{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Concepts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This tutorial makes you familiar with the basic concepts of pairinteraction's Python interface.\n",
    "It provides insights how the pairinteraction library is structured and how to use it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Structure of the pairinteraction Library\n",
    "\n",
    "The library is structured around Python classes that can be used to model systems of Rydberg atoms.\n",
    "Typically, we start a simulation by describing in which atomic state we are interested.\n",
    "For this, the following class is available:\n",
    "\n",
    "* `KetAtom` (see also Section 5 bellow): State of a single Rydberg atom, constructed from quantum numbers (if the specified quantum numbers do not match any of the pre-calculated states precisely, the closest state is used).\n",
    "You can display information about a state by using Python's `print` function on a `KetAtom` object.\n",
    "This class also provides methods to get properties of the state such as its energy or lifetime.\n",
    "\n",
    "For modelling a single atom, the following classes are available:\n",
    "\n",
    "* `BasisAtom` (see also Section 6a bellow): Basis of the single-atom Hilbert space, constructed from ranges of quantum numbers.\n",
    "The basis is initialized as the canonical basis of the Hilbert space, i.e., the basis is made up of basis vectors that each have a single non-zero element corresponding to a particular `KetAtom` state.\n",
    "\n",
    "* `SystemAtom` (see also Section 6b bellow): System of a single Rydberg atom, constructed from a `BasisAtom` and the electric and magnetic fields acting on the atom.\n",
    "The class provides access to the atom's Hamiltonian.\n",
    "\n",
    "Two single-atom systems can be combined to model a pair of atoms using the following classes:\n",
    "\n",
    "* `BasisPair` (see also Section 7a bellow): Basis of a pair of atoms, constructed from two `SystemAtom` objects.\n",
    "For constructing the basis, the eigenstates of the Hamiltonians of the two atoms are used.\n",
    "The basis is initialized as the canonical basis where each basis vector has a single non-zero element corresponding to a tensor product of the eigenstates.\n",
    "The energy of the state, that is described by such a basis vector, is the sum of the eigenenergies.\n",
    "To keep the basis size manageable, you can truncate it by specifying an energy range.\n",
    "\n",
    "* `SystemPair` (see also Section 7b bellow): System of a pair of atoms, constructed from a `BasisPair` and the interaction between the atoms. This class provides access to the two-atom Hamiltonian.\n",
    "\n",
    "### Helper Functions\n",
    "\n",
    "In addition, the library provides helper functions to improve the visualization of pair potentials, calculate effective Hamiltonians, or properties of a system such as $C_3$ or $C_6$ coefficients. Moreover, we provide a helper function that can be used to diagonalize the Hamiltonians of several systems in parallel.\n",
    "\n",
    "### Convenience Functionality\n",
    "\n",
    "To make the library easier to use, we have added some convenience functionality:\n",
    "\n",
    "* **Unit Conversions:** Many methods accept a `unit` parameter, such as `set_electric_field` and `get_eigenenergies`.\n",
    "This parameter allows you to choose in which units you want to set or obtain values by specifying the unit as a string, for example, `unit=\"V/cm\"`.\n",
    "The pairinteraction software automatically performs the required unit conversions.\n",
    "It uses the spectroscopy context of the [pint library](https://github.com/hgrecco/pint), so that energies can also be expressed in frequency units or wave numbers.\n",
    "\n",
    "* **Strict Typing:** The library makes extensive use of Python's type annotations.\n",
    "This has two advantages for you: First, you can directly see what types of arguments are expected for a function.\n",
    "Second, if you use a Python development environment that supports type checking, you will get warnings in your code editor if you pass the wrong type of argument to a function.\n",
    "\n",
    "* **Code Completion:** The Python API of pairinteraction is designed so that code completion should work in Python development environments.\n",
    "For example, if you type `pi.BasisAtom(` and then press `Ctrl+Space` in Visual Studio Code, you should see a list of available arguments for the `BasisAtom` constructor.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modelling Rydberg Systems\n",
    "\n",
    "In the following, we show steps for modelling systems of one or two Rydberg atoms using the pairinteraction library."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Choose a Datatype\n",
    "\n",
    "Before you can use the pairnteraction library to study Rydberg atoms, you must decide whether you want to use real or complex numbers to represent the Hamiltonian of your system. In general, real numbers are sufficient if no fields or interactions are applied along the y-direction. After you have chosen a datatype, you can import the corresponding backend. In the following, we use the backend for real numbers. Changing the backend might require restarting the Jupyter kernel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install matplotlib numpy pairinteraction\n",
    "\n",
    "import pairinteraction.real as pi  # possible backend data types: real, complex"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To improve the output of the Jupyter notebook, we limit the number of values that will be shown if we print a numpy array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "np.set_printoptions(linewidth=120, threshold=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Optionally, Configure Logging\n",
    "\n",
    "The pairinteraction software supports Python's logging module. You can adopt the following code to configure the log level and output format:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import logging\n",
    "\n",
    "logging.basicConfig(\n",
    "    level=logging.WARNING,\n",
    "    format=\"%(levelname)-8s [%(asctime)s.%(msecs)03d] [%(filename)s:%(lineno)d] %(message)s\",\n",
    "    datefmt=\"%H:%M:%S\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Set up the Database\n",
    "\n",
    "The `Database` object is responsible for storing and looking up the allowed atomic states with their corresponding energies, quantum numbers and electric dipole, etc. matrix elements with other atomic states.\n",
    "These matrix elements are pre-calculated (either via explicit calculation of the overlap integrals and using the Numerov method to get the radial wavefunctions, or alternatively for Earth Alkali atoms via Multichannel Quantum Defect Theory (MQDT)) and stored online in their own github repositories \\[[1](https://github.com/pairinteraction/database-sqdt/releases),[2](https://github.com/pairinteraction/database-mqdt/releases)\\].\n",
    "The `Database` object is able to download the necessary tables on the fly if `download_missing=True` is passed to the `Database`. Once downloaded, the tables are stored in the cache directory of the user's computer and are reused in subsequent calculations so that the software can be used without an internet connection.\n",
    "\n",
    "You can either create a `Database` object via `database = pi.Database(download_missing=True)` and use this database for the creation of the kets and basis objects below,\n",
    "or alternatively you can once create a global instance of the `Database` object via `pi.Database.initialize_global_database(download_missing=True)` and then the ket and basis classes will use this global instance by default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": [
    "### 4. Optionally, Run a Self-Test\n",
    "\n",
    "The pairinteraction software includes self tests that checks if the pairinteraction python module is working correctly. You can run the tests as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pairinteraction import run_module_tests\n",
    "\n",
    "database = pi.Database.get_global_database()\n",
    "assert run_module_tests(database.download_missing, database.database_dir) == 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. Create an Atomic State (`KetAtom`)\n",
    "\n",
    "The simplest object you can create is a simple ket via the `KetAtom` class, representing a single atomic state.\n",
    "\n",
    "The first argument to the constructor of a `KetAtom` object has to be the specifier of the atomic species, for example, 'Rb', 'Sr88_singlet', 'Sr88_triplet', 'Sr87_mqdt', 'Sr88_mqdt', 'Yb171_mqdt', 'Yb174_mqdt'. Here, the ending `_mqdt' specifies that the matrix elements were calculated via multi-channel quantum defect theory (MQDT). Matrix elements of other species were calculated via single-channel quantum defect theory (SQDT) using the Numerov method to obtain radial wavefunctions. For a full list of supported species, see the \"Identifier\" column in the \"quantum defect references\" table of pairinteraction's [README](https://www.pairinteraction.org/pairinteraction/sphinx/html/index.html#quantum-defects).\n",
    "\n",
    "In addition, you must pass quantum numbers as keyword arguments to uniquely specify a state. You can pass whatever combination of quantum numbers you like, as long as they uniquely specify exactly one state (e.g. `pi.KetAtom(\"Rb\", n=60, l=0, j=0.5, m=0.5)` and `pi.KetAtom(\"Rb\", n=60, l=0, m=0.5)` are both equivalent and specify the same state)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "You successfully created a ket object: |Rb:60,P_1/2,1/2⟩ with quantum numbers n=60, l=1.0, j=0.5, m=0.5 and energy=0.15335520073991077 bohr ** 2 * electron_mass / atomic_unit_of_time ** 2\n",
      "And getting its energy in GHz is as simple as ket.get_energy(unit='GHz')=1009028.7484337102\n",
      "\n",
      "Even the energy difference between two states is easily calculated and converted:\n",
      "delta_energy = 1.403362628490945e-05 bohr ** 2 * electron_mass / atomic_unit_of_time ** 2\n",
      "             = 92.33682521314954 gigahertz (as frequency)\n",
      "             = 3.0800249555694146 / centimeter (as wavenumber)\n",
      "             = 0.0003818744252705271 electron_volt \n",
      "             = 3.2467269402858667 millimeter (as wavelength)\n"
     ]
    }
   ],
   "source": [
    "ket = pi.KetAtom(\"Rb\", n=60, l=1, j=0.5, m=0.5)\n",
    "\n",
    "print(\n",
    "    f\"You successfully created a ket object: {ket} \"\n",
    "    f\"with quantum numbers n={ket.n}, l={ket.l}, j={ket.j}, \"\n",
    "    f\"m={ket.m} and energy={ket.get_energy()}\"\n",
    ")\n",
    "print(f\"And getting its energy in GHz is as simple as {ket.get_energy(unit='GHz')=}\")\n",
    "\n",
    "ket2 = pi.KetAtom(\"Rb\", n=58, l=0, j=0.5, m=0.5)\n",
    "delta_energy = ket.get_energy() - ket2.get_energy()  # this is a pint.Quantity object\n",
    "\n",
    "print(\"\\nEven the energy difference between two states is easily calculated and converted:\")\n",
    "print(f\"delta_energy = {delta_energy}\")\n",
    "print(13 * \" \" + f\"= {delta_energy.to('GHz', 'spectroscopy')} (as frequency)\")\n",
    "print(13 * \" \" + f\"= {delta_energy.to('cm^-1', 'spectroscopy')} (as wavenumber)\")\n",
    "print(13 * \" \" + f\"= {delta_energy.to('eV', 'spectroscopy')} \")\n",
    "print(13 * \" \" + f\"= {delta_energy.to('mm', 'spectroscopy')} (as wavelength)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6a. Create a Single-Atom Basis (`BasisAtom`)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, you can create a basis object.\n",
    "A basis object consists of a list of kets which define a canonical basis for the Hilbert space.\n",
    "Furthermore, the basis object defines basis states via its coefficients matrix, where each column in the coefficients matrix corresponds to one basis state.\n",
    "When created, the coefficients matrix is initialized to the identity matrix, i.e. each basis state correspond to one ket.\n",
    "However, in general a state (and therefore each column of the basis coefficients matrix) can be a superposition of multiple kets.\n",
    "\n",
    "The list of which kets should be considered in the basis can be restricted by passing to the `BasisAtom` class tuples of (min, max) values for the quantum numbers and energy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This basis contains 224 kets (=atomic states)\n",
      "The first and last kets are |Rb:57,S_1/2,-1/2⟩ and |Rb:63,F_5/2,5/2⟩\n",
      "The coefficient matrix has shape (224, 224) and the following entries:\n",
      "[[1. 0. 0. ... 0. 0. 0.]\n",
      " [0. 1. 0. ... 0. 0. 0.]\n",
      " [0. 0. 1. ... 0. 0. 0.]\n",
      " ...\n",
      " [0. 0. 0. ... 1. 0. 0.]\n",
      " [0. 0. 0. ... 0. 1. 0.]\n",
      " [0. 0. 0. ... 0. 0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "basis = pi.BasisAtom(\"Rb\", n=(ket.n - 3, ket.n + 3), l=(0, ket.l + 2))\n",
    "coefficients = basis.get_coefficients()  # this is a scipy.sparse.csr_matrix object\n",
    "\n",
    "print(f\"This basis contains {basis.number_of_kets} kets (=atomic states)\")\n",
    "print(f\"The first and last kets are {basis.kets[0]} and {basis.kets[-1]}\")\n",
    "print(f\"The coefficient matrix has shape {coefficients.shape} and the following entries:\")\n",
    "print(f\"{coefficients.toarray()}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6b. Create a Single-Atom System (`SystemAtom`)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `SystemAtom` object describes the single-atom system.\n",
    "It is created by passing a `BasisAtom` object in, which defines the basis of the Hilbert space.\n",
    "You can now set external fields and enable or disable the diamagnetic term. Then you can inspect the resulting Hamiltonian and diagonalize it to get the eigenstates and eigenenergies of the system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Hamiltonian of the system with magnetic and electric fields is (in GHz):\n",
      "[[1.00889546e+06 0.00000000e+00 2.15041225e+00 ... 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
      " [0.00000000e+00 1.00889547e+06 0.00000000e+00 ... 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
      " [2.15041225e+00 0.00000000e+00 1.00891525e+06 ... 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
      " ...\n",
      " [0.00000000e+00 0.00000000e+00 0.00000000e+00 ... 1.00919985e+06 0.00000000e+00 0.00000000e+00]\n",
      " [0.00000000e+00 0.00000000e+00 0.00000000e+00 ... 0.00000000e+00 1.00919985e+06 0.00000000e+00]\n",
      " [0.00000000e+00 0.00000000e+00 0.00000000e+00 ... 0.00000000e+00 0.00000000e+00 1.00919985e+06]]\n",
      "\n",
      "The eigenenergies are (in GHz):\n",
      "[1008894.79667278 1008894.79947523 1008915.27803518 ... 1009199.85429622 1009199.85536555 1009199.85630439]\n",
      "\n",
      "The eigenstate with index 2 is: StateAtom(0.99 |Rb:57,P_1/2,-1/2⟩ + ... ); \n",
      "and its coefficients are:\n",
      "\n",
      "[0.09730863 0.         0.98920897 ... 0.         0.         0.        ]\n",
      "It has the largest overlap with the ket: |Rb:57,P_1/2,-1/2⟩\n",
      "\n",
      "The state corresponding to the ket |Rb:60,P_1/2,1/2⟩ is:\n",
      "StateAtom(0.88 |Rb:60,P_1/2,1/2⟩ + 0.33 |Rb:59,D_3/2,1/2⟩ + -0.18 |Rb:60,P_3/2,1/2⟩ + ... )\n",
      "The overlap |<state|ket>|^2 is 0.7817048662479265\n"
     ]
    }
   ],
   "source": [
    "system = pi.SystemAtom(basis)\n",
    "system.set_magnetic_field([0, 0, 1], unit=\"gauss\")\n",
    "system.set_electric_field([0, 0, 1.5], unit=\"V/cm\")\n",
    "system.set_diamagnetism_enabled(True)\n",
    "\n",
    "print(\"The Hamiltonian of the system with magnetic and electric fields is (in GHz):\")\n",
    "print(f\"{system.get_hamiltonian(unit='GHz').toarray()}\")\n",
    "\n",
    "system.diagonalize()\n",
    "eigenbasis = system.get_eigenbasis()\n",
    "eigenenergies = system.get_eigenenergies(unit=\"GHz\")\n",
    "\n",
    "print(\"\\nThe eigenenergies are (in GHz):\")\n",
    "print(eigenenergies)\n",
    "\n",
    "eigenstate_number = 2\n",
    "eigenstate = eigenbasis.states[eigenstate_number]\n",
    "\n",
    "print(f\"\\nThe eigenstate with index {eigenstate_number} is: {eigenstate}; \")\n",
    "print(\"and its coefficients are:\\n\")\n",
    "print(f\"{eigenstate.get_coefficients()}\")\n",
    "print(f\"It has the largest overlap with the ket: {eigenstate.get_corresponding_ket()}\")\n",
    "\n",
    "corresponding_state = eigenbasis.get_corresponding_state(ket)\n",
    "print(f\"\\nThe state corresponding to the ket {ket} is:\")\n",
    "print(f\"{corresponding_state}\")\n",
    "print(f\"The overlap |<state|ket>|^2 is {corresponding_state.get_overlap(ket)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7a. Create a Two-Atom Basis (`BasisPair`)\n",
    "\n",
    "The `BasisPair` object consists of a list of `KetPair` objects.\n",
    "Again, we view these KetPair kets as forming a canonical basis for the pair Hilbert space.\n",
    "However, in contrast to the `KetAtom` objects, the `KetPair` objects are not atomic states (or product states of atomic states), but rather product states of the eigenstates of the single atom Hamiltonian.\n",
    "\n",
    "Again, the `BasisPair` object has a coefficients matrix, which defines the basis states (with respect to the list of `KetPair` objects).\n",
    "The coefficients matrix is initialized to the identity matrix.\n",
    "This corresponds to the eigenstates of the pair Hamiltonian with external fields but without any interaction between the atoms.\n",
    "In general, when adding interactions, the pair-states (=the columns of the coefficent matrix) can be a superposition of multiple KetPair objects.\n",
    "\n",
    "Similar to the `BasisAtom` object, we can restrict the list of kets that should be considered in the basis by passing in tuples of (min, max) values for the energy of the pair states and the quantum number m if it is conserved.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The pair-basis contains 352 KetPair (=pair-states)\n",
      "The first KetPair corresponds to a pair-state close to the product state |Rb:57,S_1/2,-1/2; Rb:63,D_5/2,3/2⟩\n",
      "The coefficient matrix has shape (352, 352) and the following entries:\n",
      "[[1. 0. 0. ... 0. 0. 0.]\n",
      " [0. 1. 0. ... 0. 0. 0.]\n",
      " [0. 0. 1. ... 0. 0. 0.]\n",
      " ...\n",
      " [0. 0. 0. ... 1. 0. 0.]\n",
      " [0. 0. 0. ... 0. 1. 0.]\n",
      " [0. 0. 0. ... 0. 0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "pair_energy = 2 * system.get_corresponding_energy(ket, unit=\"GHz\")\n",
    "delta_energy = 10  # GHz\n",
    "pair_basis = pi.BasisPair(\n",
    "    [system, system],\n",
    "    m=(2 * ket.m, 2 * ket.m),\n",
    "    energy=(pair_energy - delta_energy, pair_energy + delta_energy),\n",
    "    energy_unit=\"GHz\",\n",
    ")\n",
    "coefficients = pair_basis.get_coefficients()\n",
    "\n",
    "print(f\"The pair-basis contains {pair_basis.number_of_kets} KetPair (=pair-states)\")\n",
    "print(\n",
    "    \"The first KetPair corresponds to a pair-state \"\n",
    "    f\"close to the product state {pair_basis.kets[0]}\"\n",
    ")\n",
    "print(f\"The coefficient matrix has shape {coefficients.shape} and the following entries:\")\n",
    "print(f\"{coefficients.toarray()}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7b. Create a Two-Atom System (`SystemPair`)\n",
    "\n",
    "The `SystemPair` object describes the pair system.\n",
    "Similar to the `SystemAtom` object, it is created by passing a `BasisPair` object in, which defines the basis of the pair Hilbert space.\n",
    "You can now set the interatomic distance between the atoms and the order of the multipole expansion.\n",
    "Then you can inspect the resulting Hamiltonian and diagonalize it to get the eigenstates and eigenenergies of the system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Hamiltonian of the SystemPair (in GHz) for the given distance=5um is:\n",
      "[[ 2.01805691e+06 -1.50501903e-04  1.06486289e-09 ...  1.25246904e-09  0.00000000e+00  0.00000000e+00]\n",
      " [-1.50501903e-04  2.01805740e+06 -2.49059846e-10 ...  4.01258629e-10  0.00000000e+00  0.00000000e+00]\n",
      " [ 1.06486289e-09 -2.49059846e-10  2.01805675e+06 ...  6.42578942e-10  9.02572743e-11  2.89160922e-11]\n",
      " ...\n",
      " [ 1.25246904e-09  4.01258629e-10  6.42578942e-10 ...  2.01805690e+06 -3.38649247e-11 -2.85118877e-09]\n",
      " [ 0.00000000e+00  0.00000000e+00  9.02572743e-11 ... -3.38649247e-11  2.01805691e+06 -1.50501903e-04]\n",
      " [ 0.00000000e+00  0.00000000e+00  2.89160922e-11 ... -2.85118877e-09 -1.50501903e-04  2.01805740e+06]]\n",
      "\n",
      "The eigenenergies in GHz are:\n",
      "[2018046.54203192 2018046.54203914 2018047.03989477 ... 2018065.1183288  2018065.12218846 2018065.12218861]\n"
     ]
    }
   ],
   "source": [
    "pair_system = pi.SystemPair(pair_basis)\n",
    "distance = 5  # micrometer\n",
    "pair_system.set_distance(distance, unit=\"micrometer\")\n",
    "pair_system.set_interaction_order(3)\n",
    "\n",
    "print(f\"The Hamiltonian of the SystemPair (in GHz) for the given {distance=}um is:\")\n",
    "print(f\"{pair_system.get_hamiltonian(unit='GHz').toarray()}\")\n",
    "\n",
    "pair_system.diagonalize()\n",
    "eigenenergies = pair_system.get_eigenenergies(unit=\"GHz\")\n",
    "\n",
    "print(\"\\nThe eigenenergies in GHz are:\")\n",
    "print(eigenenergies)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analyzing Rydberg Systems\n",
    "\n",
    "Once you have created a `KetAtom`, `SystemAtom`, or `SystemPair` object, you can use different methods to obtain information about the object.\n",
    "\n",
    "For example, you can obtain the eigenenergies of a system to plot Stark maps, Zeeman maps, or pair potentials. Because this requires diagonalizing Hamiltonians of many systems for different parameters, we provide a function `diagonalize` that can be used to diagonalize the Hamiltonians in parallel. This function is implemented in C++ and thus avoids Python's global interpreter lock (GIL). To accelerate the diagonalization, you can reduce the precision by passing `float_type=\"float32\"` as an argument. The resulting numerical errors are typically negligible. A further speedup can be achieved by using `diagonalizer=\"lapacke_evr\"` to compute eigenenergies only in a specified energy range, for example, by passing `energy_range=(-1, 1), energy_unit=\"MHz\"` to the `diagonalize` function. The relative error in the eigenenergies can be controlled by setting `rtol` (the default is 1e-6, which is usually sufficient and compatible with float32). In the following, we demonstrate how this function can be used to obtain pair potentials."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from pairinteraction.visualization.colormaps import alphamagma\n",
    "\n",
    "# Use pair basis from before to construct systems with different distances between atoms\n",
    "distances = np.linspace(2, 5, 100)  # micrometer\n",
    "pair_systems = [\n",
    "    pi.SystemPair(pair_basis).set_distance(d, unit=\"micrometer\") for d in distances\n",
    "]\n",
    "\n",
    "# Diagonalize all systems in parallel and get the eigenenergies and overlaps\n",
    "pi.diagonalize(pair_systems, float_type=\"float32\")\n",
    "pair_eigenenergies = np.array([s.get_eigenenergies(unit=\"GHz\") for s in pair_systems])\n",
    "pair_overlaps = np.array([s.get_eigenbasis().get_overlaps([ket, ket]) for s in pair_systems])\n",
    "\n",
    "# Plot the eigenenergies  and overlaps as a function of distance\n",
    "distances_repeated = np.hstack(\n",
    "    [d * np.ones_like(e) for d, e in zip(distances, pair_eigenenergies)]\n",
    ")\n",
    "pair_eigenenergies_flattened = np.hstack(pair_eigenenergies)\n",
    "pair_overlaps_flattened = np.hstack(pair_overlaps)\n",
    "sorter = np.argsort(pair_eigenenergies_flattened)\n",
    "\n",
    "plt.plot(distances, pair_eigenenergies - pair_energy, \"-\", color=\"0.8\", zorder=-10)\n",
    "scat = plt.scatter(\n",
    "    distances_repeated[sorter],\n",
    "    pair_eigenenergies_flattened[sorter] - pair_energy,\n",
    "    c=pair_overlaps_flattened[sorter],\n",
    "    s=10,\n",
    "    cmap=alphamagma,\n",
    "    vmin=0,\n",
    "    vmax=1,\n",
    ")\n",
    "plt.colorbar(scat, label=f\"Overlap with 2x{ket}\")\n",
    "plt.xlabel(\"Distance (μm)\")\n",
    "plt.ylabel(\"Eigenenergy (GHz)\")\n",
    "plt.ylim(-2, 2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example applications and additional ways to analyze systems are described in the next tutorials."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "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": "3.13.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}