Reproduction Package for:

Strong Reduction of Quasiparticle Fluctuations in a Superconductor due to Decoupling of the Quasiparticle Number and Lifetime

arXiv:2103.04777

This is a package of data and code to reproduce the results of the paper by S. A. H. de Rooij et al. (2021). The code in this package is also on github. The python code is a scaled down fork of this repository. This document will explain the content of the package and the steps needed to reproduce the results.

For any questions or remarks, contact: [email protected]

Software prerequisites

• Python 3 environment with jupyter, numpy, scipy and matplotlib
• MATLAB (2020+) with curve fitting toolbox

Package Contents

• figures -- raw figure files, which are presented in the paper
• data -- all the needed raw and processed data needed to reproduce the figures.
  • A#/B#/C# are subfolder containing the data for different devices as listed in the supplemental material. These have the following subfolders:
    • Noise_vs_T/TD_2D contains the raw Time Domain (TD) data, for different Kinetic Inductance Detectors (KIDs, i.e. the superconducting resonators) on the chip. Both read power and temperature are varied.
    • NoiseTDanalyse contains the file TDresults.mat, that stores the Power Spectral Densities (PSDs) calculated from the data in Noise_vs_T
    • S21/2D, contains the raw $S_{21}$ measurements (.dat-files) for different KIDs, with varying read power and temperature. It also contains .csv-files with extracted quality factors, responsivities and various other parameters, at different temperatures. The .png-files show summaries of $S_{21}$ analysis
    • KIDparam.txt is used in the $S_{21}$ analysis script and contains a table of design resonance frequencies, design Q-factors and lengths of the Al strips, for each KID.
• notebooks -- Jupyter notebooks that generate and save the figures
• python_code -- all necessary scripts for data analysis and plotting

  • Packages:

    • kidata is a package that deals with data from experiments. It contains the modules:
      • io, to find, read and write data
      • calc, which uses (multiple) raw data files to calculate Kinetic Inductance Detector (KID, which are the superconducting resonators) parameters, such as the kinetic induction fraction, phonon escape time and the quasiparticle lifetime from a Lorentzian fit to a PSD.
        • filters, to manipulate PSDs. For instance, to remove amplifier noise
      • noise, which processes the raw TD noise files: filter pulses and calculate PSDs, which are then stored in NoiseTDanalyse/TDresults.mat
        • plot, which contain (rather elaborate) plotting function to plot the data in various ways

  • Modules:

    • kidcalc implements superconductor theory that governs the behavior of MKIDs (mostly BSC, Mattis-Bardeen and Kaplan et al.)

      • trapmodels is used for trapping models, based on modified Rothwarf-Taylor equations, to explain the observed reduction in noise level

    • Ddata:

      • Ddata contains calculated gap energies over temperature for different $T_c$, to speed up the calculation of $\Delta(T)$.
• MATLAB_code contains the code to process the $S_{21}$ measurement raw data and write the .csv-files with the extracted parameters, such as Q-factors and responsivities.
  • S21analysisV5.m, the script to process the files
  • subroutines needed to run S21analysisV5.m

Reproducing the Results

The Jupyter notebooks in the notebooks directory can be directly executed to obtain the figures presented in both the main text of the paper and the supplemental information. These notebooks mostly use the plot functions, in the kidata.plot module.

In order for these to work, the raw data needs to be processed. The processed data files are present in the package, so that the notebooks work right away, but in order to reproduce these files two analyses must be done:

1. The PSDs need to be calculated from the raw TD noise files. This is done via the function kidata.noise.do_TDanalysis(), which takes the chipnumber (e.g. 'A1A2') as only required argument. This must be done for each chip separately. The calculated PSDs are stored in data/NoiseTDanalyse/TDresults.mat

2. The KID parameters from the $S_{21}$ measurement need to be calculated. This is done with the MATLAB script S21analysisV5.m in the MATLAB_code folder. In order to run this properly, the ChipInfo variable should be set correctly at the top of the .m-file. This includes: Chipnumber in the path, $T_c$ and Al thickness and width. The scripts loads the KIDparam.txt- file, which is in the data folder of the chip, for the Al length for each KID.

   Furthermore, to calculate the correct responsivities, the stopoffset variable should be set such that the high temperature data points, where the $S_{21}$-fits go wrong, are not included in the analysis. The index of the stopoffset vector corresponds to the KID number that is processed. Setting this variable can be done by setting it to 0 for every KID first, after which the threshold can be determined from the generated .png-images. Then, run the script again with the appropriate stopoffset-vector. The results are stored in .cvs-files in the same folder (e.g. A1A2/S21/2D/KID2_99dBm_Tdep.csv)