Data repository underlying the publication: Microwave spectroscopy of interacting Andreev spins

Data repository for: Microwave spectroscopy of interacting Andreev spins<em>Andreev bound states are fermionic states localized in weak links between superconductors which can be occupied with spinful quasiparticles. Microwave experiments using superconducting circuits with InAs/Al nanowire Josephson junctions have recently enabled probing and coherent manipulation of Andreev states but have remained limited to zero or small magnetic fields. Here we use a flux-tunable superconducting circuit compatible in magnetic fields up to 1T to perform spectroscopy of spin-polarized Andreev states up to ∼ 250 mT, beyond which the spectrum becomes gapless. We identify singlet and triplet states of two quasiparticles occupying different Andreev states through their dispersion in magnetic field. These states are split by exchange interaction and couple via spinorbit coupling, analogously to two-electron states in quantum dots. We also show that the magnetic field allows to drive a direct spin-flip transition of a single quasiparticle trapped in the junction. Finally, we measure a gate- and field-dependent anomalous phase shift of the Andreev spectrum, of magnitude up to ∼ 0.7π. Our observations demonstrate new ways to manipulate Andreev states in a magnetic field and reveal spin-polarized triplet states that carry supercurrent.</em><br>README CONTENTS (also included in the .ZIP)---------------------------------------------------------------------------<br># Data repository for: Microwave spectroscopy of interacting Andreev spins<br>Manuscript located at https://arxiv.org/abs/2208.11198<br>Authors: J. J. Wesdorp, F. J. Matute-Caňadas, A. Vaartjes, L. Grünhaupt, T. Laeven, S. Roelofs, L. J. Splitthoff, M. Pita-Vidal, A. Bargerbos, D. J. van Woerkom, P. Krogstrup, L. P. Kouwenhoven, C. K. Andersen, A. Levy Yeyati, B. van Heck, G. de Lange<br>This is a self-contained repository with the code that analyses the raw data (exported to .nc format).Required packages are:* matplotlib* xarray * h5py* h5netcdf * lmfit * scipy* numpy* jupyter-notebook* jupyter_contrib_nbextensions (recommended to see the table of content per notebook)* imageio (for gif generation)* qcodes (only for the notebook qcodes to xarray conversion, the rest of the code is qcodes independent). <br>*An environment.yaml file is provided for conda based installations. The exact versions are denoted there.*<br><br>Folder structure:- ./ : The top level folder contains the analysis notebooks that were used to process the data and fit to the minimal theoretical model. The Figures.ipynb contains the figure generation code and can be run standalone. - data : All data files used to generate the figures in the paper. The data is stored in netcdf format with h5netcdf as engine for loading with xarray. - data/processing is where intermediate analysis results are stored- data/processing/phi_0 analysis tool/verification_gifs : The GIF are stored here that show the phi_0 two tone data with traced minima/maxima for verification. - img : The raw output (separate panels) of the figure generation code is stored in the img folder - lib: custom code used for analysis and plotting of the data- kwant_simulation : code used for simulating and generating the figures the non-interacting model used for figure S19-S22.- kwant_simulation/data : simulation output of the kwant simulations. <br>One dataset (20201109_1372_parity_selection.nc) for figure S11 is added as a separate file and should be copied to the data folder because of its large file size. This allows for a direct preview of the rest of the repository in the 4TU repository. <br><br>

本数据集关联研究：相互作用安德列夫自旋的微波谱学
安德列夫束缚态（Andreev bound states）是局域于超导体间弱连接区域的费米子态，可被携带自旋的准粒子占据。近期，基于搭载InAs/Al纳米线约瑟夫森结（Josephson junctions）的超导电路开展的微波实验，已实现对安德列夫态的探测与相干调控，但此类实验仅能在零磁场或弱磁场环境下进行。本研究采用可兼容最高1T磁场的磁通可调超导电路，对自旋极化安德列夫态开展最高约250 mT磁场下的谱学研究；当磁场超过该阈值时，能谱将变为无带隙状态。研究团队通过准粒子在磁场中的色散关系，识别出占据不同安德列夫态的两个准粒子的单态与三重态。此类态会因交换相互作用发生能级劈裂，并通过自旋轨道耦合（spin-orbit coupling）发生耦合，这与量子点中的双电子态特征类似。本研究还证实，磁场可驱动结区中被俘获的单个准粒子发生直接的自旋翻转跃迁。最终，我们测得安德列夫能谱存在受栅极电压与磁场共同调控的反常相移，其最大幅值可达约0.7π。本研究的观测结果为磁场环境下安德列夫态的调控提供了新路径，并揭示了可携带超电流的自旋极化三重态。

README内容（同时包含在压缩包内）---------------------------------------------------------------------------
# 数据集关联研究：相互作用安德列夫自旋的微波谱学
相关论文已上传至arXiv：https://arxiv.org/abs/2208.11198
作者：J. J. Wesdorp, F. J. Matute-Caňadas, A. Vaartjes, L. Grünhaupt, T. Laeven, S. Roelofs, L. J. Splitthoff, M. Pita-Vidal, A. Bargerbos, D. J. van Woerkom, P. Krogstrup, L. P. Kouwenhoven, C. K. Andersen, A. Levy Yeyati, B. van Heck, G. de Lange

本数据集为独立完整的代码仓库，包含对导出为.nc格式的原始数据进行分析的代码。所需依赖包如下：
* matplotlib
* xarray
* h5py
* h5netcdf
* lmfit
* scipy
* numpy
* jupyter-notebook
* jupyter_contrib_nbextensions（推荐安装，用于查看各笔记本的目录结构）
* imageio（用于生成GIF动图）
* qcodes（仅用于将qcodes格式数据转换为xarray格式的笔记本代码，其余代码均不依赖qcodes）

仓库中提供了用于Conda环境安装的environment.yaml文件，其中标注了各依赖包的精确版本号。

## 文件夹结构
- ./ ：顶层目录包含用于处理数据并拟合极简理论模型的分析笔记本。其中Figures.ipynb包含论文配图生成代码，可独立运行。
- data/ ：存放生成论文配图所需的全部数据文件，数据以netCDF格式存储，加载时需通过xarray搭配h5netcdf引擎。
- data/processing/ ：存储中间分析结果
- data/processing/phi_0 analysis tool/verification_gifs ：存放用于验证的GIF动图，展示phi_0双音数据及追踪得到的极值点轨迹。
- img/ ：存储配图生成代码输出的原始单帧图像
- lib/ ：用于数据分析与绘图的自定义代码库
- kwant_simulation/ ：用于模拟并生成非相互作用模型相关配图的代码，对应论文补充图S19~S22。
- kwant_simulation/data/ ：Kwant模拟的输出结果文件

由于文件体积较大，用于生成补充图S11的数据集（20201109_1372_parity_selection.nc）以单独文件形式提供，需将其复制至data目录下。此举可让4TU仓库中本数据集的其余内容可直接预览。