{ "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 [PRX Quantum 6, 020332 (2025)](https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.6.020332) 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": 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.real as pi\n", "from pairinteraction import perturbative" ] }, { "cell_type": "code", "execution_count": 2, "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": [ "Let us define all single atom states of interest, as well as the fields and distances between the atoms used in the paper." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "ket_atoms = {\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", "\n", "magnetic_field = [0, 0, 60.7] # in gauss\n", "\n", "theta_list = np.linspace(0, 90, 20) # degree\n", "theta_default = 35.1 # degree\n", "\n", "distance_list = np.linspace(8, 14, 20) # mum\n", "distance_default = 11.6 # mum" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# $M_\\mathrm{tot} = 0\\,$ subspace\n", "We start by considering the $M_\\mathrm{tot} = 0\\,$ two atom subspace, which contains the following states:\n", "- |+, ->\n", "- |0, 0>\n", "- |-, +> \n", "\n", "And create the corresponding effective Hamiltonian for this subspace.\n", "\n", "Note, that we can set the magnetic field as well as the interaction order of the effective Hamiltonian like we are used t from the `SystemAtom` class and the `SystemPair` class." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "ket_tuples = [\n", " (ket_atoms[\"+\"], ket_atoms[\"-\"]),\n", " (ket_atoms[\"0\"], ket_atoms[\"0\"]),\n", " (ket_atoms[\"-\"], ket_atoms[\"+\"]),\n", "]\n", "\n", "eff_system = perturbative.EffectiveSystemPair(ket_tuples)\n", "eff_system.set_perturbation_order(3)\n", "\n", "# Set single atom properties\n", "eff_system.set_magnetic_field([0, 0, 60.7], \"gauss\")\n", "eff_system.set_diamagnetism_enabled(True)\n", "\n", "# create a pair basis with at least 5000 ket pairs\n", "eff_system.set_minimum_number_of_ket_pairs(5_000)\n", "\n", "# set two atom properties\n", "eff_system.set_interaction_order(3);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can create the effective Hamiltonian for different distances and angles between the atoms.\n", "Then from the effective Hamiltonians we can extract the parameters $V^\\mathrm{offd}$, $V^\\mathrm{diag}$, and $J^{00}$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "eff_h_dict = {\"theta\": [], \"distance\": []}\n", "for theta in theta_list:\n", " eff_system.set_distance(distance_default, theta, \"micrometer\")\n", " eff_h_dict[\"theta\"].append(eff_system.get_effective_hamiltonian(unit=\"MHz\"))\n", "\n", "for distance in distance_list:\n", " eff_system.set_distance(distance, theta_default, \"micrometer\")\n", " eff_h_dict[\"distance\"].append(eff_system.get_effective_hamiltonian(unit=\"MHz\"))\n", "\n", "pair_energy_pm = eff_system.get_pair_energies(\"MHz\")[0]\n", "J00 = {k: [eff_h[0, 1] for eff_h in eff_h_lists] for k, eff_h_lists in eff_h_dict.items()}\n", "Voffd = {k: [eff_h[0, 2] for eff_h in eff_h_lists] for k, eff_h_lists in eff_h_dict.items()}\n", "Vdiag = {\n", " k: [eff_h[0, 0] - pair_energy_pm for eff_h in eff_h_lists]\n", " for k, eff_h_lists in eff_h_dict.items()\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can plot the results for the different distances and angles to reproduce the $V^\\mathrm{offd}$, $V^\\mathrm{diag}$, and $J^{00}$ lines from the paper." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(1, 2, figsize=(8, 4), sharey=True)\n", "\n", "axs[0].plot(theta_list, J00[\"theta\"], \"C1-\", label=r\"$J^{00}$\")\n", "axs[0].plot(theta_list, Voffd[\"theta\"], \"C2-\", label=r\"$V^\\text{offd}$\")\n", "axs[0].plot(theta_list, Vdiag[\"theta\"], \"C2--\", label=r\"$V^\\text{diag}$\")\n", "axs[0].set_xlabel(r\"$\\theta$ (degree)\")\n", "\n", "axs[1].plot(distance_list, J00[\"distance\"], \"C1-\", label=r\"$J^{00}$\")\n", "axs[1].plot(distance_list, Voffd[\"distance\"], \"C2-\", label=r\"$V^\\text{offd}$\")\n", "axs[1].plot(distance_list, Vdiag[\"distance\"], \"C2--\", label=r\"$V^\\text{diag}$\")\n", "axs[1].set_xlabel(r\"$r$ ($\\mu$m)\")\n", "\n", "axs[0].set_ylabel(r\"(MHz)\")\n", "axs[1].legend()\n", "\n", "fig.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# $M_\\mathrm{tot} = +1\\,$ subspace\n", "To also reproduce e.g. the $J^{+0}$ line from the paper, we can also consider the $M_\\mathrm{tot} = +1\\,$ two atom subspace, which contains the following states:\n", "- |+, 0>\n", "- |0, +>\n", "\n", "And create the corresponding effective Hamiltonian for this subspace." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "ket_tuples = [\n", " (ket_atoms[\"+\"], ket_atoms[\"0\"]),\n", " (ket_atoms[\"0\"], ket_atoms[\"+\"]),\n", "]\n", "\n", "eff_system = perturbative.EffectiveSystemPair(ket_tuples)\n", "eff_system.set_perturbation_order(3)\n", "eff_system.set_magnetic_field([0, 0, 60.7], \"gauss\")\n", "eff_system.set_diamagnetism_enabled(True)\n", "eff_system.set_minimum_number_of_ket_pairs(5_000)\n", "eff_system.set_interaction_order(3)\n", "\n", "eff_h_dict = {\"theta\": [], \"distance\": []}\n", "for theta in theta_list:\n", " eff_system.set_distance(distance_default, theta, \"micrometer\")\n", " eff_h_dict[\"theta\"].append(eff_system.get_effective_hamiltonian(unit=\"MHz\"))\n", "\n", "for distance in distance_list:\n", " eff_system.set_distance(distance, theta_default, \"micrometer\")\n", " eff_h_dict[\"distance\"].append(eff_system.get_effective_hamiltonian(unit=\"MHz\"))\n", "\n", "Jp0 = {k: [eff_h[0, 1] for eff_h in eff_h_lists] for k, eff_h_lists in eff_h_dict.items()}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting the results together with the previous results, we can reproduce the entire figure 2c) and d) from the paper." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(1, 2, figsize=(8, 4), sharey=True)\n", "\n", "axs[0].plot(theta_list, Jp0[\"theta\"], \"C0-\", label=r\"$J^{+0}$\")\n", "axs[0].plot(theta_list, J00[\"theta\"], \"C1-\", label=r\"$J^{00}$\")\n", "axs[0].plot(theta_list, Voffd[\"theta\"], \"C2-\", label=r\"$V^\\text{offd}$\")\n", "axs[0].plot(theta_list, Vdiag[\"theta\"], \"C2--\", label=r\"$V^\\text{diag}$\")\n", "axs[0].set_xlabel(r\"$\\theta$ (degree)\")\n", "\n", "axs[1].plot(distance_list, Jp0[\"distance\"], \"C0-\", label=r\"$J^{+0}$\")\n", "axs[1].plot(distance_list, J00[\"distance\"], \"C1-\", label=r\"$J^{00}$\")\n", "axs[1].plot(distance_list, Voffd[\"distance\"], \"C2-\", label=r\"$V^\\text{offd}$\")\n", "axs[1].plot(distance_list, Vdiag[\"distance\"], \"C2--\", label=r\"$V^\\text{diag}$\")\n", "axs[1].set_xlabel(r\"$r$ ($\\mu$m)\")\n", "\n", "axs[0].set_ylabel(r\"(MHz)\")\n", "axs[1].legend()\n", "\n", "fig.tight_layout()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "pairinteraction (3.11.2)", "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": "3.11.2" } }, "nbformat": 4, "nbformat_minor": 2 }