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arXiv:1901.05683 · Physical Review Letters

Observation of Topological Magnon Insulator States in a Superconducting Circuit

Weizhou Cai, J. Han, Feng Mei, Yuan Xu, Yuxin Ma, Xuegang Li, Hanrui Wang, Yipu Song, Zheng‐Yuan Xue, Zhang‐qi Yin, Suotang Jia, Luyan Sun

Published Aug 20, 2019• 129 citations
arXivHTMLPDF

Abstract

Searching topological states in artificial systems has recently become a rapidly growing field of research. Meanwhile, significant experimental progress on observing topological phenomena has been made in superconducting circuits. However, topological insulator states have not yet been reported in this system. Here, for the first time, we experimentally realize a tunable dimerized spin chain model and observe the topological magnon insulator states in a superconducting qubit chain. Via parametric modulations of the qubit frequencies, we show that the qubit chain can be flexibly tuned into topologically trivial or nontrivial magnon insulator states. Based on monitoring the quantum dynamics of a single-qubit excitation in the chain, we not only measure the topological winding numbers, but also observe the topological magnon edge and defect states. Our experiment exhibits the great potential of tunable superconducting qubit chain as a versatile platform for exploring noninteracting and interacting symmetry-protected topological states.

DOI
10.1103/physrevlett.123.080501

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Searching topological states in artificial systems has recently become a rapidly growing field of research. Meanwhile, significant experimental progress on observing topological phenomena has been made in superconducting circuits. However, topological insulator states have not yet been reported in this system. Here, for the first time, we experimentally realize a tunable dimerized spin chain model and observe the topological magnon insulator states in a superconducting qubit chain. Via parametric modulations of the qubit frequencies, we show that the qubit chain can be flexibly tuned into topologically trivial or nontrivial magnon insulator states. Based on monitoring the quantum dynamics of a single-qubit excitation in the chain, we not only measure the topological winding numbers, but also observe the topological magnon edge and defect states. Our experiment exhibits the great potential of tunable superconducting qubit chain as a versatile platform for exploring noninteracting and interacting symmetry-protected topological states.
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.
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Abstract Topological phases of matter are an exotic phenomenon in modern condensed matter physics, which has attracted much attention due to the unique boundary states and transport properties. Recently, this topological concept in electronic materials has been exploited in many other fields of physics. Motivated by designing and controlling the behavior of electromagnetic waves in optical, microwave, and sound frequencies, topological photonics emerges as a rapid growing research field. Due to the flexibility and diversity of superconducting quantum circuits system, it is a promising platform to realize exotic topological phases of matter and to probe and explore topologically‐protected effects in new ways. Here, theoretical and experimental advances of topological photonics on superconducting quantum circuits—via the experimentally demonstrated parametric tunable coupling techniques, including using of the superconducting transmission line resonator, superconducting qubits, and their coupled system—are reviewed. On superconducting circuits, the flexible interactions and intrinsic nonlinearity make topological photonics in this system not only a simple photonic analog of topological effects for novel devices, but also a realm of exotic but less‐explored fundamental physics.
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.
Robust quantum state transfer (QST) is an indispensable ingredient in scalable quantum information processing. Here we present an experimentally feasible scheme for robust QST via topologically protected edge states in superconducting circuits. Using superconducting X-mon qubits with tunable couplings, the generalized Su-Schrieffer-Heeger models with topological magnon bands can be constructed. A novel entanglement-dependent topological Thouless pumping can be directly observed in this system. More importantly, we show that single-qubit states and entanglement can be robustly transferred with high fidelity in the presence of qubit-coupling imperfection, which is a hallmark of topological protection. This approach is experimentally applicable to a variety of quantum systems.
The recent experimental realization of a programmable two-dimensional square superconducting qubit array opens a new avenue for quantum simulation with qubits [Science 372, 948 (2021)]. Here, we present an experimentally feasible method to achieve two-dimensional superconducting qubit lattice with tunable coupling strengths. A configuration with higher-order topological phases is constructed, featuring topologically protected boundary states in lower dimension (corner states). We show that the quadrupole topological phases can be effectively characterized by the dynamics of the single-excitation quantum state. Moreover, we also explore the detection and dynamics of the corner modes in our qubit lattice system. Particularly, we propose an effective scheme to realize quantum information transfer via the corner states. Our work suggests that superconducting circuits systems are a fertile platform to study novel topological quantum phases and may shed light on the ongoing exploration of topologically protected quantum information processing.