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Observing interaction-induced topological doublon states

Julius Beck, Helena Drüeke, Marcus J. Meschede, Matthias Heinrich, Francesco S. Piccioli, Sebastian Weidemann, D. Bauer, Alexander Szameit

Published Jan 1, 2023• 0 citations
Publisher

Abstract

We present the first observation of propagating topologically protected doublon states in an anomalous Floquet driven 1D array. Using dimensional mapping, the two interacting particles in 1D were observed in 2D laser-written waveguide lattices.
DOI
10.1364/cleo_fs.2023.ff1d.3

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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.
When studying systems of interacting particles, few-particle systems are of particular interest as the mean-field approximation breaks down for a small number of particles. Two particles with attractive or repulsive long-range interactions may form a bound state [1], the so-called doublon, showing a number of peculiar features: topologically protected doublon states can not only persist outside the parameter regime for topological single particles [2], but also break the bulk boundary correspondence for large interactions [3]. So far doublons were only considered as doubly-occupied lattice sites [1], [4], whereas this work focuses on the general form of quasi-particles extending over multiple lattice sites.
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.