Long-range interactions (LRIs) are ubiquitous in nature. Higher-order topological (HOT) insulator represents a new phase of matter. A critical issue is how LRI dictates the HOT phases. In this work, we discover four topologically distinct phases, i.e., HOT phase, the bound state in the continuum, Dirac semimetal (DSM) phase, and trivial insulator phase in a breathing kagome circuit with tunable LRIs. We find an emerging type-III corner state in the HOT phase, which splits from the edge state continuum and originates from the strong couplings between nodes at different edges. We experimentally detect this novel state by impedance and voltage measurements. In the DSM phase, the Dirac cone exhibits an itinerant feature with a tunable position that depends on the LRI strength. Our findings provide a deeper understanding of the LRI effect on exotic topological states and pave the way for regulating interactions in topolectrical circuits. 

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Observation of type-III corner states induced by long-range interactions

A circuit system consisting of LC-oscillators is mathematically shown to emulate quantum circuits. Here we develop a SPICE-based framework for emulating universal quantum gates (the phase-shift, the Hadamard, and the CNOT gates). To reconstruct each gate behavior, the inductors and capacitors are chosen and tuned precisely. Each quantum state is perfectly described by the phase and amplitude of each oscillator. In principle, our framework can simulate a quantum system with any arbitrary number of qubits since each gate process is perfectly achieved. Finally, we have simulated a quantum circuit with 3 qubits as input that consists of all the universal quantum gates. Our simulation result shows that our framework can classically emulate the result of any quantum circuit with an arbitrary number of qubits and quantum logic components. 

A SPICE-based Framework to Emulate Quantum Circuits with classical LC Resonators

Abstract The synergy between non-Hermitian concepts and topological ideas have led to very fruitful activity in the recent years. Their interplay has resulted in a wide variety of new non-Hermitian topological phenomena being discovered. In this review, we present the key principles underpinning the topological features of non-Hermitian phases. Using paradigmatic models—Hatano–Nelson, non-Hermitian Su–Schrieffer–Heeger and non-Hermitian Chern insulator—we illustrate the central features of non-Hermitian topological systems, including exceptional points, complex energy gaps and non-Hermitian symmetry classification. We discuss the non-Hermitian skin effect and the notion of the generalized Brillouin zone, which allows restoring the bulk-boundary correspondence. Using concrete examples, we examine the role of disorder, describe the Floquet engineering, present the linear response framework, and analyze the Hall transport properties of non-Hermitian topological systems. We also survey the rapidly growing experimental advances in this field. Finally, we end by highlighting possible directions which, in our view, may be promising for explorations in the near future. 

Non-Hermitian Topological Phases: Principles and Prospects

We propose an resistors, inductors and capacitors (RLC) electrical circuit to theoretically analyze and fully simulate a new type of non-Hermitian Su-Schrieffer-Heeger (SSH) model with complex hoppings. We formulate its construction and investigate its properties by taking advantage of the circuits versatility. Rich physical properties can be identified in this system from the normal modes of oscillation of the RLC circuit, including the highly tunable bulk-edge correspondence between topological winding numbers and edge states and the non-Hermitian skin phenomenon originating from a novel complex energy plane topology. The present study is able to show the wide and appealing topological physics inherent to electric circuits, which is readily generalizable to a plenty of both Hermitian and non-Hermitian nontrivial systems.

David-Andres Galeano

Papers

Topological circuit of a versatile non-Hermitian quantum system