{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Comparison of the dipole matrix elements with pairinteraction(v0.9) and ARC(v3.8.1)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from pathlib import Path\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "from rydstate.rydberg_state import RydbergStateAlkali\n", "from rydstate.units import ureg" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# A few exemplary test cases, where pairinteraction(v0.9) and ARC do fail in various ways\n", "n_list = list(range(20, 150))\n", "\n", "choose = \"circular\"\n", "\n", "dn, dl, dj, dm = [\n", " (3, 1, 0, 0),\n", " (1, 0, 0, 0),\n", " (2, 0, 0, 0),\n", " (2, 2, 2, 0),\n", " (5, 1, 0, 0),\n", " (5, 2, 1, 0),\n", "][0]\n", "\n", "##### Circular states\n", "if choose == \"circular\":\n", " qn1_list = [(n1, n1 - 1, n1 - 0.5, n1 - 0.5) for n1 in n_list]\n", " qn2_list = [(n + dn, l + dl, j + dj, m + dm) for n, l, j, m in qn1_list]\n", "\n", "###### Other states\n", "if choose == \"close_to_circular\":\n", " dl1 = 5\n", " qn1_list = [(n1, n1 - dl1, n1 - dl1 + 0.5, n1 - dl1 + 0.5) for n1 in n_list]\n", " qn2_list = [(n + dn, l + dl, j + dj, m + dm) for n, l, j, m in qn1_list]\n", "\n", "if choose == \"works_fine\":\n", " n_list = list(range(30, 100))\n", " l1 = 25\n", " qn1_list = [(n, l1, l1 + 0.5, l1 + 0.5) for n in n_list]\n", " qn2_list = [(n + dn, l + dl, j + dj, m + dm) for n, l, j, m in qn1_list]\n", "\n", "if choose == \"sign_error\":\n", " n_list = list(range(7, 80))\n", " qn1_list = [(n, 0, 0.5, 0.5) for n in n_list]\n", " qn2_list = [(n + 2, 1, 1.5, 0.5) for n in n_list]" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "results = {}" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n=149\r" ] } ], "source": [ "matrixelements = []\n", "for qn1, qn2 in zip(qn1_list, qn2_list):\n", " print(f\"n={qn1[0]}\", end=\"\\r\")\n", " q = round(qn2[-1] - qn1[-1])\n", " state_i = RydbergStateAlkali(\"Rb\", n=qn1[0], l=qn1[1], j=qn1[2], m=qn1[3])\n", " state_f = RydbergStateAlkali(\"Rb\", n=qn2[0], l=qn2[1], j=qn2[2], m=qn2[3])\n", " dipole_me = state_i.calc_matrix_element(state_f, \"electric_dipole\", q, unit=\"a.u.\")\n", " matrixelements.append(dipole_me)\n", "\n", "results[\"rydstate\"] = np.array(matrixelements)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n=149\r" ] } ], "source": [ "from pairinteraction import pireal as pi\n", "\n", "Path(\"./.pairinteraction_cache\").mkdir(exist_ok=True)\n", "cache = pi.MatrixElementCache(\"./.pairinteraction_cache/\")\n", "pi_unit_to_au = (ureg.Quantity(1, \"cm/V\") * ureg.Quantity(1, \"GHz\").to(\"J\", \"spectroscopy\")).to(\"e * a_0\").magnitude\n", "\n", "for method in [\"Numerov\", \"Whittaker\"]:\n", " key = f\"Pairinteraction v0.9, {method}\"\n", " cache.setMethod(pi.NUMEROV if method == \"Numerov\" else pi.WHITTAKER)\n", " matrixelements = []\n", " for qn1, qn2 in zip(qn1_list, qn2_list):\n", " print(f\"n={qn1[0]}\", end=\"\\r\")\n", " state_i = pi.StateOne(\"Rb\", int(qn1[0]), int(qn1[1]), qn1[2], qn1[3])\n", " state_f = pi.StateOne(\"Rb\", int(qn2[0]), int(qn2[1]), qn2[2], qn2[3])\n", "\n", " dipole_me = cache.getElectricMultipole(state_i, state_f, 1, 1)\n", " matrixelements.append(dipole_me)\n", "\n", " results[key] = np.array(matrixelements) * pi_unit_to_au" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n=149\r" ] } ], "source": [ "import arc\n", "\n", "atom = arc.Rubidium87()\n", "\n", "matrixelements = []\n", "for qn1, qn2 in zip(qn1_list, qn2_list):\n", " print(f\"n={qn1[0]}\", end=\"\\r\")\n", " q = int(qn2[-1] - qn1[-1])\n", " v = atom.getDipoleMatrixElement(\n", " int(qn1[0]),\n", " int(qn1[1]),\n", " float(qn1[2]),\n", " float(qn1[3]),\n", " int(qn2[0]),\n", " int(qn2[1]),\n", " float(qn2[2]),\n", " float(qn2[3]),\n", " q=int(q),\n", " )\n", " matrixelements.append(v)\n", "\n", "results[f\"ARC v{arc.__version__}\"] = np.array(matrixelements)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "\n", "ls_dict = {\"Pairinteraction v0.9, Numerov\": \"-.\", \"ARC v3.8.1\": \":\", \"Pairinteraction v0.9, Whittaker\": \"--\"}\n", "for key, values in results.items():\n", " ls = ls_dict.get(key, \"-\")\n", " ax.plot(n_list, values, ls=ls, label=key)\n", "\n", "ax.set_xlabel(\"n\")\n", "ax.set_ylabel(r\"Dipole Matrix element [$e \\cdot a_0$]\")\n", "\n", "ax.legend()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "rydstate", "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 }