{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QuTiP example: Groundstate of an ultra-strong coupled atom-cavity system" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "J.R. Johansson and P.D. Nation\n", "\n", "For more information about QuTiP see [http://qutip.org](http://qutip.org)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "from qutip import *\n", "import time\n", "from mpl_toolkits.mplot3d import Axes3D" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "time elapsed = 1.351557731628418\n" ] } ], "source": [ "def compute(N, wc, wa, glist, use_rwa):\n", "\n", " # Pre-compute operators for the hamiltonian\n", " a = tensor(destroy(N), qeye(2))\n", " sm = tensor(qeye(N), destroy(2))\n", " nc = a.dag() * a\n", " na = sm.dag() * sm\n", " \n", " idx = 0\n", " na_expt = np.zeros(shape(glist))\n", " nc_expt = np.zeros(shape(glist))\n", " for g in glist:\n", "\n", " # recalculate the hamiltonian for each value of g\n", " if use_rwa: \n", " H = wc * nc + wa * na + g * (a.dag() * sm + a * sm.dag())\n", " else:\n", " H = wc * nc + wa * na + g * (a.dag() + a) * (sm + sm.dag())\n", "\n", " # find the groundstate of the composite system\n", " evals, ekets = H.eigenstates()\n", " psi_gnd = ekets[0]\n", " na_expt[idx] = expect(na, psi_gnd)\n", " nc_expt[idx] = expect(nc, psi_gnd)\n", "\n", " idx += 1\n", "\n", " return nc_expt, na_expt, ket2dm(psi_gnd)\n", " \n", "#\n", "# set up the calculation\n", "#\n", "wc = 1.0 * 2 * np.pi # cavity frequency\n", "wa = 1.0 * 2 * np.pi # atom frequency\n", "N = 20 # number of cavity fock states\n", "use_rwa = False # Set to True to see that non-RWA is necessary in this regime\n", "\n", "glist = np.linspace(0, 2.5, 50) * 2 * np.pi # coupling strength vector\n", "\n", "start_time = time.time()\n", "nc, na, rhoss_final = compute(N, wc, wa, glist, use_rwa)\n", "print('time elapsed = ' + str(time.time() - start_time)) " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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DM4sGUoFNzrnzD3U7IiJy+HILfNw0NpXMvEI+vu14mifFe12ShKC80+DXOufe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\nMys4J2szM7OC+zeNtOTTOK2aRAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#\n", "# plot the cavity and atom occupation numbers as a function of \n", "#\n", "fig, ax = plt.subplots(figsize=(8,6))\n", "\n", "ax.plot(glist/(2*np.pi), nc)\n", "ax.plot(glist/(2*np.pi), na)\n", "ax.legend((\"Cavity\", \"Atom excited state\"))\n", "ax.set_xlabel('g - coupling strength')\n", "ax.set_ylabel('Occupation probability')\n", "ax.set_title('# photons in the groundstate');" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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ejbS0NFitVvy///f/sG3bNuzcuRMAAqJe1B8s0Xi93riKHpVKhS+//HJE69Jc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cv+jIzOZmOByJHHAGU6aO5+YK9kW5NqAbqFxMrWxSHMNzHCvAUro2YNEEYNnYH1vAPQVE6jqh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\nb7PJfFXZpcR1XaysrCCU+dakQq1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IIYQQIhEUzAghhBBCJIKCGSGE\nEEKIRFAwI4QQQgiRCApmhBBCCCESQcGMEEIIIUQiKJgRQgghhEgEBTNCCCGEEImgYEYIIYQQIhEU\nzAghhBBCJOJ/0p+c0hQusL8AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#\n", "# plot the cavity wigner function for the cavity state (final coupling strenght)\n", "#\n", "fig = plt.figure(2, figsize=(9, 6))\n", "rho_cavity = ptrace(rhoss_final, 0)\n", "xvec = np.linspace(-7.5,7.5,100)\n", "X,Y = np.meshgrid(xvec, xvec)\n", "W = wigner(rho_cavity, xvec, xvec)\n", "ax = Axes3D(fig, azim=-107, elev=49)\n", "surf=ax.plot_surface(X, Y, W, rstride=1, cstride=1, cmap=plt.cm.RdBu, alpha=1.0, linewidth=0.05, \n", " vmax=0.25, vmin=-0.25)\n", "ax.set_xlim3d(-7.5, 7.5)\n", "ax.set_ylim3d(-7.5, 7.5)\n", "fig.colorbar(surf, shrink=0.65, aspect=20)\n", "ax.set_title(\"Wigner function for the cavity groundstate\\n(ultra-strong coupling to a qubit)\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Software version:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
SoftwareVersion
QuTiP4.3.0.dev0+6e5b1d43
Numpy1.13.1
SciPy0.19.1
matplotlib2.0.2
Cython0.25.2
Number of CPUs2
BLAS InfoINTEL MKL
IPython6.1.0
Python3.6.2 |Anaconda custom (x86_64)| (default, Jul 20 2017, 13:14:59) \n", "[GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]
OSposix [darwin]
Thu Jul 20 23:01:57 2017 MDT
" ], "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from qutip.ipynbtools import version_table\n", "\n", "version_table()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.6.2" } }, "nbformat": 4, "nbformat_minor": 1 }