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arXiv:1810.13286 · Science

Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms

Sylvain de Léséleuc, Vincent Lienhard, Pascal Scholl, Daniel Barredo, Sebastian Weber, Nicolai Lang, Hans Peter Büchler, Thierry Lahaye, Antoine Browaeys

Published Aug 1, 2019• 552 citations
arXivHTMLPDF

Abstract

The concept of topological phases is a powerful framework for characterizing ground states of quantum many-body systems that goes beyond the paradigm of symmetry breaking. Topological phases can appear in condensed-matter systems naturally, whereas the implementation and study of such quantum many-body ground states in artificial matter require careful engineering. Here, we report the experimental realization of a symmetry-protected topological phase of interacting bosons in a one-dimensional lattice and demonstrate a robust ground state degeneracy attributed to protected zero-energy edge states. The experimental setup is based on atoms trapped in an array of optical tweezers and excited into Rydberg levels, which gives rise to hard-core bosons with an effective hopping generated by dipolar exchange interaction.

DOI
10.1126/science.aav9105

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Progress of Theoretical and Experimental Physics•Mar 16, 2022•1 citation
The concept of topological phases is a powerful framework for characterizing ground states of quantum many-body systems that goes beyond the paradigm of symmetry breaking. Topological phases can appear in condensed-matter systems naturally, whereas the implementation and study of such quantum many-body ground states in artificial matter require careful engineering. Here, we report the experimental realization of a symmetry-protected topological phase of interacting bosons in a one-dimensional lattice and demonstrate a robust ground state degeneracy attributed to protected zero-energy edge states. The experimental setup is based on atoms trapped in an array of optical tweezers and excited into Rydberg levels, which gives rise to hard-core bosons with an effective hopping generated by dipolar exchange interaction.
We propose a simple setup of Rydberg atoms in a honeycomb lattice which gives rise to topologically protected edge states. The proposal is based on the combination of dipolar exchange interaction, which couples the internal angular momentum and the orbital degree of freedom of a Rydberg excitation, and a static magnetic field breaking time reversal symmetry. We demonstrate that for realistic experimental parameters, signatures of topologically protected edge states are present in small systems with as few as 10 atoms. Our analysis paves the way for the experimental realization of Rydberg systems characterized by a topological invariant, providing a promising setup for future application in quantum information.
Abstract Topological phases of matter can appear in noninteracting systems, as in band topology, or interacting systems, such as in spin models, with their defining features typically robust against weak disorder. Intriguingly, disorder itself can also induce topological phases--exemplified by the Anderson topological insulator in noninteracting systems. Experimental studies on disorder-induced topology have so far been limited to band topology. Here we report direct observations of disorder-induced many-body interacting average topological order in an atom array at half-filling, whereby random offsets to tweezer locations forming a lattice implement structural disorder, causing fluctuating long-range dipolar interactions between tweezer confined single atoms. The ground state degeneracy in disordered configurations is detected and compared to the regular lattice. The induced topological phase is vindicated by the spatially resolved atom-atom correlation functions for different forms of dimer compositions. By probing the quench dynamics of a highly excited state, we observe markedly slower decay of edge spin magnetization in comparison to the bulk spin, consistent with the presence of topologically protected edge modes in disordered lattices. Our experiments open a new direction for studying the interplay between disorder and strongly interacting topological matter in Rydberg atom arrays.
We propose a simple setup of Rydberg atoms in a honeycomb lattice which gives rise to topologically protected edge states. The proposal is based on the combination of dipolar exchange interaction, which couples the internal angular momentum and the orbital degree of freedom of a Rydberg excitation, and a static magnetic field breaking time reversal symmetry. We demonstrate that for realistic experimental parameters, signatures of topologically protected edge states are present in small systems with as few as 10 atoms. Our analysis paves the way for the experimental realization of Rydberg systems characterized by a topological invariant, providing a promising setup for future application in quantum information.
Recent theoretical studies predict that structural disorder, serving as a bridge connecting a crystalline material to an amorphous material, can induce a topological insulator from a trivial phase. However, to experimentally observe such a topological phase transition is very challenging due to the difficulty in controlling structural disorder in a quantum material. Given experimental realization of randomly positioned Rydberg atoms, such a system is naturally suited to studying structural disorder induced topological phase transitions and topological amorphous phases. Motivated by the development, we study topological phases in an experimentally accessible one-dimensional amorphous Rydberg atom chain with random atom configurations. In the single-particle level, we find symmetry-protected topological amorphous insulators and a structural disorder induced topological phase transition, indicating that Rydberg atoms provide an ideal platform to experimentally observe the phenomenon using state-of-the-art technologies. Furthermore, we predict the existence of a gapless symmetry-protected topological phase of interacting bosons in the experimentally accessible system. The resultant many-body topological amorphous phase is characterized by a Z_{2} invariant.
Topological phases have greatly improved our understanding of modern conception of phases of matter that go beyond the paradigm of symmetry breaking and are not described by local order parameters. Instead, characterization of topological phases requires the robust topological invariants, whereas measuring these global quantities presents an outstanding challenge for experiments, especially in interacting systems. Here we report the real-space observation of a symmetry-protected topological phase with interacting nuclear spins, and probe the interaction-induced transition between two topologically distinct phases, both of which are classified by many-body Chern numbers obtained from the dynamical response to the external magnetic fields. The resulting value of Chern number (Chˉ=1.958±0.070\bar{\mathcal{C}h} = 1.958 \pm 0.070Chˉ=1.958±0.070) demonstrates the robust ground state degeneracy, and also determines the number of nontrivial edge states. Our findings enable direct characterization of topological features of quantum many-body states through gradually decreasing the strength of the introduced external fields.
One problem of paramount importance in physics over various fields such as elementary particle physics, condensed matter physics, and statistical mechanics has been to make classification of phases of matter, including nontrivial structures of the vacuum. The triumphant history of theory on the phase classification and the phase transition can be traced back to Landau, which is based on the spontaneous breaking of symmetry. It is known, however, that other kinds of phases exist that cannot be characterized by conventional arguments of symmetry breaking, namely, topological phases. Topological phases are gapped phases at zero temperature without symmetry breaking. Examples of the topological phases include a quantum phase in a fractional quantum Hall system, where the ground state exhibits degeneracy, and an anyon, a quasi-particle with nontrivial statistical nature, neither boson nor fermion, emerges as a low-energy excitation. In contemporary physics of the 21st century, it has been revealed that, among various topological states, there exists a nontrivial ground state that does not have ground state degeneracy and yet can be distinguished from a trivial state. This nontrivial ground state, i.e., a topological insulator, has been recognized first in free electron systems [1–3] and later extended to more general quantum many-body systems with interactions including bosonic (spin) systems. Now, such a generalized situation is called a symmetry protected topological (SPT) phase [4–7]. From the point of a modern view of the SPT phase, nontrivial states, such as the Haldane state proposed in antiferromagnetic quantum spin systems in the 1980’s [8] and the ground state in the Affleck-Kennedy-Lieb-Tasaki model [9], belong to the SPT phase. A remarkable feature of the SPT phase is that, if the system has a surface, gapless surface states appear and they are stable against disturbances which do not break the symmetry. One way to understand these surface states is the quantum anomaly on the surface. That is, as long as the surface is concerned, the quantum anomaly arises, but the whole system has no quantum anomaly, and the symmetry is preserved due to cancellation from the bulk contribution. This canceling mechanism of the quantum anomaly has been long known as the anomaly inflow in elementary particle physics [10]. In fact, the classification of the SPT phases can be identified as the classification of the quantum anomaly through the bulk-boundary correspondence. This type of the quantum anomaly closely related to the SPT phase can provide us with a useful theoretical device to constrain phases that can or cannot be realized under the ’t Hooft anomaly matching condition [11–13]. It is quite difficult to scrutinize nonperturbatively interacting systems, but the ’t Hooft anomaly matching condition can be applied to those systems, and possible phases can be constrained. Nowadays, our understanding of the SPT phases has been so developed that applications of the anomaly matching condition can cover systems with finite groups and/or extending objects [14–16]. In this way, the concept of the topological phases has been essential by now in a wide range of physics, particularly in elementary particle physics, condensed matter physics, and statistical mechanics, as mentioned in the beginning. This special section is a collection of papers related to the topological aspects of physics including the topological phases. We would like to express our sincere gratitude to all the authors who made excellent contributions.