{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QuTiP Example: Steady State for an Optomechanical System in the Single-Photon Strong-Coupling Regime" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "P.D. Nation and J.R. Johansson\n", "\n", "For more information about QuTiP see [http://qutip.org](http://qutip.org)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from IPython.display import Image" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from qutip import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Optomechanical Hamiltonian" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The optomechanical Hamiltonian arrises from the radiation pressure interaction of light in an optical cavity where one of the cavity mirrors is mechanically compliant." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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RIEWK6UY6S6V8PpfLZnOYJKRIcSqCpb8dGYdv0XaWJJIjiYI69lhbBPkGpQUA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REc/O53v5sRjlQkQXpkeeTQZ8E12ThCEBaO5KeeemrGgVc31De5/ugswTI8iqRhT4dxijYtgSKo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\nx07bbZ/sRmDnlw5Ppyo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"text/plain": [ "" ] }, "execution_count": 6, "metadata": { "image/png": { "width": 500 } }, "output_type": "execute_result" } ], "source": [ "Image(filename='images/optomechanical_setup.png', width=500, embed=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Assuming that $a^{+}$, $a$ and $b^{+}$,$b$ are the raising and lowering operators for the cavity and mechanical oscillator, respectively, the Hamiltonian for an optomechanical system driven by a classical monochromatic pump term can be written as " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\\begin{equation}\n", "\\frac{\\hat{H}}{\\hbar}=-\\Delta\\hat{a}^{+}\\hat{a}+\\omega_{m}\\hat{b}^{+}\\hat{b}+g_{0}(\\hat{b}+\\hat{b}^{+})\\hat{a}^{+}\\hat{a}+E\\left(\\hat{a}+\\hat{a}^{+}\\right),\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "where $\\Delta=\\omega_{p}-\\omega_{c}$ is the detuning between the pump ($\\omega_{p}$) and cavity ($\\omega_{c}$) mode frequencies, $g_{0}$ is the single-photon coupling strength, and $E$ is the amplitude of the pump mode. It is known that in the single-photon strong-coupling regime, where the cavity frequency shift per phonon is larger than the cavity line width, $g_{0}/\\kappa \\gtrsim 1$ where $\\kappa$ is the decay rate of the cavity, and a single single photon displaces the mechanical oscillator by more than its zero-point amplitude $g_{0}/\\omega_{m} \\gtrsim 1$, or equiviently, $g^{2}_{0}/\\kappa\\omega_{m} \\gtrsim 1$, the mechanical oscillator can be driven into a nonclassical steady state of the system$+$environment dynamics. Here, we will use the steady state solvers in QuTiP to explore such a state and compare the various solvers." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solving for the Steady State Density Matrix" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The steady state density matrix of the optomechanical system plus the environment can be found from the Liouvillian superoperator $\\mathcal{L}$ via\n", "\n", "\\begin{equation}\n", "\\frac{d\\rho}{dt}=\\mathcal{L}\\rho=0\\rho,\n", "\\end{equation}\n", "\n", "where $\\mathcal{L}$ is typically given in Lindblad form\n", "\\begin{align}\n", "\\mathcal{L}[\\hat{\\rho}]=&-i[\\hat{H},\\hat{\\rho}]+\\kappa \\mathcal{D}\\left[\\hat{a},\\hat{\\rho}\\right]\\\\\n", "&+\\Gamma_{m}(1+n_{\\rm{th}})\\mathcal{D}[\\hat{b},\\hat{\\rho}]+\\Gamma_{m}n_{\\rm th}\\mathcal{D}[\\hat{b}^{+},\\hat{\\rho}], \\nonumber\n", "\\end{align}\n", "\n", "where $\\Gamma_{m}$ is the coulping strength of the mechanical oscillator to its thermal environment with average occupation number $n_{th}$. As is customary, here we assume that the cavity mode is coupled to the vacuum.\n", "\n", "Although, the steady state solution is nothing but an eigenvalue equation, the numerical solution to this equation is anything but trivial due to the non-Hermitian structure of $\\mathcal{L}$ and its worsening condition number has the dimensionality of the truncated Hilbert space increases." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Steady State Solvers in QuTiP v3.0+" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As of QuTiP version 3.0, the following steady state solvers are available:\n", "\n", "- **direct**: Direct LU factorization\n", "- **eigen**: Calculates the eigenvector associated with the zero eigenvalue of $\\mathcal{L}\\rho$.\n", "- **power**: Finds zero eigenvector using inverse-power method.\n", "- **iterative-gmres**: Iterative solution via the GMRES solver.\n", "- **iterative-lgmres**: Iterative solution via the LGMRES solver.\n", "- **iterative-bicgstab**: Iterative solution via the BICGSTAB solver.\n", "- **svd**: Solution via SVD decomposition (dense matrices only)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Setup and Solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### System Parameters" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# System Parameters (in units of wm)\n", "#-----------------------------------\n", "Nc = 4 # Number of cavity states\n", "Nm = 80 # Number of mech states\n", "kappa = 0.3 # Cavity damping rate\n", "E = 0.1 # Driving Amplitude \n", "g0 = 2.4*kappa # Coupling strength\n", "Qm = 1e4 # Mech quality factor\n", "gamma = 1/Qm # Mech damping rate\n", "n_th = 1 # Mech bath temperature\n", "delta = -0.43 # Detuning" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Build Hamiltonian and Collapse Operators" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Operators\n", "#----------\n", "a = tensor(destroy(Nc), qeye(Nm))\n", "b = tensor(qeye(Nc), destroy(Nm))\n", "num_b = b.dag()*b\n", "num_a = a.dag()*a\n", "\n", "# Hamiltonian\n", "#------------\n", "H = -delta*(num_a)+num_b+g0*(b.dag()+b)*num_a+E*(a.dag()+a)\n", "\n", "# Collapse operators\n", "#-------------------\n", "cc = np.sqrt(kappa)*a\n", "cm = np.sqrt(gamma*(1.0 + n_th))*b\n", "cp = np.sqrt(gamma*n_th)*b.dag()\n", "c_ops = [cc,cm,cp]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Run Steady State Solvers" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "direct solution time = 23.896480083465576\n", "eigen solution time = 383.4311008453369\n", "power solution time = 13.483030796051025\n", "iterative-gmres solution time = 142.33112359046936\n", "iterative-bicgstab solution time = 239.15512800216675\n" ] } ], "source": [ "solvers = ['direct','eigen','power','iterative-gmres','iterative-bicgstab']\n", "mech_dms = []\n", "\n", "for ss in solvers:\n", " if ss in ['iterative-gmres','iterative-bicgstab']:\n", " use_rcm = True\n", " else:\n", " use_rcm = False\n", " rho_ss, info = steadystate(H, c_ops, method=ss,use_precond=True, \n", " use_rcm=use_rcm, tol=1e-15, return_info=True)\n", " print(ss,'solution time =',info['solution_time'])\n", " rho_mech = ptrace(rho_ss, 1)\n", " mech_dms.append(rho_mech)\n", "mech_dms = np.asarray(mech_dms)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Check Consistancy of Solutions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Can check to see if the solutions are the same by looking at the number of nonzero elements (NNZ) in the difference between mechanical density matrices." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0\n", "98\n", "0\n", "0\n", "0\n" ] } ], "source": [ "for kk in range(len(mech_dms)):\n", " print((mech_dms[kk]-mech_dms[0]).data.nnz)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It seems that the eigensolver solution is not exactly the same. Lets check the magnitude of the elements to see if they are small." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "False\n", "False\n", "False\n", "False\n", "False\n" ] } ], "source": [ "for kk in range(len(mech_dms)):\n", " print(any(abs((mech_dms[kk] - mech_dms[0]).data.data)>1e-11))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot the Mechanical Oscillator Wigner Function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is known that the density matrix for the mechanical oscillator is diagoinal in the Fock basis due to phase diffusion. However some small off-diagonal terms show up during the factorization process" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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AVnRp1guSPmX7i5I+q0mzfkzSBUlnbF+RdLqZt2WMFw9wwinLTjjldOpCl3eDfDEi7omI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\n/wM6N3/OmdFChwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(8,6))\n", "plt.spy(rho_mech.data, ms=1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Therefore, to remove this error, let use explicitly take the diagonal elements are form a new operator out of them" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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aJZe1NCAbtmbJDCJJDeCylkbkCUdNk8taGpEnHDVNNmtpRJ5w1DS5rKURecJR02QGkWpi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\npAZwWUtSA7isJakBXNaS1AAua0lqgP8HvK2sXyWs5b8AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "diag = rho_mech.diag()\n", "rho_mech2 = qdiags(diag, 0, dims=rho_mech.dims, shape=rho_mech.shape)\n", "fig = plt.figure(figsize=(8,6))\n", "plt.spy(rho_mech2.data, ms=1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now lets compute the oscillator Wigner function and plot it to see if there are any regions of negativity." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "xvec = np.linspace(-20, 20, 256)\n", "W = wigner(rho_mech2, xvec, xvec)\n", "wmap = wigner_cmap(W, shift=-1e-5)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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us37/QXsdRJBrof5+OCP48wCeJaIPW2t/Vaz2BrjeLC8H8BSA7/f/AeAH4Txk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\n0rQO4NvGJO2FQxrM+oGX316+9lRHaFuDpSJcLZowe52bcln7KZg1ZrV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CTZGjaVuUXW5/\nK/TiHbBq7dTmWutjp8ylaHrTUMaXGXaiSanQsKwJH4ffrKbXNtyUB2AeVto09Q4Q1KZP/ebtmS53\nbiexs1bR/xscoQzUWv8cgJ87y+1I/m+CTgxAvfc3WhnTRLJp/eFU8czr4jHTOPd9WxsDhk2pceS9\n8xg8KdTbVtm6874GfRB7t8pl8nrtzgXCurIomLBu6uLslOM+n1WYTSeYTktMqgJFLgNq3ijlmVcc\ngWMM7nEaIbAduHPaPaTcVQDirRUechEiT9lzv8VCAHSM49ANX3AF5+uIscPNlSzmnnzHMjPcwlGZ\neua5iScXuaHm206hKhXKonCLDwLbUjNvr9eOsvfbOD41jIG8tsCV8uRpPHY2Hq8yI/gMqHobTphO\nS7Sdws68wbqZucqK1PyorltMJ34hKrsMUOFC3oz3DHkiFl9V5r4sC0v3dygLG4vPjUCRN26hTnOx\n2C4ZUjtCbBecXzGWE29oetftzqrpN5lLm3MFgXTksIQtZMlu9zi8wHkM/jR2T1Wy2xR/DzzgKP2E\nlNWB0rgfeu/UWIZT8/w+9tqPk/vObYyeT6fGxRXCqMFM628Npcq1AUVN4Em/L4R2TAR5Q7NJibkt\narM7J4regPxsNsF8Zrz3PM9dShxR86r3/8Pj7nz/OLiTktwdB7bwSsXXefydiqd4YPcNbOrGhypc\nSlYE7jGwxwVx6LykFmLbElL8c57eBqgUrNZ+oo8r1WWZQKFIAW480YJtLzU2KVUPVeRswVq4cZ0T\nXV/AdonLEE8RNNm64je0CMlMFTwTix+CvLlUzPWilKfqlcocVb9418dQvu21mFQmHl/XE6zWDXbn\nNZarKXaXa6zWU9O2eF1bAahZlJIAlgCW9q+zxXLKggv3aAHbuRuNi6JTUDm7drLeerR6VGy3DU0/\nlhM/mBPieaPz72k9LHpD48R5872Zr3rtMyFobnDnQt9BcXhxG27THWR3NcBvUiyPpccNKfmQnufg\nP2a+cUxaPR83Dzlq+47aN749PDUuSKFhXjynLoOYexMq56nBCt8nIYTNLy5QVaWNvxsvnrz3uQV2\naiBTFqY0aAM4ar6z3rRXuftJKOXJxq9ROloglEuAO6fUOwbsRMn7fe6c1960LbpW2Thv+DvGCw5F\nmSkvnW/vadN8wng2A/ueys72ruKZlBkKZTqUtXmOqrCpf0URiDC1BvPih9MAj8OH00T4PC5tK7SJ\nxROlHFP1phqeDS9YAM0ZVV9QOKEqbV2FCut6isWqxmK5xmJZYzlbY7GssFw3KIsCRd56L5t0GT1p\nTzKvqG+KcKzTrejQVmpA0/PYNXm+7lo7Jk2fskyY0rVOjGvV9JnoAjU9CQnHxoZj7di4VKpHn4fx\ndxNzDxeSm+Lw5zT9nW93FcCPeb+nib9zQR2/UFKWKm5D6mdX1Y7nvG9J06dy32l/Y1o4FteRp+xS\nvhgl3dh848bS0rUtJELAGe9rlvmiNlWZYzYpTfx9xsDdpsoZcC8suDNhXaSapw5iqXM0JqqLi9iE\nue0c9NPgTiEJozsg0VYbefAtS4dTzmPvVKiQHzN6LwXuKY/kKM8//i8OoOY49baJiakdTx67Ugpl\nXySPlckWKUa2wU8Npow273DXs/dEQFeTTiMW3fH9UH0P0Su0nc8kcVS9Fdyponcth9d1i5351AH8\nYrXGfFY7L361lihUDq1bB4S91shY6Ka147uyoE7jnoR2TdNiUhVoO4WyV+j7HNRznVLmDKMh3ELl\nuJXtuBHtzrMlwqp2EiLrBkVvUhY7JjSvnTYOP3j9BRLanefBn9zuKoDf1jbF3+m5p7yH1aHMZ/gk\nB/aYUW1HFLdx3zkGPT9mgWK294VtYu/d94A3NGWnlPPaufCMvOpMCFf3O8ts7N21g7WV66beYydw\nr6oSVWmEdVJmWFthXU8LD7Zt3HvnNhZ350p1Ls4LvPe+3wjutave1wRePHnt4XHog//k25cCeT4h\npeLoKZMypLTNOfXvb/of8uy11i5uzDuPmcVebid9Sqvs2XfN/WTwD7nZ3i702gVVqBNmMcHL2sbx\neGB4rbma9qKHkr2Ld+cyN7URbH2FqiwxnXSYz1rMl2vMZxPszqc4XKxwOF1hOqmsKr60ixcF2BYt\nmWU8+Ngw2Ro09m1Fu65kKZoKpaJ7s21BSM7S9CfJhwdCmp6u9SBMx0JRmfBtpjmDFWPdxqp2g1j8\neBz+di1bK7CZ6Ty3zXbPAPxR8XcOjvxCcUIkTmu5iTi84AIPPfOr8riuONHzY5P9UfQ84L1YTrvy\nfaTH3INpW0bJB15857x3LnYjepEml1yablymY5xRz8fgPp1WLiWuKg0172LvTFgXp5eZ4xkK63it\nADIuqnMFZoKOZCoZc/dA7tvj1k3jKHleFjUQ7I1oAwDfJpeff3qdT9qkxt4E8nFandbDc8k/58YB\n2yaltPMe417gSoUFeAI9idbQVQnA0PYDKwChlN/2LtxfAIDMHNXLqXoKJfDzS+cvE8ZDjgV3i3d9\nDPMfeD2qMkdTFWY8WWZosVy7kNBiusZqXZj89lai6yQa4WvgOy++7x1zVdsF3tTG5mlMdPb6aIvc\ngHuKuet9fXqttcuJh880TNoYTc87zAXgzuaNeD5RrBUEzT8csHm6XJwaF7OQ52Vr7367ZwB+WxuL\nvwPDGvaxcdpd2pKilAZjlPOZm/jJTlqaNmVx5bpOhaVXO0eNUwqYER11Xef7cEcKcUqLA2zluqJw\ndeTntmscgftsUmI2KW3cvUCeS0fN55Jim6Gwbhtq3u0fW7RQCCKuUBemwoViOu6xm6I+tqCKBf2O\nLYSorO0mOp4AK1b5G7El6wIXeWhJ+jNaoAVtaFncXwh95DaRoM1rBHoURe49OwYCKSOWyTwOhY3u\n9V5AMdCnhcRxqfpYcEdefP2eTyB/8yuDTI3lZO3G2s3FGvPVBKtVg7JYmS5xTefGCy/TmrOQTWfT\nIuumxZRdC66IUefDWp2tT89pelOmIzSKVR+HpqeiN/x4u7LEUiLLOluSWAXzSpwPH573MA4f58Pf\nqXbuwJ/c7lqAP0pgx+NUY/F3vnKPy9PGltkGHe4CFb5aFaliKT1OjEzyJ9pPtgiJ9yNNz6uoLKwv\n5ELU9Fhhm9w28KCKdCSwm00nmE8rzGYTTCcVqqqw3nuOters94meD4V13FJgGcfdKfzQsYWIo2It\nKHes3Sin5alpTgrcTQ68ZzDof/i5Ton/XDnijDcRytwCj1efi0vQunPIWCLd66Aq3qCb3YaQAQB2\n7hkbYl/L89x/ZkM4KK5WGJwf5el5c/OtTXlcOp06Nxy7seCOvPhOdZjkOapSoWltxsZsgvly7cbd\n4cKMtUlVoq5bV66XK80BnzJn6HfqUEcdFTvXXbHtWDOmLkeeD+PXm9T0JzE+H1AnOQrv0TihqnZj\nFs9LwUKRzWeDuc7G4W9roZ3AOUV/CrtrAH5bgd3459L57/QbXMxmXgu/7ye80PuU2bCoTap63bbx\ndxc7ZRd0ip4n+rplQE63NqInW/a6YS38sZDSl9wtcp8ex0GeKNTZpERlvfeyKFyeNNWbp6I2Jo0n\nrUAH0qp5H0smcIvy3ANxXTiBU8ydaPl13Q5i77z+/FEiuoxNyFRBjpq+yEwiL6j2u6kVz2sgGI84\nnLRMuWFfkc+l9iUyA4L8ftEFLENsnu0IafKxkrmAZ6EAQNhYsHnsM0MALij1gJ9lxmvnYEEePC/U\n4jMzwNJQM/S5ObeUNkeM0aRSqKrSijpNOIjG3WxaYVIVWJU5itrU3ddao3fhCr/PfJy7MJXNlpiy\n6yMIIdFir++DNrLuurP7uy0QxiwHMkDr4RzBHYP4Fp5j/zim4Mfy4VMxhTgf/nYT2p3byeyuAfhN\nlpr8AE/HxyvfQKjCQHTst7j37orcJOLvHLhOG393j932Jej54OYV5d5bN5Xb2q5jHnHoWZN3Wlhx\nXVWVNj2uxMxSp3PnuZuCNlVpQM/R80+82qeZaR8THhPWpVTzKWqex8cd3cuakXixnO9pzz35TeA+\nZnROc2mbuBTSZQoUuQF3k7olXcZBUfgUSSHCMrR0Ds2iCoGGwIdUwuwHyv2WMkPWmja+JFxLjikL\ndLR/sYVaAT5WW3ceuq5jVLIR12WZQNaHOdo8Pz4uZZsS3JlYvAio9OKJV6O2ivr8iddY1sinZU4n\npRt3hwvj0S/XDcq6RZE36PseWa+h2P90SiFXkrVL9tdBx2j6oKWwZU2ojawHyMweRz8+jwy16fF0\nOSDsXSFEN5hLgrBJgqbnaXz+P9MCYXoshE7KB7bJAni+TOBcRX8auycAHvBeOOAFdmSxd85jlHF7\n2DHzgrAsirf6PHieHreNjaXHxe/HGgEefnCAYYEhpuf9rRvExOkiz23f8SKXqIocs0mF2bRyXeSm\nk8rG3o3giajSUeU8m5xSwjog1Cbw8AOn5inVi6h55/G2noolESFVMavrxtDyQVEf7wkTSA6oaUpj\nyjKXGWCamBSo7P2kKlyFv6rMURDQW4DP89xN1sRu0P65rABWdY9X16PSwnFoobAV65qmtXHsoSCQ\nKHspM3TKlIzlFoMTUe+ZEGhl58ZtK7qgSYpS3LP0NL0BDnYeFRWfGQruALhmKcQ6xYr6PA8LK00n\nZtxN7IJyUpWobK2F3KYHdp0KQIpi/gbQ84DNorCVY0t6X8hI9yFAkpcs7fW2qejNtkAZpM1mhhlq\nXK16kxcvmKI+VbaW/pvrh/j85cYa8/LN2BsWvLndAPV2WWzciXbPAHzKuMI0RcP7iyUEpHj1HCip\nrcdDgO6p2Sh+ewJ6Pt52t41xHJ7H3/vedYML4vB0z0A3JbziublU3KZy3lRp68wXjpp40L4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MczHFPGe9buWCppvHjOBrn3lEJvy8JS7/kxsV0sQuM0PRACCF/YEbhSHF6pDrn14vn4owJLuav/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Q3Xfvx9aBVIpPmvv4tLe+7xMA58Ae6sxnDvk81h73Pd2W3CWfg3Up3s6BnRz1fGHg6v2XG8fw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\nKCJXq+ptifa3AidU9bS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8,6))\n", "c = ax.contourf(xvec, xvec, W, 256, cmap=wmap)\n", "ax.set_xlim([-10, 10])\n", "ax.set_ylim([-10, 10])\n", "plt.colorbar(c, ax=ax);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Versions" ] }, { "cell_type": "code", "execution_count": 27, "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 22:26:43 2017 MDT
" ], "text/plain": [ "" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from qutip.ipynbtools import version_table\n", "\n", "version_table()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "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 }