{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Comparison of the dipole matrix elements with pairinteraction(v0.9) and ARC" ] }, { "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 ryd_numerov.rydberg import RydbergState\n", "from ryd_numerov.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": 4, "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 = RydbergState(\"Rb\", n=qn1[0], l=qn1[1], j=qn1[2], m=qn1[3])\n", " state_f = RydbergState(\"Rb\", n=qn2[0], l=qn2[1], j=qn2[2], m=qn2[3])\n", " dipole_me = state_i.calc_matrix_element(state_f, \"ELECTRIC\", 1, 1, q, unit=\"a.u.\")\n", " matrixelements.append(dipole_me)\n", "\n", "results[\"ryd-numerov\"] = 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[\"ARC\"] = np.array(matrixelements)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "\n", "ls_dict = {\"Pairinteraction(v0.9) Numerov\": \"-.\", \"ARC\": \":\", \"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": ".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 }