{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# StateAtom Objects" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In PairInteraction we define `KetAtom` objects, which form the canonical basis using the atomic states defined by their quantum numbers.\n", "Ket objects are immutable and used to span the Hilbert space of the single atom system.\n", "In addition, we also define `StateAtom` objects, which can also represent arbitrary superpositions in the basis spanned by the `KetAtom` objects.\n", "In this tutorial we will show how to use the `StateAtom` object to create superposition states and calculate overlaps with other states." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%pip install -q matplotlib numpy pairinteraction\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pairinteraction as pi\n", "from pairinteraction.visualization.colormaps import alphamagma\n", "\n", "if pi.Database.get_global_database() is None:\n", " pi.Database.initialize_global_database(download_missing=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simple example: create a superposition\n", "As a first example, we demonstrate how to create a superposition of two or more `KetAtom` objects.\n", "To do so, we first need to define a `BasisAtom`, in which the state will live.\n", "Then we can create a `StateAtom` corresponding to a single `KetAtom` by passing the ket and the basis to the `StateAtom` constructor.\n", "\n", "Finally, you can add multiple `StateAtom` objects together or multiply them by a scalar by simply using the built-in operators `+`, `-`, `*` and `/`.\n", "If you want to calculate overlaps and expectation values, don't forget to normalize the states using the `normalize()` method.\n", "\n", "The coefficients of a `StateAtom` can be accessed using the `get_coefficients()` method, which returns a numpy array containing the coefficients in the order of the `KetAtom` objects in the basis." ] }, { "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: 449\n", "state1.get_coefficients().nonzero()=(array([183]),)\n", "State1: StateAtom(1.00 |Sr88_singlet:60,59_59,58⟩)\n", "State2: StateAtom(1.00 |Sr88_singlet:60,58_58,58⟩)\n", "State plus: StateAtom(0.71 |Sr88_singlet:60,58_58,58⟩ + 0.71 |Sr88_singlet:60,59_59,58⟩)\n", "State minus: StateAtom(-0.71 |Sr88_singlet:60,58_58,58⟩ + 0.71 |Sr88_singlet:60,59_59,58⟩)\n", "1.1 * state1 + 0.6 * state2 - 0.4 * state3 = StateAtom(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": [ "ket1 = pi.KetAtom(\"Sr88_singlet\", n=60, l=59, m=58)\n", "print(f\"Ket of interest: {ket1}\")\n", "basis = pi.BasisAtom(\"Sr88_singlet\", n=(ket1.n - 4, ket1.n + 4), l=(50, 60), m=(50, 60))\n", "print(f\"Number of basis states: {basis.number_of_states}\")\n", "\n", "state1 = pi.StateAtom(ket1, basis)\n", "# this state only has one entry in its coefficient vector\n", "print(f\"{state1.get_coefficients().nonzero()=}\")\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}\")\n", "\n", "# 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": "markdown", "metadata": {}, "source": [ "One can use the `StateAtom` objects to calculate overlaps and expectation values.\n", "In PairInteraction, three kinds of objects can calculate overlaps (`get_overlap(s)`) and expectation values (`get_matrix_element(s)`):\n", "- `BasisAtom` / `BasisPair`\n", " - `get_overlaps(basis)` -> returns a matrix containing all pair-wise overlaps between states of the two bases\n", " - `get_overlaps(state)` -> returns a vector containing the overlaps between all basis states and the given state\n", " - `get_overlaps(ket)` -> returns a vector containing the overlaps between all basis states and the given ket\n", "- `StateAtom` / `StatePair`\n", " - `get_overlap(state)` -> returns the overlap between this state and another state\n", " - `get_overlap(ket)` -> returns the overlap between this state and a ket\n", "- `KetAtom` / `KetPair`\n", " - `get_overlap(ket)` -> returns the overlap between this ket and another ket\n" ] }, { "cell_type": "code", "execution_count": 4, "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+0j) atomic_unit_of_current * atomic_unit_of_time * bohr\n" ] } ], "source": [ "ov = state_plus.get_overlap(ket1)\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": [ "## Stark map with overlap to a superposition state" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For circular states with an external electric field along the z-direction, the eigenstates are superpositions of states with different l but the same m quantum number.\n", "\n", "For the special case defined above (ket1 with n=60, l=59, m=58 and ket2 with n=60, l=58, m=58), the eigenstates are the symmetric and antisymmetric superpositions of these two kets.\n", "This can be visualized by calculating the Stark map and the overlap of the eigenstates with these two superposition states.\n", "\n", "Note for details on how to calculate Stark maps, see the tutorial [Stark maps](./stark_map.ipynb)." ] }, { "cell_type": "code", "execution_count": 5, "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 = [\n", " system.get_eigenenergies(unit=\"GHz\") - ket1.get_energy(unit=\"GHz\") for system in systems\n", "]\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": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "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": "3.9.9" } }, "nbformat": 4, "nbformat_minor": 2 }