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arXiv:1911.05057 · Physical Review Research

Interaction-induced lattices for bound states: Designing flat bands, quantized pumps, and higher-order topological insulators for doublons

G. Salerno, Giandomenico Palumbo, Nathan Goldman, Marco Fedele Di Liberto

Published Mar 20, 2020• 44 citations
arXivHTMLPDF

Abstract

The authors show that, in the presence of long ranged interactions, the center of mass of bound systems with interactions defines a distinct lattice with respect to the one experienced by noninteracting particles. As a consequence, topological and geometrical effects emerge and the paper explores several scenarios including localization, Berry phases and topological bands.

DOI
10.1103/physrevresearch.2.013348

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The authors show that, in the presence of long ranged interactions, the center of mass of bound systems with interactions defines a distinct lattice with respect to the one experienced by noninteracting particles. As a consequence, topological and geometrical effects emerge and the paper explores several scenarios including localization, Berry phases and topological bands.
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.
Higher-order topological insulators have attracted significant interest in both static single-particle and many-body lattice systems. While periodically driven (Floquet) higher-order topological phases have been explored at the single-particle level, the role of interactions in such systems remains less understood. In this paper, we extend previous studies by investigating interaction-induced higher-order topological phases through Floquet engineering. To achieve this, we construct an extended Bose-Hubbard model on a square lattice subjected to periodic driving. We demonstrate the emergence of interaction-induced normal Floquet second-order topological corner states for doublons (i.e., bound boson pairs) from a trivial phase, which exhibit robustness against disorder. Notably, beyond the normal phase, we reveal an interaction-induced anomalous Floquet second-order topological phase, where in-gap corner states of doublons emerge within the $\ensuremath{\pi}/T$ gap (TTT being the driving period). Our model, accessible with state-of-the-art ultracold atom techniques, provides a platform for realizing interaction-driven higher-order topological phases uniquely enabled by periodic driving, with no direct counterparts in static or single-particle systems.
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.
While topological single-particle systems have been extensively studied [1], topologically protected entangled two-boson states [2] and many-boson states [3] have recently come into the focus of research. However, interacting particle pairs in these systems have yet to be studied experimentally. This work focuses on the topological center-of-mass motion of bound two-particle states - so-called doublons [4], arising in a 1D lattice for discrete potentials with repulsive interaction. The tight-binding dynamics of a repulsive interacting two-particle state on such a 1D chain can be mapped onto a single particle evolving in a 2D lattice (Fig. 1a), where the main diagonal sites experience an on-site potentialUUU[5]. For the 2D case, we choose a square lattice driven by a conventional anomalous Floquet protocol with a full wave packet transfer in each hopping and uniformly distributed couplingsccc[6]. The driving scheme preserves the mapping and adds a long-range interaction between the two particles in the 1D lattice.