{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# QuTiP development notebook: test number state basis with lower cut off\n",
      "\n",
      "Copyright (C) 2013, Paul D. Nation & Robert J. Johansson"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "When we work with harmonic oscillator operators in the number state representation we always need to truncate the number of basis states at a finite number. Usually we pick an upper limit for the number state and use all the number states below this cut off. However, in some problems it can also be useful with a number basis representation that does not start with the zero number state, but rather at some lower cut off. This notebook demonstrates how to do this in QuTiP using the optional `offset` argument to oscillator operator functions."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from qutip import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Test operators with offset"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def steadystate_fock_distribution(N, offset):\n",
      "    \"\"\"\n",
      "    Solve for the steady state of a driven dissipative cavity, given\n",
      "    the upper (N) and lower (offset) cut offs for the number states in\n",
      "    in the basis. Calculate the average photon number in the steady\n",
      "    state and plot the fock state distribution.\n",
      "    \"\"\"\n",
      "    N = N - offset\n",
      "    Omega = 1.0 * 2 * pi\n",
      "    kappa = 0.9\n",
      "    \n",
      "    a = destroy(N, offset)\n",
      "    n = num(N, offset)\n",
      "    H = Omega * (a + a.dag())\n",
      "    c_ops = [sqrt(kappa) * a]\n",
      "    \n",
      "    rho_ss = steadystate(H, c_ops)\n",
      "    \n",
      "    title = \"Steady state avg. photon number = %.2f\" % expect(rho_ss, n)    \n",
      "    \n",
      "    fig, ax = fock_distribution(rho_ss, offset=offset, unit_y_range=False, title=title)\n",
      "    \n",
      "    return fig, ax"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "steadystate_fock_distribution(250, 0);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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WrVoF4F63Zv/+/eHg4AA7OzsAwMqVK+Hu7o4hQ4agS5cuGDlyJHJycgAA8+bNw+3bt2Fr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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f19cc139690>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "steadystate_fock_distribution(250, 150);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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NmoQRI0ZIbezs7JCXlwd7e3vk5ubWeM7B8uXLped+fn7w8/N76u9DRETUkCQm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\nEZGMMPiJiIhkhMFPREQkIwx+IiIiGfl/ExEgUyIW+QgAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f19be777b10>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Test states with offset"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from qutip import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Fock states"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 10\n",
      "offset = 0\n",
      "\n",
      "n = num(N, offset=offset)\n",
      "psi = (basis(N, 2, offset=offset) + basis(N, 4, offset=offset) + basis(N, 6, offset=offset)).unit()\n",
      "\n",
      "fock_distribution(psi, offset=offset, unit_y_range=False, figsize=(4,3))\n",
      "\n",
      "expect(n, psi)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "4.000000000000001"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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NGqQ2PicnB0FBQXjttdcQHx/f5LwqlQoHDhzAt99+i5ycHJw/fx47duwQrvvA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\nFPd/T4kk3835FZ4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f316e8d86d0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 5\n",
      "offset = 2\n",
      "\n",
      "n = num(N, offset=offset)\n",
      "psi = (basis(N, 2, offset=offset) + basis(N, 4, offset=offset) + basis(N, 6, offset=offset)).unit()\n",
      "\n",
      "fock_distribution(psi, offset=offset, unit_y_range=False, figsize=(4,3))\n",
      "\n",
      "expect(n, psi)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "4.000000000000001"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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13uPOnTuRnp6OnJwcnDt3Tnk/2dnZiImJwcaNG1FcXIz4+HiEh4ejqqpKGb9r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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f316e8d85d0>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Coherent states"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 75\n",
      "offset = 0\n",
      "\n",
      "n = num(N, offset=offset)\n",
      "psi = coherent(N, 6.5, offset=offset)\n",
      "\n",
      "fock_distribution(psi, offset=offset, unit_y_range=False, figsize=(4,3))\n",
      "\n",
      "expect(n, psi)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "42.24999120237548"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Rtn2RTE1NAQBKpRLV1dXo3r274B0khOiPoCOYNWvW4MCBA1i8eDH/yMzPP/8c9+/fx/Ll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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f3164eaeb90>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 50\n",
      "offset = 20\n",
      "\n",
      "n = num(N, offset=offset)\n",
      "psi = coherent(N, 6.5, offset=offset)\n",
      "\n",
      "fock_distribution(psi, offset=offset, unit_y_range=False, figsize=(4,3))\n",
      "\n",
      "expect(n, psi)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "42.244955490644436"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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K1ttk+PDGKQEGBgbw8fFBRkaGytZsamoKU1NTuLm5AQDmz5+PmzdvwsjISCXr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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f3164e1b210>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Software versions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from qutip.ipynbtools import version_table; version_table()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Cython</td><td>0.19.1</td></tr><tr><td>QuTiP</td><td>2.3.0.dev-15c5f51</td></tr><tr><td>SciPy</td><td>0.13.0.dev-7c6d92e</td></tr><tr><td>Python</td><td>3.3.1 (default, Apr 17 2013, 22:30:32) \n",
        "[GCC 4.7.3]</td></tr><tr><td>Numpy</td><td>1.8.0.dev-b307a8a</td></tr><tr><td>matplotlib</td><td>1.4.x</td></tr><tr><td>IPython</td><td>2.0.0-dev</td></tr><tr><td>OS</td><td>posix [linux]</td></tr><tr><td colspan='2'>Fri Aug 30 15:46:41 2013 JST</td></tr></table>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "<IPython.core.display.HTML at 0x7f19be441d50>"
       ]
      }
     ],
     "prompt_number": 6
    }
   ],
   "metadata": {}
  }
 ]
}