Non equilibrium transport and dynamics in conventional and topological superconducting junctions

该项目涉及与电磁环境和微波辐射耦合的超导结中的量子输运和非平衡动力学的理论研究，考虑到准粒子效应。最近的实验集中在各种纳米结构（例如原子接触和拓扑材料）中的超导结，目的是创建一种超越标准约瑟夫森隧道结的新型多功能超导结。这些系统有望实现基于单安德烈夫能级的新型量子位，并具有一些针对耗散和退相干的预想保护措施。事实上，使用拓扑材料的结预计会产生与马约拉纳态相对应的特殊安德列夫能级，马约拉纳态的明确检测目前是深入研究的主题。介观超导结中的一个重要且常见的问题是长寿命准粒子的非平衡群体。这些准粒子的弛豫动力学和非平衡特性的基本机制尚不完全清楚。准粒子激发的存在会降低甚至破坏系统的运行，因此此类粒子代表了退相干和耗散的内在来源。因此，了解准粒子的非平衡动力学是一个至关重要的问题。该项目旨在研究准粒子在最先进的新型超导结（包括原子点接触、短纳米线和拓扑结）中的影响。具体来说，受安德烈夫光谱实验最新结果的推动，该项目将研究结点受到微波照射时的特性，以揭示安德烈夫激发光谱及其动力学。对于此类系统，我们将基于随时间变化的外场与电磁环境波动之间的相互作用，为准粒子的非平衡动力学提供一个理论框架。正在进行的原子结实验需要同时包括所有这些方面的理论分析。由于这在理论上具有挑战性，因此该项目代表了该领域的开创性工作。了解这些效应是在量子电路或量子位架构中以新颖、无耗散、非线性元件的形式充分利用这种新型器件的关键先决条件。最后，该项目最大的创新是将理论研究扩展到包括拓扑结。展望未来的实验，该项目旨在通过分析理论建议来实现重大突破，利用拓扑超导结中的安德烈夫光谱测量来实验揭示马约拉纳态。

This project concerns the theoretical study of quantum transport and non-equilibrium dynamics in superconducting junctions coupled to an electromagnetic environment and microwave irradiation, taking into account quasiparticle effects.Recent experiments have focused on superconducting junctions in various kinds of nanostructures (such as atomic contacts and topological materials) with the objective of creating a novel type of versatile superconducting junction beyond the standard Josephson tunnel junctions. These systems are promising for the potential realization of new types of qubits that are based on single Andreev levels with some envisioned protection against dissipation and decoherence. Indeed, junctions using topological materials are expected to give rise to special Andreev levels that correspond to Majorana states whose unambiguous detection is currently the subject of intense study.One important and common problem in mesoscopic superconducting junctions is the non-equilibrium population of long-lived quasiparticles. The underlying mechanisms for the relaxation dynamics and non-equilibrium properties of these quasiparticles are not fully understood. The presence of quasiparticle excitations degrades or even disrupts the operation of the systems, and thus such particles represent an intrinsic source of decoherence and dissipation. Understanding the non-equilibrium dynamics of quasiparticles is therefore a crucial issue.This project sets out to study the effects of quasiparticles in state-of-the-art novel superconducting junctions including atomic point contacts, short nanowires, and topological junctions. Specifically, motivated by recent results in Andreev spectroscopy experiments, this project will study the properties of junctions when they are irradiated by microwaves to reveal the Andreev excitation spectrum and its dynamics. For such systems, we will provide a theoretical framework for the non-equilbrium dynamics of the quasiparticles based on the interplay between the time-dependent external field and the fluctuations of the electromagnetic environment.Ongoing experiments in atomic junctions call for a theoretical analysis that includes all these aspects simultaneously. As this is theoretically challenging, this project represents pioneering work in the field.Understanding these effects is a crucial prerequisite for fully exploiting this new class of device in the form of novel, dissipation-free, non-linear elements in quantum circuits or in qubits architectures.Finally, the greatest innovation of the project is its extension of the theoretical investigation to include topological junctions. Anticipating future experiments, the project aims at a major breakthrough by analyzing a theoretical proposal to experimentally reveal Majorana states using Andreev spectroscopic measurementsin topological superconducting junctions.