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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "R\u00f3wnania fundamentalne w optyce kwantowej\n",
      "=========================================\n",
      "\n",
      "1. R\u00f3wnianie Lindblada: opis dekoherencji\n",
      "2. R\u00f3wnanie Lindblada dla spinu: dekoherencja uk\u0142ad\u00f3w atomowych\n",
      "3. Wizualizacja wybranych charakterystyk dymaniki dysypatywnej\n",
      "4. Optyczne r\u00f3wnianie fundamentlane\n",
      "5. Wizualizacja charaktertyk dynamiki\n",
      "6. Dynamika splatania w obecno\u015bci dekoherencji \n",
      "7. Zadania"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Opis uk\u0142ad\u00f3w kwantowych traktowanych jako zamkni\u0119te mo\u017cna zawsze uzyska\u0107 w\u0142\u0105czaj\u0105c do badanego uk\u0142adu  jego otoczenie. Je\u015bli otoczenie bedzie dostatecznie du\u017ce mo\u017cna obliczy\u0107 ewolucj\u0119 kwantow\u0105 rozwi\u0105zuj\u0105c odpowiednie r\u00f3wanie von Neumanna (Schroedingera) dla stan\u00f3w (stan\u00f3w czystych) uk\u0142adu:  \n",
      "\n",
      "$\\dot \\rho_{\\rm tot}(t) = -\\frac{i}{\\hbar}[H_{\\rm tot}, \\rho_{\\rm tot}(t)],$\n",
      "\n",
      "Jednak w wi\u0119kszo\u015bci przypadk\u00f3w podzia\u0142 na uk\u0142ad i jedo otoczenie jest uzasadniony z praktycznego punktu widzenia:\n",
      "\n",
      "$ H_{\\rm tot} = H_{\\rm sys} + H_{\\rm env} + H_{\\rm int},$\n",
      "\n",
      "gdzie w zasadzie interesuj\u0105ca jest dynamika cz\u0119\u015bci \"sys\". Rozwi\u0105zanie r\u00f3wnania wyj\u0105ciowego i wykonanie \u015bladu cz\u0119\u015bciowego ze wzgl\u0119du na stopnie swobody otoczenia jest w og\u00f3lno\u015bci niewykonalne. Wyj\u0105tkiem jest kilka szczeg\u00f3lnych przypadk\u00f3w, w kt\u00f3rych rozwi\u0105zywalno\u015bc problemu wynika z istanienia praw zachowania (symetrii).  \n",
      "\n",
      "Na szcz\u0119\u015bcie dzi\u0119ki teorii kwantowych uk\u0142ad\u00f3w otwartych mo\u017cliwe jest wyprowadzenie efektywnych r\u00f3wna\u0144 opisujacych dynamik\u0119 poduk\u0142\u0105du \"sys\" uwzgl\u0119dniaj\u0105cych dekoherencj\u0119. Tutaj ograniczymy si\u0119 do najbardzieju podstawowego: fenomenologicznego r\u00f3wnania fundamentalnego typu Lindblada. R\u00f3wnianie to opisuje przybli\u017cenie markowowskie dynamiki uk\u0142adu i jego posta\u0107 mo\u017ce zosta\u0107 uzasadniona w drodze roachunku perturbacyjnego ze wzgl\u0119du na $H_{\\rm int}$:\n",
      "\n",
      "$ \\dot\\rho(t)=-\\frac{i}{\\hbar}[H,\\rho(t)]+\\sum_n \\frac{1}{2} \\left[2 C_n \\rho(t) C_n^{+} - \\rho(t) C_n^{+} C_n - C_n^{+} C_n \\rho(t)\\right]$ ($\\bullet$)\n",
      "\n",
      "Operatory\n",
      "\n",
      "$C_n = \\sqrt{\\gamma_n} A_n$\n",
      "\n",
      "s\u0142u\u017c\u0105 nam do fenomenologicznego opisu dekoherencji."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Przyk\u0142ady\n",
      "---------\n",
      "\n",
      "__A__. W przypadku, gdy operatory $H$ oraz $C_n$ s\u0105 wyra\u017cone macierzami spinowymi r\u00f3wnanie ($\\bullet$) opisiuje dynamik\u0119 (relaksacj\u0119) spinu (qubitu) lub mo\u017ce by\u0107 wykorzystane w opisie dekoherencji atom\u00f3w.\n",
      "\n",
      "__B__. Je\u015bli $H,C_n$ wyra\u017caj\u0105 sie przez operatory $a,a^\\dagger$ reprezentujace algebr\u0119 Heisenberga-Weyla $[a,a^\\dagger]=1$ to r\u00f3wnanie ($\\bullet$) opisuje r\u00f3\u017cnorakie problemy optyki kwantowej\n",
      "\n",
      "__C__. W przypadku, gdy w r\u00f3wnianiu ($\\bullet$) wystepuj\u0105 oba typy operator\u00f3w mo\u017cna je wykorzysta\u0107 do _nierelatywistecznego_ opisu oddzia\u0142ywania \u015bwiat\u0142a z materi\u0105.   "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from qutip import *\n",
      "from pylab import *\n",
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: pylab import has clobbered these variables: ['power', 'linalg', 'draw_if_interactive', 'random', 'save', 'load', 'info', 'fft']\n",
        "`%pylab --no-import-all` prevents importing * from pylab and numpy\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Okre\u015blmy posta\u0107 operator\u00f3w:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "H=sigmaz()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "oraz dysyspatora $D=C_1$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "D=sqrt(0.1)*sigmax()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "ustalmy warunek pocz\u0105tkowy:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "psi00=(basis(2,0)+basis(2,1)).unit()\n",
      "psi0=ket2dm(psi00)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "i obliczmy dynamik\u0119 uk\u0142adu"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tlist=linspace(0,5.0,10.0)\n",
      "outlist=zeros(len(tlist))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "qq=mesolve(H, psi0, tlist, [D], [])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "uzyskane rozwi\u0105zanie wykorzystamy do obliczenia ewolucji entropii:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i1 in range(len(tlist)):\n",
      "    rho=qq.states[i1]\n",
      "    outlist[i1]=entropy_vn(rho)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "kt\u00f3rej wizualizacj\u0119 przedstawiamy poni\u017cej:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(tlist,outlist,'-',label='', linewidth=4)\n",
      "xlabel('t',fontsize=20)\n",
      "ylabel('SvN',fontsize=20)\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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4ebLgfcOG8PjjztUjIoHr3F+YJ0yYUKKvs+32UUREBFlZWfnvs7KyiIyMtOuv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\nREQk3/8DJkyiPuKPdowAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x391c810>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Analogiczniie przeanalizujemy dynamik\u0119 uk\u0142adu optycznego, zak\u0142adaj\u0105c obci\u0119cie przestrzeni stan\u00f3\u0142 do $N=10$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N=10"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "H=create(N)*destroy(N)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "D=sqrt(0.1)*destroy(N)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Zak\u0142adamy, \u017ce w  chwili pocz\u0105tkowej pole jest w stanie $|N=2\\rangle$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "psi0=fock_dm(N,2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tlist=linspace(0,5.0,10.0)\n",
      "outlist=zeros(len(tlist))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "qq=mesolve(H, psi0, tlist, [D], [])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "tym razem obliczymy \u015bredni\u0105 liczb\u0119 foton\u00f3w w obecno\u015bci dekoherecji:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i1 in range(len(tlist)):\n",
      "    rho=qq.states[i1]\n",
      "    outlist[i1]=(rho*num(N)).tr()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "i przedstawimy wizualizacj\u0119 wyniku:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(tlist,outlist,'-',label='', linewidth=4)\n",
      "xlabel('t',fontsize=20)\n",
      "ylabel('<N>',fontsize=20)\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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/2n0kIgVm1SpzJcZPPzmOt29vioMOvrkurSmISIFp0wZ27TI/+EuUsI8vXWr6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\nEcmkoiAiIplUFEREJNP/AwKOBedf0P9UAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x391ce50>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Dynamika sp\u0142\u0105tania\n",
      "------------------\n",
      "\n",
      "Rozwa\u017cmy uk\u0142ad \n",
      "\n",
      "$H=\\sigma_z\\otimes\\sigma_z$, \n",
      "\n",
      "oraz bilokaln\u0105 dekoherencj\u0119 dan\u0105 przez \n",
      "\n",
      "$A_1= \\sigma_x\\otimes\\mathbb{I}$\n",
      "\n",
      "$A_2= \\mathbb{I}\\otimes\\sigma_x$\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "H=tensor(sigmaz(),sigmaz())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "d1=sqrt(0.1)*sigmax()\n",
      "D1=tensor(qeye(2),d1)\n",
      "D2=tensor(d1,qeye(2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Poczatkowo uk\u0142ad jest w stanie Bella:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "psi00=(tensor(basis(2,0),basis(2,0))+tensor(basis(2,1),basis(2,1))).unit()\n",
      "psi0=ket2dm(psi00)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tlist=linspace(0,5.0,10.0)\n",
      "outlist=zeros(len(tlist))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Obliczmy dynamik\u0119:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "qq=mesolve(H, psi0, tlist, [D1,D2], [])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "a intersuje nas zanik spl\u0105tania (u\u017cywamy funkcji concurrence() ) w obecno\u015bci dekoherencji: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i1 in range(len(tlist)):\n",
      "    rho=qq.states[i1]\n",
      "    outlist[i1]=concurrence(rho)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "wynik przedtawiamy w postaci wizualizacji graficznej:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(tlist,outlist,'-',label='', linewidth=4)\n",
      "xlabel('t',fontsize=20)\n",
      "ylabel('Concurrence',fontsize=20)\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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JwLvvit3S+/YpEx9RXSMrKfTu3RsbNmywWKsIAA4fPozk5GT06dPHpsERlYiM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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3a02290>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Zadania\n",
      "-------\n",
      "1. Nakre\u015bli\u0107 \u015bredni\u0105 warto\u015b\u0107 rzutu spinu na o\u015b $x$ w proceesie opisanym r\u00f3wnaniem $\\bullet$ dla kilko r\u00f3\u017cnych parametr\u00f3w\n",
      "2. Por\u00f3wna\u0107 wyniki z przypadkiem czystego defazingu, gdy $D\\sim H$\n",
      "3. Nakre\u015bli\u0107 fluktuacje liczby foton\u00f3w w uk\u0142adzie opisywanym kwantowooptycznym r\u00f3wnaniem fundamentalnym.  \n",
      "\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    }
   ],
   "metadata": {}
  }
 ]
}