Progress of photonic topological insulators in circuit-QED lattice and optomechanical array

Abstract

Topological insulators are a new kind of quantum state of the matters. Similar to the traditional insulators, topological insulators also possess the bulk gap and the insulating bulk states. The difference is that topological insulators have the conducting edge states on their surface or boundary at the same time. These conducting edge states are immune to the local disorders and perturbations since they are protected by the nonlocal topological invariant. The different values of the topological invariant usually correspond to different topological phases. The topological protection of the topological invariant originates from the topological structure of the energy bands in momentum space, which leads that the topological insulator has many potential applications in quantum information processing and quantum computing. The robust quantum state transfer can be realized with a high fidelity via the edge channel of the topological insulator, in which the process of state transfer is robust to the local disorders and perturbations since the edge channel is protected by the energy gap. Also, the topological quantum computing can be implemented by dint of the non-Abelian anyons and Majorana zero modes. These potential applications make the topological insulator have many significant research values in quantum information processing and quantum computing. However, the experimental realization of the topological insulators based on the traditional electronic system has many challenges both in experimental techniques and experimental detections. From the perspectives of energy spectrum and Bloch theorem, electron, photon, and phonon present certain similarity. So, in the field of bosons with integral spin, the quantized topological states of light, sound, mechanical motion should also be implemented similarly, which provides opportunity to conveniently realize the topological insulators in experiment based on different bosonic optical systems. With the fast-developing fields of micro-nano manufacturing and materials processing technology in recent years, all kinds of quantum optical platforms become reliable candidates for the simulations and mappings of the topological insulators, which are the so called photonic topological insulators. Based on the bosonic statistical properties in these platforms, the relevant topological issues can be easily realized and even detected directly. For example, the circuit-QED lattice, consisting of a series of superconducting resonators and qubits, is becoming a more and more appealing and reliable candidate for the mappings and the simulations of all kinds of topological insulators due to its advantages of tunability and scalability. Many topological issues based on the one dimensional circuit-QED system have been investigated, such as the mapping of the high-dimensional topological Chern insulator, the topological edge state and the topological invariant, the detection of topological edge states, etc. Another promoting quantum optical platform is the optomechanical array, which is composed by single optomechanical system. The optomechanical array contains the photons and the phonons at the same time, which has many potential advantages in the mapping and the detection of all kinds of topological issues. However, the topological phenomenon based on the optomechanical array is still rarely investigated. Thus, we summarize the development in the field of the topological insulators and review the latest research progress of photonic topological insulators in circuit-QED lattice and optomechanical array.