Topological quantum states of matter, both Abelian and non-Abelian, are characterized by excitations whose wavefunctions undergo nontrivial statistical transformations as one excitation is moved (braided) around another. Topological quantum computation proposes to use the topological protection and the braiding statistics of a non-Abelian topological state to perform quantum computation. The enormous technological prospect of topological quantum computation provides new motivation for experimentally observing a topological state. Here, we explicitly work out a realistic experimental scheme to create and braid the Abelian topological excitations in the Kitaev model built on a tunable robust system, a cold atom optical lattice. We also demonstrate how to detect the key feature of these excitations: their braiding statistics. Observation of this statistics would directly establish the existence of anyons, quantum particles that are neither fermions nor bosons. In addition to establishing topological matter, the experimental scheme we develop here can also be adapted to a non-Abelian topological state, supported by the same Kitaev model but in a different parameter regime, to eventually build topologically protected quantum gates.
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http://dx.doi.org/10.1073/pnas.0709075104 | DOI Listing |
Nat Commun
January 2025
Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan.
Recent studies on topological materials are expanding into the nonlinear regime, while the central principle, namely the bulk-edge correspondence, is yet to be elucidated in the strongly nonlinear regime. Here, we reveal that nonlinear topological edge modes can exhibit the transition to spatial chaos by increasing nonlinearity, which can be a universal mechanism of the breakdown of the bulk-edge correspondence. Specifically, we unveil the underlying dynamical system describing the spatial distribution of zero modes and show the emergence of chaos.
View Article and Find Full Text PDFNat Commun
January 2025
School of Physics, Beihang University, Haidian District, Beijing, China.
Topology is being widely adopted to understand and to categorize quantum matter in modern physics. The nexus of topology orders, which engenders distinct quantum phases with benefits to both fundamental research and practical applications for future quantum devices, can be driven by topological phase transition through modulating intrinsic or extrinsic ordering parameters. The conjoined topology, however, is still elusive in experiments due to the lack of suitable material platforms.
View Article and Find Full Text PDFSci Adv
January 2025
Department of Physics, Princeton University, Princeton, NJ 08544, USA.
Introducing superconductivity in topological materials can lead to innovative electronic phases and device functionalities. Here, we present a unique strategy for quantum engineering of superconducting junctions in moiré materials through direct, on-chip, and fully encapsulated 2D crystal growth. We achieve robust and designable superconductivity in Pd-metalized twisted bilayer molybdenum ditelluride (MoTe) and observe anomalous superconducting effects in high-quality junctions across ~20 moiré cells.
View Article and Find Full Text PDFPhys Rev Lett
December 2024
RIKEN, Condensed Matter Theory Laboratory, CPR, Wako, Saitama 351-0198, Japan.
We show that the ground-state expectation value of twisting operator is a topological order parameter for U(1)- and Z_{N}-symmetric symmetry-protected topological (SPT) phases in one-dimensional "spin" systems-it is quantized in the thermodynamic limit and can be used to identify different SPT phases and to diagnose phase transitions among them. We prove that this (nonlocal) order parameter must take values in Nth roots of unity, and its value can be changed by a generalized lattice translation acting as an N-ality transformation connecting distinct phases. This result also implies the Lieb-Schultz-Mattis (LSM) ingappability for SU(N) spins if we further impose a general translation symmetry.
View Article and Find Full Text PDFPhys Rev Lett
December 2024
University of Tokyo, Institute for Solid State Physics, Kashiwa, Chiba 277-8581, Japan.
Non-Hermiticity gives rise to distinctive topological phenomena absent in Hermitian systems. However, connection between such intrinsic non-Hermitian topology and Hermitian topology has remained largely elusive. Here, considering the bulk and boundary as an environment and system, respectively, we demonstrate that anomalous boundary states in Hermitian topological insulators exhibit non-Hermitian topology.
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