code master.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "1f333df2",
   "metadata": {},
   "source": [
    "## Import lib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "57e26643",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import qucat objects\n",
    "from qucat import GUI, Network, R,L,C,J\n",
    "import qucat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "eaf7bdad",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from copy import deepcopy\n",
    "from scipy.constants import h,hbar,e\n",
    "from time import time\n",
    "\n",
    "# Plotting imports \n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "import matplotlib.colors as colors\n",
    "%matplotlib inline\n",
    "\n",
    "# Plotting settings\n",
    "column = 3.54\n",
    "two_columns = 7.48\n",
    "matplotlib.rc\n",
    "my_font = {'sans-serif': 'Myriad Pro'}\n",
    "my_font.update({'size': 9})\n",
    "matplotlib.rc('font', **my_font)\n",
    "\n",
    "my_xticks = {'bottom':True}\n",
    "my_xticks.update({'top':True})\n",
    "my_xticks.update({'direction':'in'})\n",
    "matplotlib.rc('xtick', **my_xticks)\n",
    "\n",
    "my_yticks = {'left':True}\n",
    "my_yticks.update({'right':True})\n",
    "my_yticks.update({'direction':'in'})\n",
    "matplotlib.rc('ytick', **my_yticks)\n",
    "\n",
    "# Colors to be used \n",
    "c = cm.coolwarm(np.linspace(0.,1.,6))\n",
    "dark_blue = c[0].tolist()\n",
    "blue = c[1].tolist()\n",
    "light_blue = c[2].tolist()\n",
    "light_red = c[3].tolist()\n",
    "red = c[4].tolist()\n",
    "light_black = \"#1c1c1c\"\n",
    "mode_0_color= dark_blue\n",
    "mode_1_color = red"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ccb9b41d",
   "metadata": {},
   "source": [
    "## Menginisialisasi sirkuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "711255e6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Programmable\n",
    "\n",
    "circuit_components = [\n",
    "# transmon\n",
    "qucat.C(0,1,100e-15),\n",
    "qucat.J(0,1,'Lj'),\n",
    "# resonator\n",
    "qucat.C(0,2,100e-15),\n",
    "qucat.L(0,2,10e-9),\n",
    "# coupling capacitor\n",
    "qucat.C(1,2,1e-15),\n",
    "# external coupling capacitor\n",
    "qucat.C(2,3,0.5e-15),\n",
    "# 50 Ohm load\n",
    "qucat.R(3,0,50),\n",
    "]\n",
    "cQED = Network(circuit_components)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1b638843",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C 0 2 100 fF\n",
      "J 0 2 Lj\n",
      "C 0 1 1 fF\n",
      "C 1 2 100 fF\n",
      "L 1 2 10 nH\n",
      "C 1 3 500 aF\n",
      "R 2 3 50 Ohm\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Graphical\n",
    "\n",
    "cQED = GUI('main.txt',edit = False, plot = False, print_network=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8f530d72",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "findfont: Font family ['sans-serif'] not found. Falling back to DejaVu Sans.\n",
      "findfont: Generic family 'sans-serif' not found because none of the following families were found: Myriad Pro\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 319.2x124.236 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make circuti more compact for this figure\n",
    "cQED.plotting_parameters_show['figsize_scaling'] = 0.7\n",
    "\n",
    "# Generate the circuit figure\n",
    "fig,ax = cQED.show(plot = False, return_fig_ax = True)\n",
    "\n",
    "# Save the figure\n",
    "fig.savefig('fig1_cQED_circuit.pdf',transparent = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d3765914",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Menggenerasi dan diagonalisasi Hamiltonian\n",
    "\n",
    "# This will hold the calculated eigen-energies of the system\n",
    "eigen_energies = []\n",
    "\n",
    "# Values of the josephson inductance we will be sweeping\n",
    "L_J = np.linspace(10e-9,8e-9, 101)\n",
    "\n",
    "for x in L_J:\n",
    "    # The hamiltonian function returns a QuTiP Hamiltonian where (h=1), meaning\n",
    "    # that the hamiltonian has units of frequency (not angular frequency)\n",
    "    H = cQED.hamiltonian(\n",
    "        modes = [0,1],# Consider modes 0 and 1\n",
    "        taylor = 4,# Expand the Josephson potential up to the 8th order\n",
    "        excitations = [10,12], # Consider 10 excitations in the lower frequency mode 0, 12 in mode 1\n",
    "        Lj = x)# We have to specify a value of the josephson inductance\n",
    "                # since we didn't specify it when constructing the circuit\n",
    "        \n",
    "    # Calculate the eigenenergies (here in units of frequency) using the qutip\n",
    "    # function eigenenergies, and add the values to the eigen_energies list\n",
    "    eigen_energies.append(H.eigenenergies())\n",
    "    \n",
    "# Qutip will return complex values with 0 imaginary parts, \n",
    "# we want to convert them to real numbers here\n",
    "eigen_energies = np.real(eigen_energies)\n",
    "\n",
    "# First and second transition frequencies\n",
    "first_transition = (eigen_energies[:,1]-eigen_energies[:,0])\n",
    "second_transition = (eigen_energies[:,2]-eigen_energies[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "bc955fc9",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:matplotlib.font_manager:findfont: Font family ['sans-serif'] not found. Falling back to DejaVu Sans.\n",
      "WARNING:matplotlib.font_manager:findfont: Generic family 'sans-serif' not found because none of the following families were found: Myriad Pro\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting of the transition frequencies\n",
    "#fig,ax = plt.subplots(1,1,figsize = (column*0.7,column*0.45))\n",
    "\n",
    "fig,ax = plt.subplots(1, 1, figsize = (6, 4))\n",
    "lw = 0.8\n",
    "plt.plot(L_J*1e9,first_transition/1e9, color = mode_0_color, lw = lw)\n",
    "plt.plot(L_J*1e9,second_transition/1e9, color = mode_1_color, lw = lw)\n",
    "plt.xlabel('Lj (nH)')\n",
    "plt.ylabel('Transitions (GHz)')\n",
    "plt.tight_layout()\n",
    "fig.savefig('fig4.pdf',transparent = True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "72d997c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Normal mode analysis\n",
    "\n",
    "# Values of the josephson inductance we will be sweeping\n",
    "L_J_list = np.linspace(11e-9,9e-9,101)\n",
    "# Calculate normal mode frequencies, dissipaiton rates, \n",
    "# anharmonicity and cross-Kerr\n",
    "f,k,A,chi = cQED.f_k_A_chi(Lj = L_J_list)\n",
    "\n",
    "# Alternative method\n",
    "f = cQED.eigenfrequencies(Lj = L_J_list)\n",
    "k = cQED.loss_rates(Lj = L_J_list)\n",
    "A = cQED.anharmonicities(Lj = L_J_list)\n",
    "chi = cQED.kerr(Lj = L_J_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b787bc69",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mukhamad-a/.local/lib/python3.9/site-packages/matplotlib/cbook/__init__.py:1298: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return np.asarray(x, float)\n",
      "/home/mukhamad-a/.local/lib/python3.9/site-packages/matplotlib/cbook/__init__.py:1298: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return np.asarray(x, float)\n",
      "/home/mukhamad-a/.local/lib/python3.9/site-packages/matplotlib/cbook/__init__.py:1298: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return np.asarray(x, float)\n",
      "/home/mukhamad-a/.local/lib/python3.9/site-packages/matplotlib/cbook/__init__.py:1298: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return np.asarray(x, float)\n",
      "/home/mukhamad-a/.local/lib/python3.9/site-packages/matplotlib/cbook/__init__.py:1298: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return np.asarray(x, float)\n",
      "/home/mukhamad-a/.local/lib/python3.9/site-packages/matplotlib/cbook/__init__.py:1298: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return np.asarray(x, float)\n",
      "/home/mukhamad-a/.local/lib/python3.9/site-packages/matplotlib/cbook/__init__.py:1298: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return np.asarray(x, float)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot these results\n",
    "lw = 0.8\n",
    "\n",
    "fig,ax = plt.subplots(2,2,sharex = True,figsize = (6,4))\n",
    "ax[0][0].plot(L_J_list*1e9,f[0]/1e9,label = 'mode #0',color = mode_0_color,lw = lw)\n",
    "ax[0][0].plot(L_J_list*1e9,f[1]/1e9,label = 'mode #1',color = mode_1_color,lw = lw)\n",
    "ax[0][0].set_ylabel(r'$\\omega_m/2\\pi$ (GHz)')\n",
    "\n",
    "ax[0][1].plot(L_J_list*1e9,k[0]/1e3,color = mode_0_color,lw = lw)\n",
    "ax[0][1].plot(L_J_list*1e9,k[1]/1e3,color = mode_1_color,lw = lw)\n",
    "ax[0][1].set_ylabel(r'$\\kappa_m/2\\pi$ (kHz)')\n",
    "\n",
    "ax[1][0].plot(L_J_list*1e9,A[0]/1e6,color = mode_0_color,lw = lw)\n",
    "ax[1][0].plot(L_J_list*1e9,A[1]/1e6,color = mode_1_color,lw = lw)\n",
    "ax[1][0].set_ylabel('$A_m/h$ (MHz)')\n",
    "\n",
    "ax[1][1].plot(L_J_list*1e9,chi[0][1]/1e6,color = mode_0_color,lw = lw)\n",
    "ax[1][1].set_ylabel('$\\chi_{01}/h$ (MHz)')\n",
    "\n",
    "ax[1][0].set_xlabel('$L_J$ (nH)')\n",
    "ax[1][1].set_xlabel('$L_J$ (nH)')\n",
    "\n",
    "plt.tight_layout()\n",
    "fig.savefig('fig2_w_k_A_chi.pdf',transparent = True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ad7e556b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         mode |       freq.  |       diss.  |       anha.  |\n",
      "            0 |     4.98 GHz |     11.8 kHz |     27.2 MHz |\n",
      "            1 |     5.03 GHz |      7.5 kHz |     74.6 MHz |\n",
      "\n",
      "Kerr coefficients (diagonal = Kerr, off-diagonal = cross-Kerr)\n",
      "         mode |         0    |         1    |\n",
      "            0 |     27.2 MHz |              |\n",
      "            1 |       90 MHz |     74.6 MHz |\n",
      "\n"
     ]
    }
   ],
   "source": [
    "f,k,A,chi = cQED.f_k_A_chi(Lj = 10e-9, pretty_print = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b41a9f61",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum calculation -- Rabi splitting is 49.335 MHz\n",
      "Classical calculation -- normal-mode splitting is 49.343 MHz\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_2219/3975823838.py:9: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  print(\"Classical calculation -- normal-mode splitting is %.3f MHz\"%mode_splitting)\n"
     ]
    }
   ],
   "source": [
    "# Sanity check: compare the avoided crossing \n",
    "# as calculated from the Hamiltonian and \n",
    "# form the eigenfrequencies\n",
    "rabi_splitting = min(second_transition-first_transition)/1e6\n",
    "mode_splitting = min(cQED.eigenfrequencies(Lj=np.linspace(9.8e-9,10.2e-9, 101))[1]\\\n",
    "                     -cQED.eigenfrequencies(Lj=np.linspace(9.8e-9,10.2e-9, 101))[0])/1e6\n",
    "\n",
    "print(\"Quantum calculation -- Rabi splitting is %.3f MHz\"%rabi_splitting)\n",
    "print(\"Classical calculation -- normal-mode splitting is %.3f MHz\"%mode_splitting)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a9bc6950",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Mode Visualisasi\n",
    "\n",
    "# Modify the plotting parameters \n",
    "# to make the figure more pretty\n",
    "pp = deepcopy(cQED.plotting_parameters_show)\n",
    "pp[\"y_fig_margin\"]= 0.7\n",
    "\n",
    "scale = 1\n",
    "pp[\"figsize_scaling\"] = scale\n",
    "pp[\"C\"][\"gap\"] /= scale\n",
    "pp[\"C\"][\"height\"] /= scale\n",
    "pp[\"J\"][\"width\"] /= scale\n",
    "pp[\"L\"][\"width\"] /= scale\n",
    "pp[\"L\"][\"height\"] /= scale\n",
    "pp[\"R\"][\"width\"] /= scale\n",
    "pp[\"R\"][\"height\"] /= scale\n",
    "pp[\"label\"]= {\n",
    "        \"fontsize\": 10,\n",
    "        \"text_position_horizontal\": [0.,-pp[\"C\"][\"height\"]/2-0.07],\n",
    "        \"text_position_vertical\": [pp[\"C\"][\"height\"]/2+0.05,-0.08]\n",
    "    }\n",
    "pp[\"normal_mode_label\"]= {\n",
    "        \"fontsize\": 10,\n",
    "        \"color\": dark_blue,\n",
    "        \"y_arrow\": pp[\"C\"][\"height\"]/2+0.1,\n",
    "        \"text_position_horizontal\": [0.,pp[\"C\"][\"height\"]/2+0.28],\n",
    "        \"text_position_vertical\": [-pp[\"C\"][\"height\"]/2-0.15,+0.07]\n",
    "    }\n",
    "pp[\"normal_mode_arrow\"]= {\n",
    "        \"min_width\": 0.1,\n",
    "        \"max_width\": 0.4,\n",
    "        \"min_lw\": 1,\n",
    "        \"max_lw\": 3,\n",
    "        \"min_head\": 0.05,\n",
    "        \"max_head\": 0.071,\n",
    "        \"color\": dark_blue\n",
    "    }\n",
    "cQED.plotting_parameters_normal_modes = pp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "67dffa95",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 456x206.28 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 456x206.28 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visulize the normal modes\n",
    "fig,ax = cQED.show_normal_mode(mode=0, Lj = 10e-9, quantity = 'voltage',\n",
    "                               return_fig_ax=True, add_title=False, add_legend=False)\n",
    "fig.savefig('fig3_mode0_resonance.pdf',transparent = True)\n",
    "\n",
    "fig,ax = cQED.show_normal_mode(mode=1, Lj = 10e-9, quantity = 'voltage',\n",
    "                               return_fig_ax=True, add_title=False, add_legend=False)\n",
    "fig.savefig('fig3_mode1_resonance.pdf',transparent = True,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "dd49faf0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum calculation -- Rabi splitting is 49.335 MHz\n",
      "Classical calculation -- normal-mode splitting is 49.343 MHz\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_2219/580746428.py:6: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  print(\"Classical calculation -- normal-mode splitting is %.3f MHz\"%mode_splitting)\n"
     ]
    }
   ],
   "source": [
    "rabi_splitting = min(second_transition-first_transition)/1e6\n",
    "mode_splitting = min(cQED.eigenfrequencies(Lj=np.linspace(9.8e-9,10.2e-9, 101))[1]\\\n",
    "                     -cQED.eigenfrequencies(Lj=np.linspace(9.8e-9,10.2e-9, 101))[0])/1e6\n",
    "\n",
    "print(\"Quantum calculation -- Rabi splitting is %.3f MHz\"%rabi_splitting)\n",
    "print(\"Classical calculation -- normal-mode splitting is %.3f MHz\"%mode_splitting)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45e2a3f7",
   "metadata": {},
   "source": [
    "### Filtered cavity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "0bca8635",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 390x115.362 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Build circuit\n",
    "filtered_cavity = GUI('filtered_cavity.txt',plot = False,edit = False)\n",
    "# Adapt plotting parameters to make more pretty\n",
    "filtered_cavity.plotting_parameters_show['figsize_scaling'] = 0.65\n",
    "# Plot circuit\n",
    "fig,ax = filtered_cavity.show(plot = False, return_fig_ax = True)\n",
    "fig.savefig('fig_filtered_cavity.pdf',transparent = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b5787de4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         mode |       freq.  |       diss.  |       anha.  |\n",
      "            0 |      173 MHz |     18.8 MHz |          0Hz |\n",
      "            1 |      464 MHz |     7.76 MHz |          0Hz |\n",
      "            2 |     5.28 GHz |     68.2 mHz |          0Hz |\n",
      "\n",
      "Kerr coefficients (diagonal = Kerr, off-diagonal = cross-Kerr)\n",
      "         mode |         0    |         1    |         2    |\n",
      "            0 |          0Hz |              |              |\n",
      "            1 |          0Hz |          0Hz |              |\n",
      "            2 |          0Hz |          0Hz |          0Hz |\n",
      "\n"
     ]
    }
   ],
   "source": [
    "f,k,A,chi = filtered_cavity.f_k_A_chi(pretty_print=True, L = 0.3e-6, C = 1e-12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3d746256",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mukhamad-a/.local/lib/python3.9/site-packages/qucat/core.py:2446: RuntimeWarning: invalid value encountered in sqrt\n",
      "  return np.sqrt(hbar/np.real(z)/np.imag(dY(z,**kwargs)))\n"
     ]
    }
   ],
   "source": [
    "# The resonance modes of the filter\n",
    "# have a very low quality factors, which make\n",
    "# them inadequate for quantization\n",
    "# by default QuCAT will discard these modes\n",
    "# and notify the user with a warning, here\n",
    "# we disactivate these warnings\n",
    "filtered_cavity.warn_discarded_mode = False\n",
    "\n",
    "# Build a list of inductances and capacitances\n",
    "points = 31\n",
    "C_list = np.logspace(-13.5,-11.8,points)\n",
    "L_list = np.logspace(-8.5,-6.8,points)\n",
    "\n",
    "# Initialize an array to store the resonator loss rates\n",
    "k = np.zeros((points,points))\n",
    "\n",
    "# Sweep over capacitances and inductances\n",
    "for i,capacitance in enumerate(C_list):\n",
    "    for j,inductance in enumerate(L_list):\n",
    "        # Calculate loss rates (for all modes)\n",
    "        k_all_modes = filtered_cavity.loss_rates(\n",
    "                    C = capacitance,\n",
    "                    L = inductance)\n",
    "        # Store the resonator loss rate\n",
    "        k[i,j] = k_all_modes[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "2c5b886a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plt.pcolor(C_list,L_list,k)\n",
    "#cbar = plt.colorbar()\n",
    "#fig,ax = plt.subplots(1,1,figsize = (column*1,column*0.7))\n",
    "\n",
    "fig,ax = plt.subplots(1, 1, figsize = (6, 4))\n",
    "plt.pcolor(C_list,L_list,k,norm=colors.LogNorm(vmin=k.min(), vmax=k.max()),\n",
    "               cmap = plt.get_cmap('coolwarm_r'))\n",
    "cbar = plt.colorbar()\n",
    "cbar.ax.tick_params(axis='both', which='major', labelsize=9)\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.xlabel(\"C (F)\")\n",
    "plt.ylabel(\"L (H)\")\n",
    "cbar.ax.set_ylabel('k (Hz)')\n",
    "fig.savefig('fig_filtered_cavity_k_vs_LC.png', transparent = True,dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8dacf0c4",
   "metadata": {},
   "source": [
    "## Tunable coupler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "1eda1194",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 422.4x198.72 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Build and plot circuit\n",
    "import scipy.constants as cst\n",
    "from scipy.constants import pi, hbar, h, e\n",
    "\n",
    "tuneable_coupler = GUI('tuneable_coupler.txt',plot = False,edit = True)\n",
    "tuneable_coupler.plotting_parameters_show['figsize_scaling'] = 0.8\n",
    "fig,ax = tuneable_coupler.show(plot = False, return_fig_ax = True)\n",
    "fig.savefig('fig_tuneable_coupler_circuit.pdf',transparent = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "5bd0b786",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Lj(phi):\n",
    "    # maximum Josephson energy\n",
    "    Ejmax = 6.5e9\n",
    "    # junction asymmetry\n",
    "    d = 0.0769\n",
    "    # flux to Josephson energy\n",
    "    Ej = Ejmax*np.cos(pi*phi) *np.sqrt(1+d**2 *np.tan(pi*phi)**2)\n",
    "    # Josephson energy to inductance\n",
    "    return (hbar/2/e)**2/(Ej*h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "7c0531a6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         mode |       freq.  |       diss.  |       anha.  |\n",
      "            0 |     3.27 GHz |          0Hz |      165 MHz |\n",
      "            1 |     6.84 GHz |          0Hz |      128 MHz |\n",
      "            2 |     6.98 GHz |          0Hz |      117 MHz |\n",
      "\n",
      "Kerr coefficients (diagonal = Kerr, off-diagonal = cross-Kerr)\n",
      "         mode |         0    |         1    |         2    |\n",
      "            0 |      165 MHz |              |              |\n",
      "            1 |       13 MHz |      128 MHz |              |\n",
      "            2 |     94.8 MHz |      234 MHz |      117 MHz |\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mukhamad-a/.local/lib/python3.9/site-packages/qucat/core.py:2446: RuntimeWarning: invalid value encountered in sqrt\n",
      "  return np.sqrt(hbar/np.real(z)/np.imag(dY(z,**kwargs)))\n"
     ]
    }
   ],
   "source": [
    "f,k,A,chi = tuneable_coupler.f_k_A_chi(pretty_print=True, Lj=Lj(0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "59023917",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:matplotlib.font_manager:findfont: Font family ['sans-serif'] not found. Falling back to DejaVu Sans.\n",
      "WARNING:matplotlib.font_manager:findfont: Generic family 'sans-serif' not found because none of the following families were found: Myriad Pro\n",
      "WARNING:matplotlib.font_manager:findfont: Font family ['sans-serif'] not found. Falling back to DejaVu Sans.\n",
      "WARNING:matplotlib.font_manager:findfont: Generic family 'sans-serif' not found because none of the following families were found: Myriad Pro\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 792x411.84 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tuneable_coupler.show_normal_mode(mode = 2,\n",
    "    quantity = 'current',\n",
    "    Lj=Lj(0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "adc87de1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 792x411.84 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tuneable_coupler.show_normal_mode(mode = 1,\n",
    "    quantity = 'current',\n",
    "    Lj=Lj(0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "f4557582",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Circuit characteristics\n",
    "\n",
    "Ejmax = 6.5e9 # Maximum Josephson energy of the coupler SQUID\n",
    "d = 0.0769 # Coupler SQUID assymetry\n",
    "Ej_t = 22.8e9 # Coupled transmon Josephson energy\n",
    "Lt = (cst.hbar/2/cst.e)**2/(Ej_t*cst.h) # Coupled transmon inductance\n",
    "\n",
    "# Function to transform Josephson energy into\n",
    "# Josephson inductance\n",
    "def Lc(phi):\n",
    "    Ej = Ejmax*np.cos(cst.pi*phi)*np.sqrt(1+d**2*np.tan(cst.pi*phi)**2)\n",
    "    return (cst.hbar/2/cst.e)**2/(Ej*cst.h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "0bae5ab9",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mukhamad-a/.local/lib/python3.9/site-packages/qucat/core.py:2446: RuntimeWarning: invalid value encountered in sqrt\n",
      "  return np.sqrt(hbar/np.real(z)/np.imag(dY(z,**kwargs)))\n"
     ]
    }
   ],
   "source": [
    "# modes to include when generating the system Hamiltonian\n",
    "modes_to_include = [1,2]\n",
    "\n",
    "# Values of the bias flux to sweep\n",
    "phi_list = np.linspace(-0.25,0.5,201)\n",
    "\n",
    "# Iitialize a list of transition frequencies\n",
    "fs = [np.zeros(len(phi_list)) for mode in modes_to_include]\n",
    "\n",
    "for i,phi in enumerate(phi_list):\n",
    "    # Generate the Hamiltonian\n",
    "    H = tuneable_coupler.hamiltonian(\n",
    "        Lj = Lc(phi), \n",
    "        excitations = 7, \n",
    "        taylor = 4, \n",
    "        modes = modes_to_include)\n",
    "    \n",
    "    # compute eigenenergies and eigenstates\n",
    "    ee,es = H.eigenstates()\n",
    "    \n",
    "    # Add the first two transition frequencies of the \n",
    "    # two modes considered to the list of transition frequencies\n",
    "    for m,mode in enumerate(modes_to_include):\n",
    "        fs[m][i] = ee[m+1]-ee[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "ee62ce1b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the eigenfrequencies\n",
    "\n",
    "#fig,ax = plt.subplots(1,1,figsize = (column*0.55,column*0.45))\n",
    "fig,ax = plt.subplots(1, 1, figsize = (6, 4))\n",
    "# Since the two curves cross, we define \n",
    "# an index cutoff_i at which the curves should switch colors\n",
    "cutoff_i = np.argmin(np.absolute(fs[0]-fs[1]))\n",
    "lw = 1\n",
    "mode_1 = 1\n",
    "mode_2 = 0\n",
    "ax.plot(phi_list[:cutoff_i],fs[mode_1][:cutoff_i]/1e9,color = dark_blue, lw = lw)\n",
    "ax.plot(phi_list[cutoff_i+1:],fs[mode_1][cutoff_i+1:]/1e9,color = light_blue, lw = lw)\n",
    "ax.plot(phi_list[:cutoff_i],fs[mode_2][:cutoff_i]/1e9,color = light_blue, lw = lw)\n",
    "ax.plot(phi_list[cutoff_i+1:],fs[mode_2][cutoff_i+1:]/1e9,color = dark_blue, lw = lw)\n",
    "ax.set_yticks([6.4,6.6,6.8])\n",
    "ax.set_xlim(-0.25,0.5)\n",
    "ax.set_ylim(6.4,6.8)\n",
    "plt.tight_layout()\n",
    "plt.xlabel('Flux $\\phi$ (flux quanta)')\n",
    "plt.ylabel('Transition frequencies (GHz))')\n",
    "fig.savefig('fig_freq_vs_flux.pdf',transparent = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "1a2c73e9",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mukhamad-a/.local/lib/python3.9/site-packages/qucat/core.py:2446: RuntimeWarning: invalid value encountered in sqrt\n",
      "  return np.sqrt(hbar/np.real(z)/np.imag(dY(z,**kwargs)))\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 528x274.56 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_2219/3024139927.py:8: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n",
      "  fig.show()\n"
     ]
    }
   ],
   "source": [
    "# Visualize the symmetric normal mode\n",
    "tuneable_coupler.plotting_parameters_normal_modes['figsize_scaling'] = 1\n",
    "tuneable_coupler.plotting_parameters_normal_modes[\"normal_mode_arrow\"][ \"color\"]= dark_blue\n",
    "tuneable_coupler.plotting_parameters_normal_modes[\"normal_mode_label\"][ \"color\"]= dark_blue\n",
    "fig,ax = tuneable_coupler.show_normal_mode(2,quantity = 'current',Lj = Lc(0),\n",
    "        return_fig_ax=True,add_legend=False,add_title=False)\n",
    "fig.savefig(\"tuneable_coupler_mode_2.pdf\",transparent =True)\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "4ddb6779",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 528x274.56 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the antisymmetric normal mode\n",
    "tuneable_coupler.show_normal_mode(1,quantity = 'current',Lj = Lc(0))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9551489",
   "metadata": {},
   "source": [
    "## Algorithmic Method"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8061c70a",
   "metadata": {},
   "source": [
    "### Example circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "0dcff0ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 268.8x124.236 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f_finder = GUI('f_finder_example_circuit.txt',plot = False, edit = True)\n",
    "f_finder.plotting_parameters_show['figsize_scaling'] = 0.7\n",
    "fig,ax = f_finder.show(plot = False, return_fig_ax = True)\n",
    "fig.savefig('fig_f_finder_example_circuit.pdf',transparent = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e50beafa",
   "metadata": {},
   "source": [
    "### Differentiating admittance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "ab49859b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_2219/2422360324.py:34: MatplotlibDeprecationWarning: savefig() got unexpected keyword argument \"clip_on\" which is no longer supported as of 3.3 and will become an error in 3.6\n",
      "  fig.savefig(\"fig_dY_from_differentiation.pdf\",transparent = True,clip_on=False)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x504 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Analytical expression for the circuit admittance of \n",
    "# a coupled transmon/resonator\n",
    "def Y(w):\n",
    "    return 1j*C1*w+1/L1/1j/w+1/(1/Cc/1j/w+1/(C2*1j*w+1/L2/1j/w+1/(1/Cc2/1j/w+R)))\n",
    "\n",
    "# System parameters\n",
    "C1,C2 = 1e-13,1e-13\n",
    "L1,L2 = 12e-9,1e-8\n",
    "Cc = 1e-15\n",
    "Cc2 = 0.5e-15\n",
    "R = 50\n",
    "\n",
    "# Frequencies to sweep\n",
    "f = np.linspace(4e9,5.5e9,5001)\n",
    "\n",
    "# Plot admittance for different coupling capacitors\n",
    "#fig,ax = plt.subplots(3,1,sharex = True,figsize = (column*0.65,column*0.6))\n",
    "fig,ax = plt.subplots(3, 1, figsize = (8, 7))\n",
    "plt.subplots_adjust(left = 0.2, bottom = 0.2)\n",
    "fig.set\n",
    "ymax = 3.5\n",
    "for i,Cc in enumerate([10e-15,2e-15,1e-16]):\n",
    "    to_plot = Y(2*np.pi*f)\n",
    "    stop = np.argmax(to_plot[1:]-to_plot[:-1])\n",
    "    ax[i].plot(f[:stop-2]/1e9,np.imag(Y(2*np.pi*f[:stop-2]))*1e3, color = blue)\n",
    "    ax[i].plot(f[stop+2:]/1e9,np.imag(Y(2*np.pi*f[stop+2:]))*1e3, color = blue)\n",
    "    ax[i].axhline(0, ls='--', lw = 0.5, color = blue)\n",
    "    ax[i].set_xlim(4,5.5)\n",
    "    ax[i].set_ylim(-ymax,ymax)\n",
    "    ax[i].set_yticks([-3,0,3])\n",
    "    ax[i].text(4.07,1.1,'Cc = %.0e'%Cc)\n",
    "ax[1].set_ylabel(r\"$Im[Y]\\times10^3$\")\n",
    "ax[-1].set_xlabel(\"Frequency (GHz)\")\n",
    "fig.savefig(\"fig_dY_from_differentiation.pdf\",transparent = True,clip_on=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f2608b1",
   "metadata": {},
   "source": [
    "### Choice of reference element"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "67cebf15",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 268.8x124.236 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "J 0 2 L1\n",
      "C 0 2 C1\n",
      "C 0 1 Cc\n",
      "C 1 2 C2\n",
      "L 1 2 L2\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Build and plot example circuit\n",
    "c = GUI('best_ref_elt.txt', edit = True, plot = True, print_network=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "8b451356",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n",
      "0\n",
      "2\n",
      "1\n"
     ]
    }
   ],
   "source": [
    "print(c.components['C1'].node_minus)\n",
    "print(c.components['C1'].node_plus)\n",
    "print(c.components['C2'].node_minus)\n",
    "print(c.components['C2'].node_plus)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "967873da",
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyError",
     "evalue": "(1, 0, 1, 2)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_2219/4106877770.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      9\u001b[0m     to_plot.append([c.components['L1']._flux_zpf_r(c.zeta[1],**kwargs),\n\u001b[1;32m     10\u001b[0m         c.components['L2']._flux_zpf_r(c.zeta[1],**kwargs)])\n\u001b[0;32m---> 11\u001b[0;31m     \u001b[0mtransfer_functions\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_flux_transformation_dict\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpi\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m \u001b[0mEj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcomponents\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'L2'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_Ej\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyError\u001b[0m: (1, 0, 1, 2)"
     ]
    }
   ],
   "source": [
    "# Construct list of zero-point fluctuations in flux\n",
    "# as a function of coupling capacitance\n",
    "C_list = np.logspace(-14.5,-21,301) # Coupling capacitance\n",
    "to_plot = []\n",
    "transfer_functions = []\n",
    "for i,Cc in enumerate(C_list):\n",
    "    kwargs = {'Cc':Cc,'C1':100e-15,'L2':8e-9,'C2':100e-15,'L1':10e-9}\n",
    "    f,_,A,_ = c.f_k_A_chi(pretty_print=False,**kwargs)\n",
    "    to_plot.append([c.components['L1']._flux_zpf_r(c.zeta[1],**kwargs),\n",
    "        c.components['L2']._flux_zpf_r(c.zeta[1],**kwargs)])\n",
    "    transfer_functions.append(c._flux_transformation_dict[1, 0, 1, 2](f[1]*np.pi*2,**kwargs))\n",
    "\n",
    "Ej = c.components['L2']._get_Ej(**kwargs)\n",
    "phi_0 = hbar/2./e\n",
    "to_plot = np.array(to_plot)/phi_0\n",
    "transfer_functions = np.array(transfer_functions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "61c5a3b6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot phi_zpf_r\n",
    "fig,ax = plt.subplots(2,1,figsize = (column*0.7,column*0.45), sharex = True)\n",
    "fig.subplots_adjust(hspace=0.4)\n",
    "lw = 1\n",
    "ax[0].loglog(C_list/1e-15,to_plot[:,0], color = red, lw = lw)\n",
    "ax[0].loglog(C_list/1e-15,to_plot[:,1], color = blue, lw = lw)\n",
    "A_L = np.absolute(to_plot[:,0]*transfer_functions)**4*Ej/2/1e6\n",
    "A_J = np.absolute(to_plot[:,1])**4*Ej/2/1e6\n",
    "ax[1].semilogx(C_list/1e-15,A_L, color = red, lw = lw)\n",
    "ax[1].semilogx(C_list/1e-15,A_J,'--', color = blue, lw = lw)\n",
    "ax[1].set_ylim(0,250)\n",
    "ax[0].set_ylim([1e-9,1])\n",
    "ax[0].set_yticks([1e-8,1e-4,1])\n",
    "ax[1].set_yticks([0,100,200])\n",
    "# plt.tight_layout()\n",
    "fig.savefig('fig_best_ref_elt.pdf',transparent = True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4cde3423",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}