuine many-body interactions. The results are presented as part of four scientific papers. In the first paper, we characterize the breakdown of quantized pumping as a function of disorder strength by employing various instantaneous and time-dependent measures. We argue that in disorder averages, the full energy gap distributions should be considered. In the second paper, we study the breakdown of quantized pumping due to electron-phonon coupling and find a resonant breakdown when the pump frequency equals the phonon frequency. The third paper introduces the possibility of a splitting of critical points in a Rice-Mele Hubbard model, which allows for interaction-induced pumping. The final paper presents experimental data of an ultracold-atom setup studying this interaction-induced pumping, as well as numerical calculations detailing the breakdown due to the crossing of a spin-gapless line.
We propose an experimental scheme to simulate and detect the properties of time-reversal invariant topological insulators, using cold atoms trapped in one-dimensional bichromatic optical lattices. This system is described by a one-dimensional Aubry-Andre model with an additional SU(2) gauge structure, which captures the essential properties of a two-dimensional Z2 topological insulator. We demonstrate that topologically protected edge states, with opposite spin orientations, can be pumped across the lattice by sweeping a laser phase adiabatically. This process is an elegant way to transfer topologically protected quantum states in a highly controllable environment. We discuss how density measurements could provide clear signatures of the topological phases emanating from our one-dimensional system.
Experimental realizations of topological quantum systems and detections of topological invariants in ultracold atomic systems have been a greatly attractive topic. In this work, we propose a scheme to realize topologically different phases in a bichromatic optical lattice subjected to a periodically driven tilt harmonic oscillation, which can be effectively described by a superlattice model with tunable long-range hopping processes. By tuning the ratio of nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping amplitudes, the system undergoes a topological phase transition accompanied by the change of topological numbers of the lowest band from $\ensuremath{-}1$ to 2. Using a slowly time-periodic modulation, the system emerges distinct quantized topological pumped charges (TPCs) of atoms in the filled band for different topological phases. Our scheme is realizable in current cold atomic technique.
Abstract Geometric properties of wave functions can explain the appearance of topological invariants in many condensed-matter and quantum systems 1 . For example, topological invariants describe the plateaux observed in the quantized Hall effect and the pumped charge in its dynamic analogue—the Thouless pump 2–4 . However, the presence of interparticle interactions can affect the topology of a material, invalidating the idealized formulation in terms of Bloch waves. Despite pioneering experiments in different platforms 5–9 , the study of topological matter under variations in interparticle interactions has proven challenging 10 . Here we experimentally realize a topological Thouless pump with fully tuneable Hubbard interactions in an optical lattice and observe regimes with robust pumping, as well as an interaction-induced breakdown. We confirm the pump’s robustness against interactions that are smaller than the protecting gap for both repulsive and attractive interactions. Furthermore, we identify that bound pairs of fermions are responsible for quantized transport at strongly attractive interactions. However, for strong repulsive interactions, topological pumping breaks down, but we show how to reinstate it by modifying the pump trajectory. Our results will prove useful for further investigations of interacting topological matter 10 , including edge effects 11 and interaction-induced topological phases 12–15 .
We propose an experimental scheme to realize the quantum anomalous Hall effect in an anisotropic square optical lattice which can be generated from available experimental setups of double-well lattices with minor modifications. A periodic gauge potential induced by atom-light interaction is introduced to give a Peierls phase for the nearest-neighbor site hopping. The quantized anomalous Hall conductivity is investigated by calculating the Chern number as well as the chiral gapless edge states of our system. Furthermore, we show in detail the feasability for its experimental detection through light Bragg scattering of the edge and bulk states with which one can determine the topological phase transition from usual insulating phase to quantum anomalous Hall phase.
We analyze strong correlation effects and topological properties of interacting fermions with a Falicov-Kimball-type interaction in circularly shaken hexagonal optical lattices, which can be effectively described by the Haldane-Falicov-Kimball model, using the real-space Floquet dynamical mean-field theory (DMFT). The Haldane model, a paradigmatic model of the Chern insulator, is experimentally relevant, because it has been realized using circularly shaken hexagonal optical lattices. We show that in the presence of staggering a charge density wave emerges, which is affected by interactions and resonant tunneling. We demonstrate that interactions smear out the edge states by introducing a finite life time of quasiparticles. Even though a general method for calculating the topological invariant of a nonequilibrium steady state is lacking, we extract the topological invariant using a Laughlin charge pump setup. We find and attribute to the dissipations into the bath connected to every lattice site, which is intrinsic to real-space Floquet DMFT methods, that the pumped charge is not an integer even for the noninteracting case at very low reservoir temperatures. Furthermore, using the rate equation based on the Floquet-Born-Markov approximation, we calculate the charge pump from the rate equations for the noninteracting case to identify the role of the spectral properties of the bath. Starting from this approach we propose an experimental protocol for measuring quantized charge pumping.