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arXiv:1910.09948 · Physical Review A

Interaction-induced topological bound states and Thouless pumping in a one-dimensional optical lattice

Ling Lin, Yongguan Ke, Chaohong Lee

Published Feb 27, 2020• 60 citations
arXivHTMLPDF

Abstract

We study topological features of interacting spin-$\frac{1}{2}$ particles in one-dimensional state-dependent optical lattices. Due to the cotranslational symmetry, we introduce the center-of-mass Zak phase with the help of center-of-mass momentum. There appear topological bound states composed by two particles in different spin states via tuning hopping and interaction strengths. Under symmetric open boundary conditions, topological edge bound states appear as a result of the nontrivial center-of-mass Zak phase of bound-state band, which is protected by the center-of-mass inversion symmetry. The interaction plays a crucial role in the appearance of topological bound states and the system becomes completely trivial if the interaction is switched off. By periodically modulating the hopping and interaction strengths, we show how to implement topological Thouless pumping of bound states, in which the quantized shift of center of mass can be described by a nontrivial center-of-mass Chern number.

DOI
10.1103/physreva.101.023620

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We study topological features of interacting spin-12\frac{1}{2}21​ particles in one-dimensional state-dependent optical lattices. Due to the cotranslational symmetry, we introduce the center-of-mass Zak phase with the help of center-of-mass momentum. There appear topological bound states composed by two particles in different spin states via tuning hopping and interaction strengths. Under symmetric open boundary conditions, topological edge bound states appear as a result of the nontrivial center-of-mass Zak phase of bound-state band, which is protected by the center-of-mass inversion symmetry. The interaction plays a crucial role in the appearance of topological bound states and the system becomes completely trivial if the interaction is switched off. By periodically modulating the hopping and interaction strengths, we show how to implement topological Thouless pumping of bound states, in which the quantized shift of center of mass can be described by a nontrivial center-of-mass Chern number.
Thouless pumping, not only achieving quantized transport but also immune to moderate disorder, has attracted growing attention in both experiments and theories. Here, we explore how particle-particle interactions affect topological transport in a periodically modulated and tilted optical lattice. Three characterized interaction effects are revealed: topological pumping of bound states, interaction blockade of scattering states, and topologically resonant tunnelings. Attributed to the tilting, we have found a linear scanning in the first Brillouin zone at each Bloch-oscillation period of multiparticle center-of-mass momentum. Not limited to multiparticle Wannier states, our scheme ensures a dispersionless quantized transport even for initial Gaussian-like wave packets of interacting bosons which do not uniformly occupy a given band. Our study deepens the understanding of correlation effects on topological states, and provides a feasible way for detecting topological properties in interacting systems.
We study topologically nontrivial excitations of a weakly interacting, spin-orbit coupled Bose-Einstein condensate in a two-dimensional square optical lattice, a system recently realized in experiment [Phys. Rev. Lett. 121, 150401 (2018)]. We focus on situations where the system is not subjected to a Zeeman field and thus does not exhibit nontrivial single-particle band topology. Of special interest then is the role of particle interaction as well as its interplay with the symmetry properties of the system in producing topologically nontrivial excitations. We find that the noninteracting system possesses a rich set of symmetries, including the PT\mathcal{PT}PT symmetry, the modified dihedral point-group symmetry ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{D}}_{4}$ and the nonsymmorphic symmetry. These combined symmetries ensure the existence of pairs of degenerate Dirac points at the edge of Brillouin zone for the single-particle energy bands. In the presence of particle interaction and with sufficient spin-orbit coupling, the atoms condense in a ground state with net magnetization which spontaneously breaks the PT\mathcal{PT}PT and ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{D}}_{4}$ symmetry. We demonstrate that this symmetry breaking leads to a gap opening at the Dirac point for the Bogoliubov spectrum and consequentially topologically nontrivial excitations. We confirm the nontrivial topology by calculating the Chern numbers of the lowest excitation bands and show that gapless edge states form at the interface of systems characterized by different values of the Chern number.
We study two-particle states in a Su-Schrieffer-Heeger (SSH) chain with periodic boundary conditions and nearest-neighbor (NN) interactions. The system is mapped into a problem of a single particle in a two-dimensional (2D) SSH lattice with potential walls along specific edges. The 2D SSH model has a trivial Chern number but a non-trivial Zak's phase, the one-dimensional (1D) topological invariant, along specific directions of the lattice, which allow for the presence of topological edge states. Using center-of-mass and relative coordinates, we calculate the energy spectrum of these two-body states for strong interactions and find that, aside from the expected appearance of doublon bands, two extra in-gap bands are present. These are identified as bands of topological states localized at the edges of the internal coordinate, the relative distance between the two particles. As such, the topological states reported here are intrinsically many-body in what concerns their real space manifestation, having no counterpart in single-particle states derived from effective models. Finally, we compare the effect of Hubbard interactions with that of NN interactions to show how the presence of the topological bound states is specific to the latter case.
Strongly interacting topological states in multiparticle quantum systems pose great challenges to both theory and experiment. Recently, bound states of elementary spin waves (magnons) in quantum magnets have been experimentally observed in quantum Heisenberg chains comprising ultracold Bose atoms in optical lattices. Here, we explore a strongly interacting topological state called topological magnon bound state in the quantum Heisenberg chain under cotranslational symmetry. We find that the cotranslational symmetry is the key to the definition of a topological invariant for multiparticle quantum states, which enables us to characterize the topological features of multimagnon excitations. We calculate energy spectra, density distributions, correlations, and Chern numbers of the two-magnon bound states and show the existence of topological protected edge bound states. Our study not only opens a prospect to pursue topological magnon bound states, but also gives insights into the characterization and understanding of strongly interacting topological states.
As the basis for generating multi-particle quantum correlations, inter-particle interaction plays a crucial role in collective quantum phenomena, quantum phase transitions, and quantum information processing. It can profoundly alter the band structure of quantum many-body systems and give rise to exotic topological phenomena. Conventional topological pumping, which has been well demonstrated in driven linear or noninteracting systems, may break down in the presence of strong interaction. However, the interplay between band topology and interaction could also induce emergent topological pumping of interacting particles, but its experimental realization has proven challenging. Here we demonstrate interaction-induced topological pumping in a solid-state quantum system comprising an array of 36 superconducting qubits. With strong interaction inherent in the qubits and site-resolved controllability of the lattice potential and hopping strength, we realize the topological Thouless pumping of single and two bounded particles. Beyond these topological phenomena with linear or noninteracting counterparts, we also observe topologically resonant tunneling and asymmetric edge-state transport of interacting particles. Our work creates a paradigm for multi-particle topological effects, and provides a new pathway to the study of exotic topological phenomena, many-body quantum transport, and quantum information transfer.