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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Observation of Interaction-Induced Topological Doublon States

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

Published Jun 26, 2023• 0 citations
Publisher

Abstract

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 potential$U$[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 couplings$c$[6]. The driving scheme preserves the mapping and adds a long-range interaction between the two particles in the 1D lattice.

DOI
10.1109/cleo/europe-eqec57999.2023.10231749

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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.
Topological boundary states are a defining feature of topological systems, providing robust transport protected against perturbations. While such states are commonly engineered in non-interacting systems, how to realize interaction-induced topological states composed of only few particles has remained experimentally unexplored thus far. In this work, we realize such states using a driven photonic lattice as a linear analogue platform. We observe the formation of spatially extended bound states of two interacting particles, in which the particles remain correlated while occupying different lattice sites. At discrete values of the local interaction, these bound states support robust transport governed by a topological phase arising from drive-induced correlated hopping. Our results establish an experimentally accessible route to interaction-driven topology beyond single-particle physics and provide a versatile framework for exploring correlated few-particle phenomena across different physical platforms.
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.
We investigate theoretically the Bose-Hubbard version of the celebrated Su-Schrieffer-Heeger topological model, which essentially describes a one-dimensional dimerized array of coupled oscillators with on-site interactions. We study the physics arising from the whole gamut of possible dimerizations of the chain, including both the weakly and the strongly dimerized limiting cases. Focusing on two-excitation subspace, we systematically uncover and characterize the different types of states which may emerge due to the competition between the inter-oscillator couplings, the intrinsic topology of the lattice, and the strength of the on-site interactions. In particular, we discuss the formation of scattering bands full of extended states, bound bands full of two-particle pairs (including so-called 'doublons', when the pair occupies the same lattice site), and different flavors of topological edge states. The features we describe may be realized in a plethora of systems, including nanoscale architectures such as photonic cavities, optical lattices and qubits, and provide perspectives for topological two-particle and many-body physics.