Circuit-QED characterization of a topological Josephson junction

The search for topological superconductivity in topological insulator (TI) nanowires have attracted a lot of interest due to potential applications in the field of topologically protected quantum computation [1-3]. One route to emulate unconventional superconductivity is to build a topological Josephson junction from a TI nanowire (Bi₂Se₃) connected to two conventional superconducting electrodes (Al). Such topological Josephson junctions are expected to host Majorana zero-energy modes (bound states) when they are phase-biased at pi. The bound state spectrum of a junction hosting several transport modes consists of topological trivial Andreev bound states and topologically protected Majorana bound states. The phase dependence of those bound states has been studied experimentally using a circuit-QED-like setup, where the topological junction is embedded in a superconducting resonator. Here the frequency response of the coupled resonator/junction system to an externally applied magnetic field (phase bias) at various temperatures is used to deduce information about the phase dependence of the bound state spectrum of the junction. I detail, the contributions to the junction dissipation (which is directly reflected in the inverse quality factor of the coupled resonator/junction system) originating from zero-energy bound states and topological trivial Andreev bound states are rather distinct, which is mainly reflected in their phase bias dependence around and their evolution in temperature.在拓扑绝缘体（topological insulator, TI）纳米线中探索拓扑超导性，因其在拓扑保护量子计算领域的潜在应用而受到广泛关注[1-3]。一种模拟非常规超导性的途径，是构建由Bi₂Se₃型TI纳米线与两个常规超导电极（Al）连接而成的拓扑约瑟夫森结（Josephson junction）。此类拓扑约瑟夫森结在相位偏置为π时，理论上可承载马约拉纳零能模（Majorana zero-energy modes，即束缚态）。当结中存在多个输运模式时，其束缚态能谱包含拓扑平庸的安德列夫束缚态（Andreev bound states）与拓扑保护的马约拉纳束缚态。此前已有实验采用类电路量子电动力学（circuit-QED）架构，对上述束缚态的相位依赖性展开研究，该架构将拓扑约瑟夫森结嵌入超导谐振腔（superconducting resonator）中。本文通过测量耦合谐振腔-结系统在外加磁场（相位偏置）下不同温度的频率响应，以此推导出结的束缚态能谱的相位依赖性相关信息。具体而言，源自零能束缚态与拓扑平庸安德列夫束缚态的结耗散贡献——其直接体现为耦合谐振腔-结系统的逆品质因数——二者特征差异显著，主要体现在其围绕相位偏置的依赖特性，以及随温度的演化规律上。