{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f6cd0a9d-6b7c-488d-a264-d51074d9bc88",
   "metadata": {},
   "source": [
    "---\n",
    "**© 2026 MaLab @ Purdue University. All rights reserved.**\n",
    "\n",
    "**Authors:** Botao Du, Qihao Guo, Ruichao Ma\n",
    "\n",
    "**Group:** [MaLab @ Purdue](https://www.ma-quantumlab.com/)\n",
    "\n",
    "This notebook and its contents are the intellectual property of the authors.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "def70527-04de-41be-8ce2-de8533b21bec",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from numpy import *\n",
    "from matplotlib.pyplot import *\n",
    "\n",
    "import math as math\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "212a2701-732c-43ff-84a7-5c653afbb67d",
   "metadata": {},
   "source": [
    "# Fig.2 (b) - (c), Load Data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d024adbc-aa45-45a2-a0ac-7b4b5c224b3f",
   "metadata": {},
   "source": [
    "Load decay rate from Fig_2_bc_data.npz\n",
    "- theta_list: relative phases between the sideband to Q1 and the sideband to Q2, unit ($\\times 2\\pi$), shape: (index_theta,) = (26,).\n",
    "- Gamma_plus_state: Engineered T1 decay rates from 2Q single-excitation plus eigenstate, unit (2$\\pi\\times$ KHz). Only Q1, Q2 are employeed in the experiment, shape: (index_theta,) = (26,).\n",
    "- Gamma_minus_state: Engineered T1 decay rates from 2Q single-excitation minus eigenstate, unit (2$\\pi\\times$ KHz). Only Q1, Q2 are employeed in the experiment, shape: (index_theta,) = (26,).\n",
    "- times: Time list for engineered decay, unit ($\\mu$s), shape (index_time,) =(54,).\n",
    "- population_minus: Population dynamics for engineered collective decay (after thermal population correction), from 2Q single-excitation minus eigenstate, shape: (index_theta, index_time) = (26, 54).\n",
    "- population_plus: Population dynamics for engineered collective decay (after thermal population correction), from 2Q single-excitation minus eigenstate, shape: (index_theta, index_time) = (26, 54). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "98735563-5070-411b-a624-db71606dfd33",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset for Fig.2 (b) - (c), Programmable Superradiance in an Interacting Qubit Array, MaLab, arXiv: 2605.12442\n",
      "['theta_list', 'Gamma_plus_state', 'Gamma_mins_state', 'times', 'population_minus', 'population_plus', 'note']\n"
     ]
    }
   ],
   "source": [
    "infile = 'data/Fig_2_bc_data.npz'\n",
    "exp_data = np.load(infile)\n",
    "print(exp_data['note'])\n",
    "print(exp_data.files)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "7e99ac69-d641-4210-9a27-2d1ec2f55e7e",
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_list = exp_data['theta_list']\n",
    "Gamma_plus_state = exp_data['Gamma_plus_state']\n",
    "Gamma_mins_state = exp_data['Gamma_mins_state']\n",
    "\n",
    "times = exp_data['times']\n",
    "population_minus = exp_data['population_minus']\n",
    "population_plus = exp_data['population_plus']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54ad99c2-59a8-4ee1-8e0d-287b8eb8ac53",
   "metadata": {},
   "source": [
    "## Plot Fig.2 (b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2ef14ac-bab6-45c1-8ef1-a827a73228c6",
   "metadata": {},
   "source": [
    "### $\\theta = 0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "cb15b8c4-d7d0-4e37-9348-aa643000eca5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x17b4c6f33d0>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(times, population_minus[0, :], label = r'$|-\\rangle$')\n",
    "plt.plot(times, population_plus[0, :], label = r'$|+\\rangle$')\n",
    "\n",
    "plt.xlabel('Times')\n",
    "plt.ylabel('Population')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c865df4d-add3-4fa2-8996-d04d15610bed",
   "metadata": {},
   "source": [
    "### $\\theta = \\pi$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "3296bb62-c6b1-4d55-91b5-4ccd765f04b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x17b4e8bbf10>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(times, population_minus[13, :], label = r'$|-\\rangle$')\n",
    "plt.plot(times, population_plus[13, :], label = r'$|+\\rangle$')\n",
    "\n",
    "plt.xlabel('Times')\n",
    "plt.ylabel('Population')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e300cb36-3e38-400e-bc43-58f05c18b127",
   "metadata": {},
   "source": [
    "# Fig.2 (d), Load Data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7c44f58-79b2-4cf4-a410-124fb1d2fda0",
   "metadata": {},
   "source": [
    "Load decay rate from Fig_2_d_data.npz\n",
    "- theta_list: relative phases between the sideband to Q1 and the sideband to Q2, unit ($\\times 2\\pi$), shape: (index_theta,) = (21,).\n",
    "- frequency_list: the frequency detuning between 2 sidebands, unit (2$\\pi\\times$ MHz), shape: (index_freq,) = (25,).\n",
    "- Gamma_plus: Engineered T1 decay rates from 2Q single-excitation plus eigenstate, unit (2$\\pi\\times$ KHz). Only Q1, Q2 are employeed in the experiment, shape: (index_freq, index_theta) = (25, 21).\n",
    "- Gamma_minus: Engineered T1 decay rates from 2Q single-excitation minus eigenstate, unit (2$\\pi\\times$ KHz). Only Q1, Q2 are employeed in the experiment, shape: (index_freq, index_theta) = (25, 21)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "c30023fd-bec5-4439-80e8-5ee90a755bd8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset for Fig.2 (d), Programmable Superradiance in an Interacting Qubit Array, MaLab, arXiv: 2605.12442\n",
      "['theta_list', 'frequency_list', 'Gamma_plus', 'Gamma_minus', 'note']\n"
     ]
    }
   ],
   "source": [
    "infile = 'data/Fig_2_d_data.npz'\n",
    "exp_data = np.load(infile)\n",
    "print(exp_data['note'])\n",
    "print(exp_data.files)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "916e94b1-4177-42e7-9e3d-f88bd1cb26f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_list = exp_data['theta_list']\n",
    "frequency_list = exp_data['frequency_list']\n",
    "Gamma_plus = exp_data['Gamma_plus']\n",
    "Gamma_minus = exp_data['Gamma_minus']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "12557834-f063-4c1d-890b-068ead739c2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x450 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=(4,3), dpi = 150)\n",
    "\n",
    "pcolor(theta_list, frequency_list, Gamma_plus - Gamma_minus, shading='auto', cmap=\"RdBu\")\n",
    "colorbar(label = r'$\\Gamma$ (kHz)')\n",
    "xlabel(r'Sideband Phase (2$\\pi$)')\n",
    "ylabel('Sideband Detuning (MHz)')\n",
    "show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "daa4e46a-8648-4c92-bf33-dd231a9133ab",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.19"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
