CSFQ energy level cal..ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# CSFQ energy level calculation\n"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "% FILE: csfq_1d.m\n",
    "% DATE: 15-Sep-2010\n",
    "% Author: Matthias Steffen <msteffe@us.ibm.com>\n",
    "%\n",
    "% Looking at CSFQ simulation using 1D potential approximation\n",
    "\n",
    "% matlab file converted to python code by Jaseung Ku, 6/13/2016.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using matplotlib backend: TkAgg\n"
     ]
    }
   ],
   "source": [
    "# This is a translation of the Steffen's original matlab code to python code.\n",
    "%matplotlib\n",
    "import numpy as np\n",
    "import numpy.linalg as LA\n",
    "import matplotlib.pyplot as plt\n",
    "from math import pi\n",
    "\n",
    "# constants\n",
    "h = 6.626e-34;\n",
    "hbar = h/2/pi;\n",
    "elec = 1.6022e-19;\n",
    "f0 = h/2/elec; #flux quantum\n",
    "\n",
    "# parameters\n",
    "N = 100 # number of flux points\n",
    "\n",
    "#flux\n",
    "fmin = 0\n",
    "fmax = 1\n",
    "flux = np.linspace(fmin,fmax,N)\n",
    "\n",
    "# junction parameters of larger junction\n",
    "I0 = 0.206e-6 # was originally 0.4e-6  \n",
    "alpha = 0.48  # was 0.35  \n",
    "Cj = 5e-15\n",
    "Cs = 51e-15 # was 90e-15\n",
    "beta = alpha + Cs/Cj\n",
    "\n",
    "n = 256; # dimension of Hamitonian matrix\n",
    "\n",
    "# calculation\n",
    "\n",
    "#plotobj = plot1D(xlabel='flux', ylabel='energy', title='CSFQ')\n",
    "#x, y = np.array([]), np.array([])\n",
    "for f1 in flux:\n",
    "    \n",
    "    f = f1 * f0\n",
    "\n",
    "    # Do 1D Potential\n",
    "    delta = np.linspace(-1.8*pi, 1.8*pi, n)\n",
    "    dd = delta[1] - delta[0]\n",
    "    \n",
    "    U = -2*I0*f0/2/pi*np.cos(delta/2) - alpha*I0*f0/2/pi*np.cos(2*pi*f/f0-2*delta/2)\n",
    "    \n",
    "    # Numerically sovle 1D potential\n",
    "    \n",
    "    Cnew = (2*Cj/4)*(1+2*beta)\n",
    "    h22m = 4*elec**2/2/Cnew\n",
    "    diffOp = -h22m/dd**2\n",
    "    onOp = +2*h22m/dd**2\n",
    "    H = np.diag(U)+ np.eye(len(U), k=1) * diffOp + np.eye(len(U), k=-1) * diffOp + np.eye(len(U)) * onOp\n",
    "    \n",
    "    eigval, eigvec = LA.eigh(H)\n",
    "    #print (eigval)\n",
    "    eigval.sort() # sort eigenvalues\n",
    "    #print ('after sort', eigval)\n",
    "    energy_diff = np.diff(eigval) / h / 1e9 # in GHz\n",
    "    numval = 5  # number of energy levels to show\n",
    "    #print ('f,w01,w12,w13(GHz)=', flux[iindex], energy_diff[0:3])\n",
    "    #print ('(w12-w01)(GHz)=', energy_diff[1]-energy_diff[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CSFQ class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using matplotlib backend: TkAgg\n"
     ]
    }
   ],
   "source": [
    "%matplotlib\n",
    "import numpy as np\n",
    "import numpy.linalg as LA\n",
    "import matplotlib.pyplot as plt\n",
    "from math import pi\n",
    "from scipy.constants import h,e,hbar\n",
    "# from matplotlib import rc\n",
    "# rc('text', usetex=True)\n",
    "\n",
    "class CSFQ(object):\n",
    "    '''\n",
    "    compute eigenvalues and eigenstates of CSFQ Hamilitonian using 1D potential\n",
    "    Args:\n",
    "           I0 : critical current of large JJ in A\n",
    "           alpha : critical current ratio of small to large JJ\n",
    "           Cj : junction capacitance of large JJ in F\n",
    "           Cs : shunt capacitance in F\n",
    "           \n",
    "    Return:\n",
    "        Tuple of eigenvalues and eigenvectors\n",
    "    '''\n",
    "    \n",
    "    def __init__(self, I0=None, alpha=None, Cj=None, Cs=None):\n",
    "        \n",
    "        self.I0 = I0\n",
    "        self.alpha = alpha \n",
    "        self.Cj = Cj\n",
    "        self.Cs = Cs\n",
    "            \n",
    "    def solveHamiltonian(self, flux):\n",
    "        \"\"\"\n",
    "        flux: normalized by flux quantum\n",
    "        \"\"\"\n",
    "        f0 = h/2/e; #flux quantum\n",
    "        n = 256 # dimension of Hamitonian matrix\n",
    "    \n",
    "        beta = self.alpha + self.Cs / self.Cj\n",
    "        \n",
    "        # Do 1D Potential\n",
    "        delta = np.linspace(-1.8*pi, 1.8*pi, n)\n",
    "        dd = delta[1] - delta[0]\n",
    "\n",
    "        U = self.potentialE(delta, flux)\n",
    "#         U = -2*self.I0*f0/2/pi*np.cos(delta/2) - self.alpha*self.I0*f0/2/pi*np.cos(2*pi*f-2*delta/2)\n",
    "\n",
    "        # Numerically sovle 1D potential\n",
    "        Cnew = (2*self.Cj/4) * (1+2*beta)\n",
    "        h22m = 4*e**2/2/Cnew\n",
    "        diffOp = -h22m/dd**2\n",
    "        onOp = +2*h22m/dd**2\n",
    "        H = np.diag(U)+ np.eye(len(U), k=1) * diffOp + np.eye(len(U), k=-1) * diffOp + np.eye(len(U)) * onOp\n",
    "        self.H = H\n",
    "        \n",
    "        eigval, eigvec = LA.eigh(H)\n",
    "        \n",
    "        eigval_sorted = np.sort(eigval)  # eigval.sort()\n",
    "        eigvec_sorted = eigvec[:, eigval.argsort()]\n",
    "        \n",
    "        energy_diff = np.diff(eigval_sorted) / h / 1e9 # in GHz\n",
    "\n",
    "        return (energy_diff, eigvec_sorted)\n",
    "    \n",
    "    def potentialE(self, delta, f):\n",
    "        \"\"\"\n",
    "        f: flux normalized by flux quantum \n",
    "        \"\"\"\n",
    "        f0 = h/2/e\n",
    "        n = 256 # dimension of Hamitonian matrix\n",
    "    \n",
    "        beta = self.alpha + self.Cs / self.Cj\n",
    "        \n",
    "        U = -2*self.I0*f0/2/pi*np.cos(delta/2) - self.alpha*self.I0*f0/2/pi*np.cos(2*pi*f-2*delta/2)\n",
    "          \n",
    "        return U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "csfq = CSFQ(I0=210e-9, alpha=0.43, Cj=9e-15, Cs=57e-15)\n",
    "value, vec  = csfq.solveHamiltonian(0.5)\n",
    "\n",
    "def plotEigenVec():\n",
    "    for i in range(3):\n",
    "        vec1 = np.fabs(vec[:,i])\n",
    "        plt.plot(vec1)\n",
    "    \n",
    "def plotUvsFlux():\n",
    "    for i in [ 0.4, 0.5]:\n",
    "        delta = np.linspace(-1.8*pi, 1.8*pi, 256)\n",
    "        U = csfq.potentialE(delta, i) \n",
    "        plt.plot(delta, U)\n",
    "\n",
    "def plotUvsAlpha():\n",
    "    flux = 0.5\n",
    "    for i in [ 0.4, 0.6]:\n",
    "        csfq.alpha = i\n",
    "        delta = np.linspace(-1.8*pi, 1.8*pi, 256)\n",
    "        U = csfq.potentialE(delta,flux) \n",
    "        plt.plot(delta, U)\n",
    "\n",
    "# plotEigenVec()\n",
    "# plotUvsFlux()\n",
    "plotUvsAlpha()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "csfq = CSFQ(I0=255e-9, Cj=8.1e-15, Cs=50e-15, alpha=alpha)\n",
    "delta = np.linspace(-1.8*pi, 1.8*pi, 256)\n",
    "for alpha in [0.1, 0.2, 0.3, 0.4]:\n",
    "    csfq.alpha = alpha\n",
    "    U = csfq.potentialE(delta, flux=0.5)\n",
    "    plt.plot(delta, U)\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f01 = 4.032 GHz\n",
      "anharm = 0.533 GHz\n"
     ]
    }
   ],
   "source": [
    "I0 =135e-9\n",
    "Cj = 10e-15\n",
    "Cs = 59e-15\n",
    "alpha = 0.43\n",
    "\n",
    "csfq = CSFQ(I0=I0, Cj=Cj, Cs=Cs, alpha=alpha)\n",
    "energy_diff, eigenvec = csfq.solveHamiltonian(0.5)\n",
    "print(f'f01 = {energy_diff[0]:.3f} GHz')\n",
    "print(f'anharm = {energy_diff[1] - energy_diff[0]:.3f} GHz')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Spectrum vs parameter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f01=4.938,anharmonicity=0.758\n",
      "x=0.533, (1-x)/(x-0.5)=14.2\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "\n",
    "# Save?\n",
    "SAVE = False\n",
    "if SAVE:\n",
    "    save_path= '/home/jaseung/Labshare/User/Jaseung/March Meeting/'\n",
    "    dataFileName = 'CSFQ_Cal'\n",
    "    dataFileName = os.path.join(save_path, dataFileName + '.txt') \n",
    "\n",
    "# get spectrum up to w34\n",
    "I0 =200e-9\n",
    "Cj = 8.1e-15\n",
    "Cs = 50e-15\n",
    "alpha = 0.446\n",
    "\n",
    "csfq = CSFQ(I0=I0, Cj=Cj, Cs=Cs, alpha=alpha)\n",
    "\n",
    "N = 101 # number of flux points\n",
    "flux = np.linspace(0.5-0.075,0.5+0.075,N)\n",
    "\n",
    "# plot set up\n",
    "f, spec = np.array([]), np.array([])\n",
    "fig, axes1 = plt.subplots(1,1)\n",
    "lines1, = axes1.plot([], [],'k-', linewidth=2)\n",
    "lines2, = axes1.plot([], [], 'r-')\n",
    "lines3, = axes1.plot([], [], 'b-')\n",
    "lines4, = axes1.plot([], [], 'g-')\n",
    "axes1.set_xlabel(r'Flux ($\\Phi_0$)', size=24, fontfamily='Times New Roman')\n",
    "axes1.set_ylabel('Energy (GHz)', size=24, fontfamily='Times New Roman')\n",
    "axes1.tick_params('x', labelsize=18)\n",
    "axes1.tick_params('y', labelsize=18)\n",
    "# axes1.grid(which='both',color='gray', linestyle='--', linewidth=0.5)\n",
    "#title = 'I0={:.3g} nA, Cj={} fF, Cs={} fF, alpha={}'.format(I0 *1e9, Cj*1e15, Cs*1e15, alpha)\n",
    "#axes1.set_title(title)\n",
    "\n",
    "for f1 in flux:\n",
    "    energy_diff = csfq.solveHamiltonian(f1)[0][0:3]\n",
    "    if spec.size ==0:\n",
    "        spec = energy_diff\n",
    "        spec.shape = (1,spec.size)\n",
    "    else:\n",
    "        spec = np.vstack((spec, energy_diff))\n",
    "        \n",
    "    f = np.append(f,f1)\n",
    "        \n",
    "    lines1.set_xdata(f)\n",
    "    lines1.set_ydata(spec[:,0])\n",
    "    lines2.set_xdata(f)\n",
    "    lines2.set_ydata(spec[:,1])\n",
    "    lines3.set_xdata(f)\n",
    "    \n",
    "    lines3.set_ydata(spec[:,2])\n",
    "  #  lines4.set_xdata(f)\n",
    "  #  lines4.set_ydata(spec[:,3])\n",
    "    \n",
    "    axes1.relim()\n",
    "    axes1.autoscale()\n",
    "    plt.draw()\n",
    "\n",
    "#save file\n",
    "if SAVE:\n",
    "    f_obj = open(dataFileName, 'wb') \n",
    "    np.savetxt(f_obj, spec, fmt='%.9g', delimiter='\\t') \n",
    "    f_obj.close()\n",
    "\n",
    "f01 = csfq.solveHamiltonian(0.5)[0][0]                                \n",
    "f12 = csfq.solveHamiltonian(0.5)[0][1]  \n",
    "\n",
    "print('f01={:.4g},anharmonicity={:.3g}'.format(f01, f12-f01))\n",
    "\n",
    "f01_arr = spec[:,0]\n",
    "x = flux[np.argmin( np.fabs(f01_arr - 6.8815))]\n",
    "if 0.5 > x :\n",
    "    x = 1 - x\n",
    "print('x={:.3g}, (1-x)/(x-0.5)={:.3g}'.format(x,(1-x)/(x-0.5)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "ax=plt.gca()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 22.52222222222222, 'Flux ($\\\\Phi_0$)')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax.set_xlabel(r'Flux ($\\Phi_0$)', fontfamily='Times New Roman')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Get anharmonicity and f01 vs alpha at LSS and USS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'I0=210.0 nA, Cj=9.0 fF, Cs=57.0 fF')"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "I0 = 210e-9\n",
    "Cj = 9e-15\n",
    "Cs = 57e-15\n",
    "flux = 0.5  # LSS\n",
    "flux1 = 0   # USS\n",
    "\n",
    "var = Cs  # change this when varying a parameter\n",
    "labelStr = str(var)\n",
    "\n",
    "csfq = CSFQ(I0=I0, Cj=Cj, Cs=Cs)\n",
    "\n",
    "alpha_arr = np.linspace(0.4, 0.5, 51)\n",
    "anharm_arr, energy_diff_arr = np.array([]), np.array([])\n",
    "anharm_arr1, energy_diff_arr1 = np.array([]), np.array([])\n",
    "\n",
    "for i in alpha_arr:\n",
    "    csfq.alpha = i\n",
    "    energy_diff = csfq.solveHamiltonian(flux)[0]\n",
    "    energy_diff1 = csfq.solveHamiltonian(flux1)[0]\n",
    "    anharm = energy_diff[1] - energy_diff[0]\n",
    "    anharm1 = energy_diff1[1] - energy_diff1[0]\n",
    "    anharm_arr = np.append(anharm_arr, anharm)\n",
    "    anharm_arr1 = np.append(anharm_arr1, anharm1)\n",
    "    energy_diff_arr = np.append(energy_diff_arr, energy_diff[0])\n",
    "    energy_diff_arr1 = np.append(energy_diff_arr1, energy_diff1[0])\n",
    "\n",
    "\n",
    "fig, (axes1, axes2) = plt.subplots(2,1)\n",
    "lines1, = axes1.plot(alpha_arr, energy_diff_arr, 'k-') \n",
    "lines11,= axes1.plot(alpha_arr, energy_diff_arr1, 'r-') \n",
    "lines2, = axes2.plot(alpha_arr, anharm_arr, 'k-') \n",
    "lines12, =axes2.plot(alpha_arr, anharm_arr1,'r-')\n",
    "\n",
    "axes1.set_ylabel('f01 (GHz)')\n",
    "axes2.set_xlabel('alpha')\n",
    "axes2.set_ylabel('anharm (GHz)')\n",
    "axes1.grid(which='both',color='gray', linestyle='--', linewidth=0.5)\n",
    "axes2.grid(which='both',color='gray', linestyle='--', linewidth=0.5)\n",
    "axes1.legend((lines1, lines11),('LSS', 'USS'))\n",
    "axes2.legend((lines2, lines12),('LSS', 'USS'))\n",
    "\n",
    "title = 'I0={} nA, Cj={} fF, Cs={} fF'.format(I0 *1e9, Cj*1e15, Cs*1e15)\n",
    "axes1.set_title(title)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Get anharmonicity and f01 vs I0 at LSS and USS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f3c86e7a160>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Cj =8.1e-15\n",
    "Cs = 50e-15\n",
    "alpha = 0.475 #0.446\n",
    "flux = 0.5\n",
    "flux1 = 0\n",
    "\n",
    "csfq = CSFQ(Cj=Cj, Cs=Cs, alpha=alpha)\n",
    "\n",
    "I0_arr = np.linspace(50e-9, 300e-9, 50)\n",
    "anharm_arr, energy_diff_arr = np.array([]), np.array([])\n",
    "anharm_arr1, energy_diff_arr1 = np.array([]), np.array([])\n",
    "\n",
    "for i in I0_arr:\n",
    "    csfq.I0 = i\n",
    "    energy_diff = csfq.solveHamiltonian(flux)[0]\n",
    "    energy_diff1 = csfq.solveHamiltonian(flux1)[0]\n",
    "    anharm = energy_diff[1] - energy_diff[0]\n",
    "    anharm1 = energy_diff1[1] - energy_diff1[0]\n",
    "    anharm_arr = np.append(anharm_arr, anharm)\n",
    "    anharm_arr1 = np.append(anharm_arr1, anharm1)\n",
    "    energy_diff_arr = np.append(energy_diff_arr, energy_diff[0])\n",
    "    energy_diff_arr1 = np.append(energy_diff_arr1, energy_diff1[0])\n",
    "\n",
    "\n",
    "fig, (axes1, axes2) = plt.subplots(2,1)\n",
    "lines1, = axes1.plot(I0_arr *1e9, energy_diff_arr, 'k-') \n",
    "lines11, = axes1.plot(I0_arr *1e9, energy_diff_arr1, 'r-') \n",
    "lines2, = axes2.plot(I0_arr *1e9, anharm_arr, 'k-') \n",
    "lines12, =axes2.plot(I0_arr *1e9, anharm_arr1,'r-')\n",
    "\n",
    "axes1.set_ylabel('f01 (GHz)')\n",
    "axes2.set_xlabel('Ic (nA)')\n",
    "axes2.set_ylabel('anharm (GHz)')\n",
    "axes1.grid(which='both',color='gray', linestyle='--', linewidth=0.5)\n",
    "axes2.grid(which='both',color='gray', linestyle='--', linewidth=0.5)\n",
    "axes1.legend((lines1, lines11),('LSS', 'USS'))\n",
    "axes2.legend((lines2, lines12),('LSS', 'USS'))\n",
    "\n",
    "title = 'Cj={} fF, Cs={} fF, alpha={}'.format(Cj*1e15, Cs*1e15, alpha)\n",
    "axes1.set_title(title)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Get anharmonicity and f01 vs Cs at LSS and USS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fd87d691860>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "I0 = 160e-9\n",
    "Cj = 8.1e-15\n",
    "Cs = 50e-15\n",
    "alpha = 0.42\n",
    "flux = 0.5\n",
    "flux1 = 0\n",
    "\n",
    "csfq = CSFQ(I0=I0, Cj=Cj, Cs=Cs, alpha=alpha)\n",
    "\n",
    "Cs_arr = np.linspace(10e-15, 100e-15, 50)\n",
    "anharm_arr, energy_diff_arr = np.array([]), np.array([])\n",
    "anharm_arr1, energy_diff_arr1 = np.array([]), np.array([])\n",
    "\n",
    "for i in Cs_arr:\n",
    "    csfq.Cs = i\n",
    "    energy_diff = csfq.solveHamiltonian(flux)[0]\n",
    "    energy_diff1 = csfq.solveHamiltonian(flux1)[0]\n",
    "    anharm = energy_diff[1] - energy_diff[0]\n",
    "    anharm1 = energy_diff1[1] - energy_diff1[0]\n",
    "    anharm_arr = np.append(anharm_arr, anharm)\n",
    "    anharm_arr1 = np.append(anharm_arr1, anharm1)\n",
    "    energy_diff_arr = np.append(energy_diff_arr, energy_diff[0])\n",
    "    energy_diff_arr1 = np.append(energy_diff_arr1, energy_diff1[0])\n",
    "\n",
    "fig, (axes1, axes2) = plt.subplots(2,1)\n",
    "lines1, = axes1.plot(Cs_arr *1e15, energy_diff_arr, 'k-') \n",
    "lines11, = axes1.plot(Cs_arr *1e15, energy_diff_arr1, 'r-') \n",
    "lines2, = axes2.plot(Cs_arr *1e15, anharm_arr, 'k-') \n",
    "lines12, =axes2.plot(Cs_arr*1e15, anharm_arr1,'r-')\n",
    "\n",
    "axes1.set_ylabel('f01 (GHz)')\n",
    "axes2.set_xlabel('Cs (fF)')\n",
    "axes2.set_ylabel('anharm (GHz)')\n",
    "axes1.grid(which='both',color='gray', linestyle='--', linewidth=0.5)\n",
    "axes2.grid(which='both',color='gray', linestyle='--', linewidth=0.5)\n",
    "axes1.legend((lines1, lines11),('LSS', 'USS'))\n",
    "axes2.legend((lines2, lines12),('LSS', 'USS'))\n",
    "\n",
    "title = 'I0={}, Cj={} fF, alpha={}'.format(I0*1e9, Cj*1e15, alpha)\n",
    "axes1.set_title(title)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAGZCAYAAABospGCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/x+SMyDUODdWJAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f86f9f5be48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "# 2D, anharmonicity vs alpha vs Cs\n",
    "csfq = CSFQ(I0=150e-9, Cj=5e-15, Cs=50e-15, alpha=0.45)\n",
    "flux = 0.5\n",
    "\n",
    "alpha = np.linspace(0.4, 0.5, 5)\n",
    "Cs = np.linspace(30e-15, 70e-15,10)\n",
    "anharm_arr_1D, anharm_arr_2D = np.array([]), np.array([])\n",
    "\n",
    "fig, axes = plt.subplots(nrows=1, figsize=(6,6))\n",
    "plt.xlabel('Cs (fF)')\n",
    "plt.ylabel('alpha*10')\n",
    "plt.title('alpha, Cs')\n",
    " \n",
    "for i in alpha:\n",
    "    csfq.alpha = i\n",
    "    anharm_arr_1D = np.array([])\n",
    "    for j in Cs:\n",
    "        csfq.Cs = j\n",
    "        energy_diff = csfq.solveHamiltonian(flux)[0]\n",
    "        anharm = energy_diff[1] - energy_diff[0]\n",
    "        anharm_arr_1D = np.append(anharm_arr_1D, anharm)\n",
    "    \n",
    "    if anharm_arr_2D.size == 0:\n",
    "        anharm_arr_2D = anharm_arr_1D\n",
    "        anharm_arr_2D.shape = (1,anharm_arr_1D.size)\n",
    "    else:\n",
    "        anharm_arr_2D = np.vstack((anharm_arr_2D, anharm_arr_1D)) \n",
    "    \n",
    "    axesimage = axes.matshow(anharm_arr_2D, cmap='gray', extent=[Cs[0]*1e15, Cs[-1]*1e15,alpha[0]*10,alpha[-1]*10], origin='lower',  aspect='auto')\n",
    "    axesimage.set_data(anharm_arr_2D)\n",
    "    axes.xaxis.set_ticks_position('bottom')  \n",
    "    axes.autoscale()\n",
    "    plt.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Gradiometer CSFQ, Flux dependence of S21"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from math import pi\n",
    "\n",
    "alpha0 = 0.43\n",
    "csfq = CSFQ(I0=255e-9, Cj=8.1e-15, Cs=50e-15, alpha=alpha0)\n",
    "cavityFreq = 10 # in GHz\n",
    "\n",
    "data2D = np.array([])\n",
    "\n",
    "for flux_glb in np.linspace(0, 1, 50):\n",
    "    csfq.alpha =alpha0 * np.fabs(np.cos(pi*flux_glb))\n",
    "    energy_diff_arr = np.array([])\n",
    "    print('flux_glb={}'.format(flux_glb))\n",
    "    \n",
    "    # get specturm, given global flux.\n",
    "    for flux_chip in np.linspace(0, 1, 100):\n",
    "        energy_diff = csfq.solveHamiltonian(flux_chip)[0]\n",
    "        energy_diff_arr = np.append(energy_diff_arr, energy_diff[0])\n",
    "    \n",
    "    mask = (energy_diff_arr - cavityFreq) >= 0\n",
    "    data1D = np.zeros(energy_diff_arr.size)\n",
    "    data1D[mask] = 1\n",
    "    if data2D.size ==0:\n",
    "        data2D = data1D\n",
    "        data2D.shape = (data1D.size, 1)\n",
    "    else:\n",
    "        data2D = np.column_stack((data2D, data1D))\n",
    "\n",
    "extend = [0, 1, 0, 1]\n",
    "plt.imshow(data2D, extent=extend)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f71b666c630>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPgAAAEACAYAAACeZ7vLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f71b6cdab38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "plt.matshow(data2D, extent=extend)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 17.58166914,  17.5696105 ,  17.53337846,  17.47280268,\n",
       "        17.38759262,  17.27732714,  17.14143888,  16.97919223,\n",
       "        16.78965316,  16.57164825,  16.32370907,  16.04399608,\n",
       "        15.7301933 ,  15.37935998,  14.98771734,  14.55033455,\n",
       "        14.06065248,  13.50973758,  12.88506905,  12.16849204,\n",
       "        11.33266622,  10.33508   ,   9.11143123,   7.60600056,\n",
       "         6.13448238,   6.13448238,   7.60600056,   9.11143123,\n",
       "        10.33508   ,  11.33266622,  12.16849204,  12.88506905,\n",
       "        13.50973758,  14.06065248,  14.55033455,  14.98771734,\n",
       "        15.37935998,  15.7301933 ,  16.04399608,  16.32370907,\n",
       "        16.57164825,  16.78965316,  16.97919223,  17.14143888,\n",
       "        17.27732714,  17.38759262,  17.47280268,  17.53337846,\n",
       "        17.5696105 ,  17.58166914])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "energy_diff_arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.0429505242983588"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "csfq.solveHamiltonian(0.55)[0][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.11111111,  0.22222222,  0.33333333,  0.44444444,\n",
       "        0.55555556,  0.66666667,  0.77777778,  0.88888889,  1.        ])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(0,1,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.5"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {
    "height": "155px",
    "width": "252px"
   },
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {
    "height": "calc(100% - 180px)",
    "left": "10px",
    "top": "150px",
    "width": "194px"
   },
   "toc_section_display": "block",
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}