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Light Science & Applications

Observation of nonlinear edge states in an interacting atomic trimer array

Huiying Du, Hongxing Zhao, Yuqing Li, Yunfei Wang, Rujiang Li, Jizhou Wu, Wenliang Liu, Yiqi Zhang, Liantuan Xiao, Suotang Jia, Jie Ma

Published Aug 28, 2025• 8 citations
Publisher

Abstract

Exploring the interplay between topology and nonlinearity leads to an emerging field of nonlinear topological physics, which extends the study of fascinating properties of topological states to a regime where interactions between the particles cannot be neglected. For ultracold atomic systems, although many exotic topological states have been recently observed, the nonlinear effect remains elusive. Here, based on the laser-driven couplings of discrete atomic momentum states, we synthesize a topological trimer array, where the atomic interactions give rise to tunable nonlinearities. We observe the formation of nonlinear edge states in the density population evolution and participation ratio with increasing interaction, in contrast to the diffusive transport in a broad interaction range in nontopological arrays. Furthermore, we show the impact of interactions on the population distribution evolved from the initialized single-site population. Our work opens the avenue for exploring emergent nonlinear topological behaviors in ultracold atomic gases.

DOI
10.1038/s41377-025-01997-6

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Exploring the interplay between topology and nonlinearity leads to an emerging field of nonlinear topological physics, which extends the study of fascinating properties of topological states to a regime where interactions between the particles cannot be neglected. For ultracold atomic systems, although many exotic topological states have been recently observed, the nonlinear effect remains elusive. Here, based on the laser-driven couplings of discrete atomic momentum states, we synthesize a topological trimer array, where the atomic interactions give rise to tunable nonlinearities. We observe the formation of nonlinear edge states in the density population evolution and participation ratio with increasing interaction, in contrast to the diffusive transport in a broad interaction range in nontopological arrays. Furthermore, we show the impact of interactions on the population distribution evolved from the initialized single-site population. Our work opens the avenue for exploring emergent nonlinear topological behaviors in ultracold atomic gases.
Realization of nonreciprocal transport is of great importance in the development of devices and systems that require the directional manipulation of signals or particles in information processing and modern physics. For ultracold atomic systems, the approaches based on synthetic dimensions have led to rapid advances in engineering quantum transport. Here, we use laser-coupled discrete momentum states of noninteracting ultracold atoms to synthesize a momentum lattice, and construct a closed ring with controllable tunneling phase in the momentum lattice. We measure the density evolution of atoms in the synthetic lattice with the single-site resolution, and observe the nonreciprocal dynamics by controlling the tunneling phase. We show the effect of both the applied phase and the coupling strength between two distinct population regions on the population distribution of atoms in the momentum lattice, and provide the optimal parameters for achieving the nonreciprocal transport.
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.
Abstract Efficient manipulation of quantum states is a key step towards applications in quantum information, quantum metrology, and nonlinear optics. Recently, atomic arrays have been shown to be a promising system for exploring topological quantum optics and robust control of quantum states, where the inherent nonlinearity is included through long-range hoppings. Here we show that a one-dimensional atomic array in a periodic magnetic field exhibits characteristic properties associated with an effective two-dimensional Hofstadter-butterfly-like model. Our work points out super- and sub-radiant topological edge states localized at the boundaries of the atomic array despite featuring long-range interactions, and opens an avenue of exploring an interacting quantum optical platform with synthetic dimensions.
Topological behavior has been observed in quantum systems including ultracold atoms. However, background harmonic traps for cold atoms hinder the direct detection of topological edge states arising at the boundary because the distortion fuses the edge states into the bulk. We propose experimentally feasible protocols to probe localized edge states and dimerization of ultracold fermions. By confining cold atoms in a ring lattice and changing the boundary condition from periodic to open using an off-resonant laser sheet to cut open the ring, topological edge states can be generated. A lattice in a topological configuration can trap a single particle released at the edge as the system evolves in time. Alternatively, depleting an initially filled lattice away from the boundary reveals the occupied edge states. Signatures of dimerization in the presence of contact interactions can be found in selected correlations as the system boundary suddenly changes from periodic to open and exhibit memory effects of the initial state distinguishing different configurations.
Interaction-induced topological systems have attracted a growing interest for their exotic properties going beyond the single-particle picture of topological insulators. In particular, the interplay between strong correlations and finite doping can give rise to nonhomogeneous solutions that break the translational symmetry. In this work, we report the appearance of a topological stripe state in an interaction-induced Chern insulator around half-filling. In contrast to similar stripe phases in nontopological systems, here we observe the appearance of chiral edge states on top of the domain wall. Furthermore, we characterize their topological nature by analyzing the quantized transferred charge of the domains in a pumping scheme. Finally, we focus on aspects relevant to observing such phases in state-of-the-art quantum simulators of ultracold atoms in optical lattices. In particular, we propose an adiabatic state preparation protocol and a detection scheme of the topology of the system in real space.
Topology and disorder have a rich combined influence on quantum transport. To probe their interplay, we synthesized one-dimensional chiral symmetric wires with controllable disorder via spectroscopic Hamiltonian engineering, based on the laser-driven coupling of discrete momentum states of ultracold atoms. Measuring the bulk evolution of a topological indicator after a sudden quench, we observed the topological Anderson insulator phase, in which added disorder drives the band structure of a wire from topologically trivial to nontrivial. In addition, we observed the robustness of topologically nontrivial wires to weak disorder and measured the transition to a trivial phase in the presence of strong disorder. Atomic interactions in this quantum simulation platform may enable realizations of strongly interacting topological fluids.