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arXiv:2404.07371 · Physical Review Research

Gate-tunable phase transition in a resonator-based Su-Schrieffer-Heeger chain

Lukas Johannes Splitthoff, Miguel Carrera Belo, Guliuxin Jin, Yu Liu, Eliška Greplová, Christian Kraglund Andersen

Published Dec 16, 2024• 8 citations
arXivHTMLPDF

Abstract

Metamaterials engineered to host topological states of matter in controllable quantum systems hold promise for the advancement of quantum simulations and quantum computing technologies. In this context, the Su-Schrieffer-Heeger (SSH) model has gained prominence due to its simplicity and practical applications. Here we present the implementation of a gate-tunable, five-unit-cell resonator-based SSH chain on a one-dimensional lattice of superconducting resonators. We achieve electrostatic control over the inductive intracell coupling using semiconductor nanowire junctions, which enables the spectroscopic observation of a transition from a trivial to a topological phase in the engineered metamaterial. In contrast to prior work, our approach offers precise and independent tuning of the coupling parameters, which is critical to directly approximate ideal tight-binding Hamiltonians via the control over local variables. Our results supplement efforts towards gate-controlled superconducting electronics and large controllable resonator-based lattices to enable quantum simulations. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.043286

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Metamaterials engineered to host topological states of matter in controllable quantum systems hold promise for the advancement of quantum simulations and quantum computing technologies. In this context, the Su-Schrieffer-Heeger (SSH) model has gained prominence due to its simplicity and practical applications. Here we present the implementation of a gate-tunable, five-unit-cell resonator-based SSH chain on a one-dimensional lattice of superconducting resonators. We achieve electrostatic control over the inductive intracell coupling using semiconductor nanowire junctions, which enables the spectroscopic observation of a transition from a trivial to a topological phase in the engineered metamaterial. In contrast to prior work, our approach offers precise and independent tuning of the coupling parameters, which is critical to directly approximate ideal tight-binding Hamiltonians via the control over local variables. Our results supplement efforts towards gate-controlled superconducting electronics and large controllable resonator-based lattices to enable quantum simulations. Published by the American Physical Society 2024
Abstract The Su–Schrieffer–Heeger (SSH) model, which captures the most striking transport properties of the conductive organic polymer trans -polyacetylene, provides perhaps the most basic model system supporting topological excitations. The alternating bond pattern of polyacetylene chains is captured by the bipartite sublattice structure of the SSH model, emblematic of one-dimensional chiral symmetric topological insulators. This structure supports two distinct nontrivial topological phases, which, when interfaced with one another or with a topologically trivial phase, give rise to topologically protected, dispersionless boundary states. Here, using 87 Rb atoms in a momentum-space lattice, we realize fully tunable condensed matter Hamiltonians, allowing us to probe the dynamics and equilibrium properties of the SSH model. We report on the experimental quantum simulation of this model and observation of the localized topological soliton state through quench dynamics, phase-sensitive injection, and adiabatic preparation.
The Su--Schrieffer--Heeger (SSH) model is one of the simplest topological lattice models and is a promising candidate for quantum simulations of topological systems. In this study we investigate an interacting SSH model with nearest-neighbor interactions using mean field theory and an exact diagonalization method after the Jordan-Wigner transformation. We obtain a rich phase diagram with six different phases. Majorana bound states are found and confirmed by analyzing wave functions and Majorana number. In addition, we propose to use superconducting devices to construct a one-dimensional quantum circuit, where Cooper pair boxes and Josephson junctions are alternately connected in series, to theoretically simulate the interacting SSH model. This approach also provides us a toolkit to simulate correlated topological systems.
Topological insulators occupy a prominent position in the realm of condensed matter physics. Nevertheless, the presence of strong disorder has the potential to disrupt the integrity of topological states, leading to the localization of all states. This study delves into the intricate interplay between topology and localization within the one-dimensional Su–Schrieffer–Heeger (SSH) model, which incorporates controllable off-diagonal quasi-periodic modulations on superconducting circuits. Through the application of external alternating current (ac) magnetic fluxes, each transmon undergoes controlled driving, enabling independent tuning of all coupling strengths. Within a framework of this model, we construct comprehensive phase diagrams delineating regions characterized by extended topologically nontrivial states, critical localization, and co-existing topological and critical localization phases. The paper also addresses the dynamics of qubit excitations, elucidating distinct quantum state transfers resulting from the intricate interplay between topology and localization. Additionally, we propose a method for detecting diverse quantum phases utilizing existing experimental setups.
In the usual Su–Schrieffer–Heeger (SSH) model with an even number of lattice sites, the topological pumping between left and right edge states cannot be easily realized since the edge states occupy two-end sites simultaneously. Here we propose a scheme to investigate the topological edge pumping in an even-sized periodically modulated SSH model mapped by a one dimensional superconducting transmission line resonators array. We find that the photon initially prepared in the first resonator can be finally observed at the two-end resonators with a certain proportion. The final photon splitting at the two-end resonators indicates that the present superconducting circuit is expected to realize the topological beam splitter. Further, we demonstrate that the splitting proportion between the two-end resonators can be arbitrarily tuned from 1 to 0, implying the potential feasibility of implementing the tunable topological beam splitter. Meanwhile, we also show that the tunable topological beam splitter is immune to the mild disorder added into the system due to the topology protection of the zero energy modes, and find that the tunable topological beam splitter is much more robust to the global on-site disorder compared with the nearest neighbor disorder. Our work greatly extends the practical application of topological matter in quantum information processing and opens up a new way towards the engineering of topological quantum optical device.
We propose a scheme to control excitation transfer between an atom and the ends of the Su-Schrieffer-Heeger (SSH) chain. When the finite SSH chain is in the topological phase, and the frequency of the atom is resonant with the center frequency of the SSH chain, an effective transition between the atomic excited state and the band-gap states can be obtained. The system can be equal to the three-states model. Under this case, we can adiabatically transfer the atomic excitation to one of the ends of the SSH chain. Which end of the SSH chain is the receiver depends on which sublattice of the cell the atom is coupled to. Furthermore, the excitation can also be transferred from the atom to the ends of the chain by fixing the parameters under the dynamic evolution. Our paper provides a method for realizing controllable quantum information transfer based on the coupling of an atom with topological matter.
We explore a topology-localization phase diagram by simulating a one-dimensional Su-Schrieffer-Heeger model with quasiperiodic disorder using a programmable superconducting simulator. We experimentally map out and identify various trivial and topological phases with extended, critical, and localized bulk states. We find that with increasing disorder strength, some extended states can be first replaced by localized states and then by critical states before the system finally becomes fully localized. The critical states exhibit typical features such as multifractality and self-similarity, which lead to surprisingly rich phases with different types of mobility edges and scaling behaviors on the phase boundaries. Our results shed light on the investigation of the topological and localization phenomena in condensed-matter physics. Published by the American Physical Society 2024