{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# F-mu-F\n",
    " \n",
    " The well known F-mu-F signal identified by J.H.Brewer et al. in PRB 33 11 (1986):\n",
    " \n",
    " $G(t)=\\frac{1}{6}\\left[3+\\cos(\\sqrt{3} \\omega_\\text{D} t)+\\left(1-\\frac{1}{\\sqrt{3}}\\right)\\cos(\\frac{3-\\sqrt{3}}{2}\\omega_\\text{D} t)+\\left(1+\\frac{1}{\\sqrt{3}}\\right)\\cos(\\frac{3+\\sqrt{3}}{2}\\omega_\\text{D} t)\\right]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing stuff...\n",
    "try:\n",
    "    from undi import MuonNuclearInteraction\n",
    "except (ImportError, ModuleNotFoundError):\n",
    "    import sys\n",
    "    sys.path.append('../undi')\n",
    "    from undi import MuonNuclearInteraction\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us consider a linear F-Mu-F molecule of total length $2r$ aligned along $z$.\n",
    " \n",
    " Remember that UNDI uses SI units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:undi.undi:Using most abundand isotope for F, i.e. 19F, 1.0 abundance\n",
      "INFO:undi.undi:Using most abundand isotope for F, i.e. 19F, 1.0 abundance\n",
      "INFO:undi.undi:Hilbert space is 8 dimensional\n",
      "INFO:undi.undi:Adding interaction between F and mu with distance 1.17e-10\n",
      "INFO:undi.undi:Dipolar contribution between 0<->1, r=1.17e-10\n",
      "INFO:undi.undi:Skipped interaction between F and F with distance 2.34e-10\n",
      "INFO:undi.undi:Adding interaction between mu and F with distance 1.17e-10\n",
      "INFO:undi.undi:Dipolar contribution between 1<->2, r=1.17e-10\n",
      "INFO:undi.undi:Storing kets in dense matrices\n",
      "INFO:undi.undi:Adding signal 0...\n",
      "INFO:undi.undi:Adding signal 1...\n",
      "INFO:undi.undi:Adding signal 2...\n",
      "INFO:undi.undi:Adding signal 3...\n",
      "INFO:undi.undi:Adding signal 4...\n",
      "INFO:undi.undi:Adding signal 5...\n",
      "INFO:undi.undi:Adding signal 6...\n",
      "INFO:undi.undi:Adding signal 7...\n",
      "INFO:undi.undi:Using most abundand isotope for F, i.e. 19F, 1.0 abundance\n",
      "INFO:undi.undi:Using most abundand isotope for F, i.e. 19F, 1.0 abundance\n",
      "INFO:undi.undi:Hilbert space is 8 dimensional\n",
      "INFO:undi.undi:Adding interaction between F and mu with distance 1.17e-10\n",
      "INFO:undi.undi:Dipolar contribution between 0<->1, r=1.17e-10\n",
      "INFO:undi.undi:Skipped interaction between F and F with distance 2.34e-10\n",
      "INFO:undi.undi:Adding interaction between mu and F with distance 1.17e-10\n",
      "INFO:undi.undi:Dipolar contribution between 1<->2, r=1.17e-10\n",
      "INFO:undi.undi:Storing kets in dense matrices\n",
      "INFO:undi.undi:Adding signal 0...\n",
      "INFO:undi.undi:Adding signal 1...\n",
      "INFO:undi.undi:Adding signal 2...\n",
      "INFO:undi.undi:Adding signal 3...\n",
      "INFO:undi.undi:Adding signal 4...\n",
      "INFO:undi.undi:Adding signal 5...\n",
      "INFO:undi.undi:Adding signal 6...\n",
      "INFO:undi.undi:Adding signal 7...\n",
      "INFO:undi.undi:Using most abundand isotope for F, i.e. 19F, 1.0 abundance\n",
      "INFO:undi.undi:Using most abundand isotope for F, i.e. 19F, 1.0 abundance\n",
      "INFO:undi.undi:Hilbert space is 8 dimensional\n",
      "INFO:undi.undi:Adding interaction between F and mu with distance 1.17e-10\n",
      "INFO:undi.undi:Dipolar contribution between 0<->1, r=1.17e-10\n",
      "INFO:undi.undi:Adding interaction between F and F with distance 2.34e-10\n",
      "INFO:undi.undi:Dipolar contribution between 0<->2, r=2.34e-10\n",
      "INFO:undi.undi:Adding interaction between mu and F with distance 1.17e-10\n",
      "INFO:undi.undi:Dipolar contribution between 1<->2, r=1.17e-10\n",
      "INFO:undi.undi:Storing kets in dense matrices\n",
      "INFO:undi.undi:Adding signal 0...\n",
      "INFO:undi.undi:Adding signal 1...\n",
      "INFO:undi.undi:Adding signal 2...\n",
      "INFO:undi.undi:Adding signal 3...\n",
      "INFO:undi.undi:Adding signal 4...\n",
      "INFO:undi.undi:Adding signal 5...\n",
      "INFO:undi.undi:Adding signal 6...\n",
      "INFO:undi.undi:Adding signal 7...\n",
      "INFO:undi.undi:Using most abundand isotope for F, i.e. 19F, 1.0 abundance\n",
      "INFO:undi.undi:Using most abundand isotope for F, i.e. 19F, 1.0 abundance\n",
      "INFO:undi.undi:Hilbert space is 8 dimensional\n",
      "INFO:undi.undi:Adding interaction between F and mu with distance 1.17e-10\n",
      "INFO:undi.undi:Dipolar contribution between 0<->1, r=1.17e-10\n",
      "INFO:undi.undi:Adding interaction between F and F with distance 2.34e-10\n",
      "INFO:undi.undi:Dipolar contribution between 0<->2, r=2.34e-10\n",
      "INFO:undi.undi:Adding interaction between mu and F with distance 1.17e-10\n",
      "INFO:undi.undi:Dipolar contribution between 1<->2, r=1.17e-10\n",
      "INFO:undi.undi:Storing kets in dense matrices\n",
      "INFO:undi.undi:Adding signal 0...\n",
      "INFO:undi.undi:Adding signal 1...\n",
      "INFO:undi.undi:Adding signal 2...\n",
      "INFO:undi.undi:Adding signal 3...\n",
      "INFO:undi.undi:Adding signal 4...\n",
      "INFO:undi.undi:Adding signal 5...\n",
      "INFO:undi.undi:Adding signal 6...\n",
      "INFO:undi.undi:Adding signal 7...\n",
      "INFO:undi.undi:Using most abundand isotope for F, i.e. 19F, 1.0 abundance\n",
      "INFO:undi.undi:Using most abundand isotope for F, i.e. 19F, 1.0 abundance\n",
      "INFO:undi.undi:Hilbert space is 8 dimensional\n",
      "INFO:undi.undi:Adding interaction between F and mu with distance 1.17e-10\n",
      "INFO:undi.undi:Dipolar contribution between 0<->1, r=1.17e-10\n",
      "INFO:undi.undi:Adding interaction between F and F with distance 2.34e-10\n",
      "INFO:undi.undi:Dipolar contribution between 0<->2, r=2.34e-10\n",
      "INFO:undi.undi:Adding interaction between mu and F with distance 1.17e-10\n",
      "INFO:undi.undi:Dipolar contribution between 1<->2, r=1.17e-10\n",
      "INFO:undi.undi:Storing kets in dense matrices\n",
      "INFO:undi.undi:Adding signal 0...\n",
      "INFO:undi.undi:Adding signal 1...\n",
      "INFO:undi.undi:Adding signal 2...\n",
      "INFO:undi.undi:Adding signal 3...\n",
      "INFO:undi.undi:Adding signal 4...\n",
      "INFO:undi.undi:Adding signal 5...\n",
      "INFO:undi.undi:Adding signal 6...\n",
      "INFO:undi.undi:Adding signal 7...\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": [
    "angtom=1.0e-10 # m\n",
    "h=6.6260693e-34 # Js\n",
    "hbar=h/(2*np.pi) # Js\n",
    "mu_0=(4e-7)*np.pi # Tm A-1\n",
    "\n",
    "# This is a linear F-mu-F along z\n",
    "r=1.17 * angtom\n",
    "atoms = [\n",
    "            {'Position': np.array([0., 0., 0.]),\n",
    "            'Label': 'F'},\n",
    "            \n",
    "            {'Position': np.array([0., 0., r ]),\n",
    "            'Label': 'mu'},\n",
    "            \n",
    "            {'Position': np.array([0., 0., 2*r]),\n",
    "            'Label': 'F'}\n",
    "        ]\n",
    "# Time values, in seconds\n",
    "tlist = np.linspace(0, 10e-6, 100)\n",
    "\n",
    "# Define main class\n",
    "NS = MuonNuclearInteraction(atoms)\n",
    "# cutoff the dipolar interaction in order to avoid F-F term,\n",
    "# Rotate sample such that axis z used to define the atomic positions\n",
    "# is aligned with quantization axis which also happens to be z.\n",
    "# Basically the next call will do nothing\n",
    "NS.translate_rotate_sample_vec([0,0,1])\n",
    "\n",
    "# cutoff the dipolar interaction in order to avoid F-F term\n",
    "signal_FmuF = NS.polarization(tlist, cutoff=1.2 * angtom)\n",
    "\n",
    "NS = MuonNuclearInteraction(atoms, log_level='info')\n",
    "NS.translate_rotate_sample_vec([0,1,0])\n",
    "signal_FmuF += NS.polarization(tlist, cutoff=1.2 * angtom)\n",
    "\n",
    "NS = MuonNuclearInteraction(atoms, log_level='info')\n",
    "NS.translate_rotate_sample_vec([1,0,0])\n",
    "signal_FmuF += NS.polarization(tlist, cutoff=1.2 * angtom)\n",
    "\n",
    "signal_FmuF /= 3.\n",
    "\n",
    "# no cutoff this time\n",
    "NS = MuonNuclearInteraction(atoms, log_level='info')\n",
    "NS.translate_rotate_sample_vec([0,0,1])\n",
    "signal_FmuF_with_Fdip = NS.polarization(tlist)\n",
    "\n",
    "NS = MuonNuclearInteraction(atoms, log_level='info')\n",
    "NS.translate_rotate_sample_vec([0,1,0])\n",
    "signal_FmuF_with_Fdip += NS.polarization(tlist)\n",
    "\n",
    "NS = MuonNuclearInteraction(atoms, log_level='info')\n",
    "NS.translate_rotate_sample_vec([1,0,0])\n",
    "signal_FmuF_with_Fdip += NS.polarization(tlist)\n",
    "\n",
    "signal_FmuF_with_Fdip /= 3.\n",
    "\n",
    "####################\n",
    "# Plot the results #\n",
    "####################\n",
    "fig, axes = plt.subplots(1,1)\n",
    "axes.plot(tlist, signal_FmuF, label='Computed', linestyle='-')\n",
    "axes.plot(tlist, signal_FmuF_with_Fdip, label='Computed, with F-F interaction', linestyle='-.')\n",
    "\n",
    "# Generate and plot analytical version for comparison\n",
    "def plot_brewer(interval,r):\n",
    "    from numpy import cos, sin, sqrt\n",
    "    omegad = (mu_0*NS.gammas['mu']*NS.gammas['F']*(hbar))\n",
    "    omegad /=(4*np.pi*((r)**3))\n",
    "    \n",
    "    tomegad=interval*omegad\n",
    "    y = (1./6.)*(3+cos(sqrt(3)*tomegad)+ \\\n",
    "                (1-1/sqrt(3))*cos(((3-sqrt(3))/2)*tomegad)+ \\\n",
    "                (1+1/sqrt(3))*cos(((3+sqrt(3))/2)*tomegad))#+0.05*(exp(-x/2.5))**1.5\n",
    "    return y\n",
    "\n",
    "axes.plot(tlist, plot_brewer(tlist, r), label='F-mu-F Brewer', linestyle=':')\n",
    "\n",
    "ticks = np.round(axes.get_xticks()*10.**6)\n",
    "axes.set_xticklabels(ticks)\n",
    "axes.set_xlabel(r'$t (\\mu s)$', fontsize=20)\n",
    "axes.set_ylabel(r'$\\left<P_z\\right>$', fontsize=20);\n",
    "axes.grid()\n",
    "fig.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "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": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}