We develop a realistic protocol to observe the robust topological dynamics of two-particle bound states in a lattice model with on-site interactions and suitably designed time-dependent hoppings. This Floquet scheme can be realistically implemented on existing digital quantum computer platforms. Marked differences from the topological single-particle dynamics of two independent particles and clear signatures of the entanglement between the two constituent particles are highlighted.
We develop a realistic protocol to observe the robust topological dynamics of two-particle bound states in a lattice model with on-site interactions and suitably designed time-dependent hoppings. This Floquet scheme can be realistically implemented on existing digital quantum computer platforms. Marked differences from the topological single-particle dynamics of two independent particles and clear signatures of the entanglement between the two constituent particles are highlighted.
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 potentialU[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 couplingsc[6]. The driving scheme preserves the mapping and adds a long-range interaction between the two particles in the 1D lattice.
Abstract We study the quantum walk on the off-diagonal Aubry-André-Harper (AAH) lattice with periodic modulation using a digital quantum computer. We investigate various initial states at the single-particle level, considering different hopping modulation strengths and phase factors. Initiating the quantum walk with a particle at the lattice edge reveals the robustness of the edge state, attributed to the topological nature of the AAH model, and displays the influence of the phase factor on this edge state. On the other hand, when the quantum walk begins with a particle in the lattice bulk, we observe a repulsion of the bulk walker from the edge, especially under strong hopping modulation. Furthermore, we extend our investigation to the quantum walk of two particles with nearest-neighbour (NN) interaction. We show the repulsion effect in the quantum walk when two walkers originate from the edge and bulk of the lattice due to the interaction. Additionally, when two particles are positioned at nearest-neighbor sites with strong hopping modulation, they unexpectedly form a local bound state at very small interaction strength, highlighting the unique interplay between hopping modulation and interaction in our quantum walk setup. We analyze these phenomena by examining physical quantities such as density evolution, two-particle correlation, and participation entropy, and discuss their potential applications in quantum technologies.
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 (T 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.
Quantum computers are a leading platform for the simulation of many-body physics. This task has been recently facilitated by the possibility to program directly the time-dependent pulses sent to the computer. Here, we use this feature to simulate quantum lattice models with long-range hopping. Our approach is based on an exact mapping between periodically driven quantum systems and one-dimensional lattices in the synthetic Floquet direction. By engineering a periodic drive with a power-law spectrum, we simulate a lattice with long-range hopping, whose decay exponent is freely tunable. We propose and realize experimentally two protocols to probe the long tails of the Floquet eigenfunctions and identify a scaling transition between long-range and short-range couplings. Our paper offers a useful benchmark of pulse engineering and opens the route towards quantum simulations of rich nonequilibrium effects.
The interplay between topology and quantum entanglement holds profound implications for fundamental physics and the advancement of quantum technologies. Topological phases of matter are characterized by robust properties impervious to local perturbations, while entanglement serves as a critical resource for quantum information processing. Floquet engineering, the manipulation of quantum systems through periodic driving, offers a powerful non-equilibrium pathway to realize novel topological states that may not exist in static systems. This paper explores the theoretical and experimental avenues for realizing topological quantum entanglement within Floquet-engineered lattices. We review the foundational concepts of Floquet topological phases and various measures of entanglement, such as entanglement entropy and entanglement spectrum. We then delve into the methodologies for designing such systems across diverse platforms, including ultracold atoms in optical lattices, photonic waveguide arrays, and superconducting circuits. The discussion highlights how Floquet driving can induce robust entanglement in topological edge and bulk states, paving the way for fault-tolerant quantum information storage and processing. We propose specific protocols for generating and detecting topologically-protected entangled states, considering the challenges associated with heating and decoherence in periodically driven systems. Ultimately, this work emphasizes the potential of Floquet engineering as a versatile tool for synthesizing exotic entangled topological states, fostering new frontiers in quantum science and engineering.