{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# State object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pairinteraction.real as pi\n",
    "from pairinteraction.visualization.colormaps import alphamagma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "if pi.Database.get_global_database() is None:\n",
    "    pi.Database.initialize_global_database(download_missing=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Create superposition state objects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ket of interest: |Sr88_singlet:60,59_59,58⟩\n",
      "Number of basis states: 58\n",
      "state1.get_coefficients()=array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0.,\n",
      "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
      "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
      "       0., 0., 0., 0., 0., 0., 0.])\n",
      "State1: StateAtom(1.00 |Sr88_singlet:60,59_59,58⟩)\n",
      "State2: StateAtom(1.00 |Sr88_singlet:60,58_58,58⟩)\n"
     ]
    }
   ],
   "source": [
    "# First create a ket of interest and a basis around this ket\n",
    "ket = pi.KetAtom(\"Sr88_singlet\", n=60, l=59, m=58)\n",
    "print(f\"Ket of interest: {ket}\")\n",
    "ket_energy = ket.get_energy(unit=\"GHz\")\n",
    "basis = pi.BasisAtom(\"Sr88_singlet\", n=(ket.n - 3, ket.n + 3), l=(57, 60), m=(56, 60))\n",
    "print(f\"Number of basis states: {basis.number_of_states}\")\n",
    "\n",
    "# now with the ket and the basis we can define a state\n",
    "state1 = pi.StateAtom(ket, basis)\n",
    "# this state only has one entry in its coefficient vector\n",
    "print(f\"{state1.get_coefficients()=}\")\n",
    "# this can also be seen by just printing the state\n",
    "print(f\"State1: {state1}\")\n",
    "\n",
    "# To showcase addition, ... of two states we also define a second state\n",
    "ket2 = pi.KetAtom(\"Sr88_singlet\", n=60, l=58, m=58)\n",
    "state2 = pi.StateAtom(ket2, basis)\n",
    "print(f\"State2: {state2}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State plus: StateAtom(0.71 |Sr88_singlet:60,59_59,58⟩ + 0.71 |Sr88_singlet:60,58_58,58⟩)\n",
      "State minus: StateAtom(0.71 |Sr88_singlet:60,59_59,58⟩ + -0.71 |Sr88_singlet:60,58_58,58⟩)\n",
      "1.1 * state1 + 0.6 * state2 - 0.4 * state3 = StateAtomReal(1.10 |Sr88_singlet:60,59_59,58⟩ + 0.60 |Sr88_singlet:60,58_58,58⟩ + -0.40 |Sr88_singlet:60,57_57,57⟩)\n"
     ]
    }
   ],
   "source": [
    "# now we can create a symmetric and anti-symmetric superposition of these two states\n",
    "state_plus = (state1 + state2).normalize()\n",
    "state_minus = (state1 - state2).normalize()\n",
    "print(f\"State plus: {state_plus}\")\n",
    "print(f\"State minus: {state_minus}\")\n",
    "\n",
    "# and you can create any linear combination of as many states as you want\n",
    "ket3 = pi.KetAtom(\"Sr88_singlet\", n=60, l=57, m=57)\n",
    "state3 = pi.StateAtom(ket3, basis)\n",
    "print(f\"{1.1 * state1 + 0.6 * state2 - 0.4 * state3 = }\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Use state objects to calculate overlaps and expectation values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overlap of state_plus with ket: 0.4999999999999999\n",
      "Matrix element of state_plus with state_plus: -90.00056153827039 atomic_unit_of_current * atomic_unit_of_time * bohr\n"
     ]
    }
   ],
   "source": [
    "ov = state_plus.get_overlap(ket)\n",
    "print(f\"Overlap of state_plus with ket: {ov}\")\n",
    "\n",
    "d = state_plus.get_matrix_element(state_plus, \"electric_dipole\", q=0)\n",
    "print(f\"Matrix element of state_plus with state_plus: {d}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example of Stark map with overlap of superposition state objects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "electric_fields = np.linspace(0, 10, 50)\n",
    "systems = [\n",
    "    pi.SystemAtom(basis).set_electric_field([0, 0, e], unit=\"V/cm\") for e in electric_fields\n",
    "]\n",
    "\n",
    "# Diagonalize the systems in parallel\n",
    "pi.diagonalize(systems, diagonalizer=\"eigen\", float_type=\"float32\")\n",
    "\n",
    "eigenenergies = [system.get_eigenenergies(unit=\"GHz\") - ket_energy for system in systems]\n",
    "overlaps_plus = [system.get_eigenbasis().get_overlaps(state_plus) for system in systems]\n",
    "overlaps_minus = [system.get_eigenbasis().get_overlaps(state_minus) for system in systems]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 2, figsize=(10, 4), sharey=True)\n",
    "\n",
    "x_repeated = np.hstack(\n",
    "    [val * np.ones_like(es) for val, es in zip(electric_fields, eigenenergies)]\n",
    ")\n",
    "energies_flattened = np.hstack(eigenenergies)\n",
    "\n",
    "for i, ax in enumerate(axs):\n",
    "    try:\n",
    "        ax.plot(electric_fields, np.array(eigenenergies), c=\"0.5\", lw=0.25, zorder=-10)\n",
    "    except ValueError:  # inhomogeneous shape -> no simple line plot possible\n",
    "        for x, es in zip(electric_fields, eigenenergies):\n",
    "            ax.plot([x] * len(es), es, c=\"0.5\", ls=\"None\", marker=\".\", zorder=-10)\n",
    "\n",
    "    if i == 0:\n",
    "        ax.set_title(\"Overlap with state plus\")\n",
    "        overlaps_flattened = np.hstack(overlaps_plus)\n",
    "    else:\n",
    "        ax.set_title(\"Overlap with state minus\")\n",
    "        overlaps_flattened = np.hstack(overlaps_minus)\n",
    "\n",
    "    sorter = np.argsort(overlaps_flattened)\n",
    "\n",
    "    scat = ax.scatter(\n",
    "        x_repeated[sorter],\n",
    "        energies_flattened[sorter],\n",
    "        c=overlaps_flattened[sorter],\n",
    "        s=15,\n",
    "        vmin=0,\n",
    "        vmax=1,\n",
    "        cmap=alphamagma,\n",
    "    )\n",
    "\n",
    "fig.colorbar(scat, ax=axs[1], label=\"Overlap with state of interest\")\n",
    "\n",
    "for ax in axs:\n",
    "    ax.set_xlabel(\"Electric Field [V/cm]\")\n",
    "    ax.set_ylim(-20, 20)\n",
    "axs[0].set_ylabel(\"Energy [GHz]\")\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "pairinteraction",
   "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": "3.11.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}