{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Effective Hamiltonian" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook demonstrates how to calculate an effective Hamiltonian with the `pairinteraction.perturbative` module.\n", "We use https://arxiv.org/pdf/2410.21424 as a reference and try to reproduce figure 2c) and d) from the paper.\n", "Note that the paper used a Schrieffer-Wolff transformation to calculate the effective Hamiltonian, while here we use perturbation theory up to third order." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%pip install matplotlib numpy pairinteraction\n", "\n", "import logging\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pairinteraction.real as pi\n", "from pairinteraction import perturbative\n", "\n", "logging.basicConfig(level=logging.ERROR)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "if pi.Database.get_global_database() is None:\n", " pi.Database.initialize_global_database(download_missing=True)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "SystemPairReal(BasisPairReal(|Rb:78,S_1/2,-1/2; Rb:83,S_1/2,-1/2⟩ ... |Rb:83,P_3/2,3/2; Rb:78,S_1/2,1/2⟩), is_diagonal=True)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kets = {\n", " \"+\": pi.KetAtom(\"Rb\", n=81, l=0, j=0.5, m=0.5),\n", " \"0\": pi.KetAtom(\"Rb\", n=80, l=1, j=1.5, m=1.5),\n", " \"-\": pi.KetAtom(\"Rb\", n=80, l=0, j=0.5, m=0.5),\n", "}\n", "pair_energy = kets[\"0\"].get_energy(\"GHz\") * 2\n", "\n", "basis = pi.BasisAtom(\n", " species=\"Rb\",\n", " n=(78, 83),\n", " l=(0, 2),\n", " j=(0.5, 4.5),\n", ")\n", "\n", "system = pi.SystemAtom(basis=basis)\n", "system.set_diamagnetism_enabled(True)\n", "system.set_magnetic_field([0, 0, 60.7], \"gauss\")\n", "system.diagonalize()\n", "\n", "delta_energy = 5 # GHZ\n", "basis_pair = pi.BasisPair(\n", " [system, system],\n", " energy=(pair_energy - delta_energy, pair_energy + delta_energy),\n", " energy_unit=\"GHz\",\n", ")\n", "system_pair = pi.SystemPair(basis_pair)\n", "system_pair.set_interaction_order(3)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "theta_list = np.linspace(0, 90, 20) # degree\n", "R_list = np.linspace(8, 14, 20) # mum\n", "\n", "theta_default = 35.1 # rad\n", "R_default = 11.6 # mum\n", "\n", "order = 3" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "kets_list = [(kets[\"+\"], kets[\"-\"]), (kets[\"0\"], kets[\"0\"]), (kets[\"-\"], kets[\"+\"])]\n", "H_eff = {\"theta\": [], \"R\": []}\n", "\n", "for theta in theta_list:\n", " system_pair.set_distance_vector(\n", " R_default * np.array([np.sin(theta * np.pi / 180), 0, np.cos(theta * np.pi / 180)]),\n", " \"micrometer\",\n", " )\n", " h_eff, _ = perturbative.get_effective_hamiltonian_from_system(\n", " kets_list, system_pair, order, unit=\"MHz\"\n", " )\n", " H_eff[\"theta\"].append(h_eff)\n", "\n", "for R in R_list:\n", " system_pair.set_distance_vector(\n", " R\n", " * np.array(\n", " [np.sin(theta_default * np.pi / 180), 0, np.cos(theta_default * np.pi / 180)]\n", " ),\n", " \"micrometer\",\n", " )\n", " h_eff, _ = perturbative.get_effective_hamiltonian_from_system(\n", " kets_list, system_pair, order, unit=\"MHz\"\n", " )\n", " H_eff[\"R\"].append(h_eff)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "pair_energy = kets[\"+\"].get_energy(\"GHz\") + kets[\"0\"].get_energy(\"GHz\")\n", "basis_pair = pi.BasisPair(\n", " [system, system],\n", " energy=(pair_energy - delta_energy, pair_energy + delta_energy),\n", " energy_unit=\"GHz\",\n", ")\n", "system_pair = pi.SystemPair(basis_pair)\n", "system_pair.set_interaction_order(3)\n", "\n", "kets_list = [(kets[\"+\"], kets[\"0\"]), (kets[\"0\"], kets[\"+\"])]\n", "H_eff_p0 = {\"theta\": [], \"R\": []}\n", "\n", "for theta in theta_list:\n", " system_pair.set_distance_vector(\n", " R_default * np.array([np.sin(theta * np.pi / 180), 0, np.cos(theta * np.pi / 180)]),\n", " \"micrometer\",\n", " )\n", " h_eff, _ = perturbative.get_effective_hamiltonian_from_system(\n", " kets_list, system_pair, order, unit=\"MHz\"\n", " )\n", " H_eff_p0[\"theta\"].append(h_eff)\n", "\n", "for R in R_list:\n", " system_pair.set_distance_vector(\n", " R\n", " * np.array(\n", " [np.sin(theta_default * np.pi / 180), 0, np.cos(theta_default * np.pi / 180)]\n", " ),\n", " \"micrometer\",\n", " )\n", " h_eff, _ = perturbative.get_effective_hamiltonian_from_system(\n", " kets_list, system_pair, order, unit=\"MHz\"\n", " )\n", " H_eff_p0[\"R\"].append(h_eff)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "H_eff = {key: np.array(value) for key, value in H_eff.items()}\n", "H_eff_p0 = {key: np.array(value) for key, value in H_eff_p0.items()}\n", "\n", "fig, axs = plt.subplots(2, 1, figsize=(6, 6))\n", "\n", "axs[0].plot(theta_list, H_eff_p0[\"theta\"][:, 0, 1], \"C0-\", label=r\"$J^{+0}$\")\n", "axs[0].plot(theta_list, H_eff[\"theta\"][:, 0, 1], \"C1-\", label=r\"$J^{00}$\")\n", "axs[0].plot(theta_list, H_eff[\"theta\"][:, 0, 2], \"C2-\", label=r\"$V^\\text{offd}$\")\n", "axs[0].set_xlabel(r\"$\\theta$ (degree)\")\n", "\n", "axs[1].plot(R_list, H_eff_p0[\"R\"][:, 0, 1], \"C0-\", label=r\"$J^{+0}$\")\n", "axs[1].plot(R_list, H_eff[\"R\"][:, 0, 1], \"C1-\", label=r\"$J^{00}$\")\n", "axs[1].plot(R_list, H_eff[\"R\"][:, 0, 2], \"C2-\", label=r\"$V^\\text{offd}$\")\n", "axs[1].set_xlabel(r\"$R$ ($\\mu$m)\")\n", "\n", "for ax in axs:\n", " ax.legend()\n", " ax.set_ylabel(r\"(MHz)\")\n", "\n", "fig.tight_layout()\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 }