{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Dispersion Coefficients Near Surfaces" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This jupyter notebook demonstrates how to compute the C6 coefficient near a surface using the `pairinteraction` library.\n", "It is comparable to the examples provided in the old `pairinteraction` software, which can be found [here](https://www.pairinteraction.org/pairinteraction/v0.9.10/examples_python/vdw_near_surface.html) and reproduces the results from [Phys. Rev. A 96, 062509 (2017)](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.062509).\n", "However, in this example here, we focus on the quantization axis point along the z-axis, which is perpendicular to the surface and interatomic axis." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# %pip install -q pairinteraction # Uncomment for installation on Colab\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pairinteraction as pi\n", "from pairinteraction.green_tensor import GreenTensorSurface\n", "\n", "if pi.Database.get_global_database() is None:\n", " pi.Database.initialize_global_database(download_missing=True)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "ket1 = pi.KetAtom(\"Rb\", n=69, l=0, j=0.5, m=0.5)\n", "ket2 = pi.KetAtom(\"Rb\", n=72, l=0, j=0.5, m=0.5)\n", "\n", "distance_atoms = 10.0 # micrometer\n", "distance_surface_list = np.linspace(0.05 * distance_atoms, 2 * distance_atoms, 100)\n", "\n", "c6_list = []\n", "for z in distance_surface_list:\n", " eff_system = pi.EffectiveSystemPair([(ket1, ket2), (ket2, ket1)])\n", " eff_system.set_magnetic_field([0, 0, 1], unit=\"gauss\")\n", "\n", " gt = GreenTensorSurface(\n", " [0, 0, 0], [distance_atoms, 0, 0], z=-z, unit=\"micrometer\", static_limit=True\n", " )\n", " eff_system.system_pair.set_green_tensor(gt)\n", "\n", " eff_h = eff_system.get_effective_hamiltonian(return_order=2, unit=\"GHz\")\n", " c6 = -eff_h[0, 0] * (distance_atoms**6) # GHz um^6\n", " c6_list.append(c6)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.plot(distance_surface_list / distance_atoms, np.abs(c6_list))\n", "ax.set_xlabel(\"distance to surface / interatomic distance\")\n", "ax.set_ylabel(\"$|C_6|$ coefficient (GHz μm$^6$)\")\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "pairinteraction_green_tensor", "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 }