Topological Matter
Adding irregularity to a system can lead to a transition from a more orderly to a less orderly phase. Meier et al. demonstrated a counterintuitive transition in the opposite direction: Controlled fluctuations in the system's parameters caused it to become topologically nontrivial. The starting point was a one-dimensional lattice of ultracold rubidium atoms in momentum space whose band structure was topologically trivial. The researchers then introduced fluctuations in the tunneling between the lattice sites and monitored the atomic “wires” as the amplitude of the fluctuations increased. The wires first became topologically nontrivial and then went back to trivial for sufficient disorder strengths.
Science , this issue p. [929][1]
[1]: /lookup/doi/10.1126/science.aat3406
Topological Matter
Adding irregularity to a system can lead to a transition from a more orderly to a less orderly phase. Meier et al. demonstrated a counterintuitive transition in the opposite direction: Controlled fluctuations in the system's parameters caused it to become topologically nontrivial. The starting point was a one-dimensional lattice of ultracold rubidium atoms in momentum space whose band structure was topologically trivial. The researchers then introduced fluctuations in the tunneling between the lattice sites and monitored the atomic “wires” as the amplitude of the fluctuations increased. The wires first became topologically nontrivial and then went back to trivial for sufficient disorder strengths.
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.
Symmetry plays a crucial role in understanding topological phases in materials. In one-dimensional systems, such as the Su-Schrieffer-Heeger (SSH) model, chiral symmetry is thought to ensure the quantization of the Zak phase and the nontrivial topological phase. However, our work demonstrates that the one-dimensional lattice system with broken chiral symmetry can still possess quantized Zak phase and nontrivial topological phase. Specifically, we use a Bose-Einstein condensate of 87Rb atoms in a momentum space lattice of ultracold atoms to effectively simulate a one-dimensional Zigzag model of 26 sites, which intrinsically breaks the chiral symmetry by additional next-nearest-neighbor coupling. To ensure the existence of the nontrivial topological phase, where the Zak phase can be measured from the time-averaged displacement during the system’s evolution, we need to preserve the inversion symmetry by modulating laser power so that all next-nearest-neighbor coupling strengths are equal. Furthermore, by changing the ratio of nearest-neighbor coupling strengths, we observe a topological phase transition from a nontrivial topological phase to a trivial topological phase at the point where the ratio equals 1. Our work demonstrates that the ultracold atom system provides a controllable platform for studying the symmetrical phase and topological phase, with the potential to explore nonlinear topological phenomena by increasing the interactions among atoms. In addition, our system can be used to investigate other interesting topological phenomena with more complex models, such as critical phenomena at the phase transitions and flat band structures in the extended SSH model with long-range coupling. By controlling the coupling strengths, we can also explore the influence of different symmetries on the topological properties of extended SSH models in the future. Moreover, our platform makes it possible to studythe models with more energy bands, such as the Aharonov-Bohm caging model with a three-level structure, which shows peculiar flat-band properties. This work provides opportunities for various studies in the fields of symmetry, topology, and the interaction of controllable quantum systems.
Nontrivial geometry of electronic Bloch states gives rise to topological insulators which are robust against sufficiently weak randomness inevitably present in any quantum material. However, increasing disorder triggers a quantum phase transition into a featureless normal insulator. As the underlying quantum critical point is approached from the topological side, small scattered droplets of normal insulators start to develop in the system and their coherent nucleation causes ultimate condensation into a trivial insulator. Unless disorder is too strong, the normal insulator accommodates disjoint tiny topological puddles. Furthermore, in the close vicinity of such a transition the emergent islands of topological and trivial insulators display spatial fractal structures, a feature that is revealed only by local topological markers. Here, we showcase this (possibly) generic phenomenon that should be apposite to dirty topological crystals of any symmetry class in any dimension from the Bott index and local Chern marker for a square-lattice-based disordered Chern insulator model.
Quantum Simulation
Most topologically nontrivial systems discovered to date consist of noninteracting particles. Their properties can therefore be explained within a single-particle picture. De Leseleuc et al. engineered a topological phase of bosonic atoms in which interactions play a crucial role. The atoms, which were in highly excited Rydberg states, were held in an array of optical tweezers. Depending on the spatial arrangement of the tweezers, the dipole-dipole interactions between the atoms gave rise to two configurations with different topological properties.
Science , this issue p. [775][1]
[1]: /lookup/doi/10.1126/science.aav9105
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.
Topological Matter
The discovery of topological phases of matter forced condensed matter physicists to question and reexamine some of the basic notions of their discipline. Wen reviews the progress of the field that took a sharp turn from Landau's broken symmetry paradigm to arrive at the modern notions of topological order and quantum entanglement in many-body systems. This development was made possible by using increasingly sophisticated mathematical formalisms.
Science , this issue p. [eaal3099][1]
[1]: /lookup/doi/10.1126/science.aal3099