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arXiv:1502.04208 · Physical Review A

Anomalous charge pumping in a one-dimensional optical superlattice

Ran Wei, Erich J. Mueller

Published Jul 7, 2015• 22 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.92.013609

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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 C=\ensuremath−1\mathcal{C}=\ensuremath{-}1C=\ensuremath−1 are readily measured.
We propose a simple method to simulate and detect topological insulators with cold atoms trapped in a one-dimensional bichromatic optical lattice subjected to a time-periodic modulation. The tight-binding form of this shaken system is equivalent to the periodically driven Aubry-Andre model. We demonstrate that this model can be mapped into a two-dimensional Chern insulator model, whose energy spectrum hosts a topological phase within an experimentally accessible parameter regime. By tuning the laser phase adiabatically, such one-dimensional system constitutes a natural platform to realize topological particle pumping. We show that the Chern number characterizing the topological features of this system can be measured by detecting the density shift after one cycle of pumping.
In this paper, we study a one-dimensional boson system in a superlattice potential. This system is experimentally feasible by using ultracold atomic gases, and attracts much attention these days. It is expected that the system has a topological phase called a topological Mott insulator (TMI). We show that in strongly-interacting cases, the competition between the superlattice potential and the on-site interaction leads to various TMIs with a non-vanishing integer Chern number. Compared to the hard-core case, the soft-core boson system exhibits rich phase diagrams including various non-trivial TMIs. By using the exact diagonalization, we obtain detailed bulk-global phase diagrams including the TMIs with high Chern numbers and also various non-topological phases. We also show that in adiabatic experimental setups, the strongly-interacting bosonic TMIs exhibit the topological particle transfer, i.e., the topological charge pumping phenomenon, similarly to weakly-interacting systems. The various TMIs are characterized by topological charge pumping as it is closely related to the Chern number, and therefore the Chern number is to be observed in feasible experiments.
Abstract We study the pumping of matter-wave solitons formed in Bose–Einstein condensates with attractive atomic interactions that are loaded into optical superlattices, in which one of the lattices is moving with respect to the other. We find that the matter-wave solitons exhibit lattice-parameter-dependent nonlinear integer (fractional) pumping and trapping. Different from the perspective of linear band Chern numbers, treating solitons as effective classical particles provides a good understanding of the quantized pumping or trapping. This reveals an unexpected insight: the nonlinear adiabatic pumping may be classical, and the quantization may be accidental, as dictated by the spatial period of the sliding sublattice. This alternative perspective on understanding soliton pumping highlights the parameter-dependent transition between soliton quantized pumping and trapping, and it exposes the nonlinear transition from a trapped soliton to a pumped soliton with increasing nonlinearity, which has never been reported before.
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.
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.
We propose to simulate and detect quantum anomalous Hall phase with ultracold atoms in a one-dimensional optical lattice, with the other synthetic dimension being realized by modulating spin-orbit coupling. We show that the system manifests a topologically nontrivial phase with two chiral edge states which can be readily detected in this synthetic two-dimensional system. Moreover, it is interesting that at the phase transition point there is a flat energy band and this system can also be in a topologically nontrivial phase with two Fermi zero modes existing at the boundaries by considering the synthetic dimension as a modulated parameter. We also show how to measure these topological phases experimentally in ultracold atoms. Another model with a random Rashba and Dresselhaus spin-orbit coupling strength is also found to exhibit topological nontrivial phase, and the impact of the disorder to the system is revealed.