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arXiv:2305.02486

Interplay between topology and localization on superconducting circuits

Xin Guan, Chen, Gang

Published May 4, 2023• 0 citations
arXivHTMLPDF

Abstract

Topological insulator lie at the forefront of condensed matter physics. However strong disorder can destroy the topological states and make all states become localized. In this paper, we investigate the competition between topology and localization in the one-dimensional Su-Schrieffer-Heeger (SSH) model with controllable off-diagonal quasi-periodic modulations on superconducting circuits. By utilizing external ac magnetic fluxes, each transmon can be driven and all coupling strengths can be tuned independently. Based on this model we construct phase diagrams that illustrate the extended topologically nontrivial, critical localization, and coexisting topological and critical localization phases. The dynamics of the qubits' excitations are also discussed in this paper, revealing distinct quantum state transfers resulting from the interplay between topology and localization. Furthermore, we propose a method for detecting different quantum phases using current experimental setups.

DOI
10.48550/arxiv.2305.02486

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Topological insulator lie at the forefront of condensed matter physics. However strong disorder can destroy the topological states and make all states become localized. In this paper, we investigate the competition between topology and localization in the one-dimensional Su-Schrieffer-Heeger (SSH) model with controllable off-diagonal quasi-periodic modulations on superconducting circuits. By utilizing external ac magnetic fluxes, each transmon can be driven and all coupling strengths can be tuned independently. Based on this model we construct phase diagrams that illustrate the extended topologically nontrivial, critical localization, and coexisting topological and critical localization phases. The dynamics of the qubits' excitations are also discussed in this paper, revealing distinct quantum state transfers resulting from the interplay between topology and localization. Furthermore, we propose a method for detecting different quantum phases using current experimental setups.
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.
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
Topological gapless systems, as the connection of the different topological quantum phases, have received much attention. Topological nonmediocre nodes are typically observed in two- or three-dimensional gapless systems. In this paper, we demonstrate that the topological nonmediocre nodes are existent in a model that lies between one dimension and two dimensions. Superconducting circuits, as essential all-solid state quantum devices, have offered a promising platform for studying the macro-controlling quantum effects. Recently, experimental achievements have enabled the realization of tunable coupling strengths between transmon qubits and the implementation of a one-dimensional Su-Schrieffer-Heeger (SSH) model [Li X et al. 2018 Phys. Rev. Appl. 10 054009 ]. According to this work, herein we present a two-leg SSH model implemented in superconducting circuits and demonstrate the existence of topological nonmediocre nodes. Firstly, two-leg superconducting circuit with transmon qubits which are coupled with their nearest-neighbor sites by capacitors is designed. To construct the two-leg SSH model, we introduce two alternating-current magnetic fluxes to drive each transmon qubit. We discover two types of phase boundaries in the SSH model and obtain the corresponding energy spectra and phase diagram. We identify two distinct topological insulating phases characterized by winding number ±1, and the corresponding edge states exhibit distinct characteristics. Moreover, we discuss the topological properties of the two phase boundaries. By representing the Bloch states as a vector field in k space, we demonstrate the existence of two kinks of nonmediocre nodes with first-type phase boundaries. These two nonmediocrenodes possess distinct topological charges of 1 and –1, respectively. On the other hand, the nonmediocre nodes with the second-type phase boundaries are topologically trivial. These results open the way for exploring novel topological states, ladder physical systems, and nodal point topological semimetals.
Topological insulators have inspired the study with various quantum simulators. Exploiting the tunability of the qubit frequency and qubit-qubit coupling, we show that a superconducting qubit chain can simulate various topological band models. When the system is restricted to the single-spin excitation subspace, the Su-Schrieffer-Heeger (SSH) model can be equivalently simulated by alternating the coupling strength between neighboring qubits. The existence of topological edge states in this qubit chain is demonstrated in the quench dynamics after the first qubit is excited. This excitation propagates along the chain where the qubit-qubit coupling is homogeneous. In contrast, in our qubit chain, the spin-up state localizes at the first qubit and the rest qubits remain in the spin-down state. We further show that the spin-up state can be transported along the chain by modulating the coupling strengths and the qubit frequencies. This demonstrates adiabatic pumping based on the Rice-Mele model. Moreover, we also discuss possible ways to construct other topological models with different topological phenomena within the current technology of superconducting qubits.
Abstract We propose a scheme to investigate the topological phase transition in the generalized one-dimensional Su–Schrieffer–Heeger (SSH) model based on a circuit quantum electrodynamics (QED) lattice with frequency modulation. We find that, if we keep the resonant counter rotating wave terms to map the p -wave superconducting pairing terms in the topological superconductor by dint of frequency modulation, the circuit QED lattice can be equivalent to the SSH model with p -wave superconducting pairing terms. The numerical results show that the existence of the superconducting pairing terms cannot close the energy gap of the SSH model within the feasible range of parameters, which means that the superconducting pairing terms cannot induce the topological phase transition. To induce the topological phase transition, we add the next-nearest-neighboring (NNN) interaction into the circuit QED-based SSH model simultaneously. We find that, for a given superconducting pairing strength, the appropriate selection of the NNN interaction can induce closing of the energy gap. It indicates that a new topological phase transition between the topologically nontrivial SSH phase and the topologically trivial SSH phase occurs in the SSH model. Our scheme provides a means to explore the topological SSH phase transition based on a circuit QED lattice with frequency modulation.
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.