{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Kwantowe oscylatory nieliniowe\n", "===========================\n", "\n", "\n", "Plan\n", "----\n", "1. Przyk\u0142ady nieliniowych o\u015brodk\u00f3w optycznych\n", "2. Stany stacjonarne kwantowych oscylator\u00f3w nieliniowych: graficzne por\u00f3wanie z oscylatorem liniowym\n", "3. Funkcje Wignera stan\u00f3w stacjonarnych, wizualizacja\n", "4. Ewolucja w czasie: por\u00f3wanie z przypadkiem liniowym\n", "5. Zadania\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "W optyce kwantowej oscylator harmoniczny odgrywa pierwszoplanow\u0105 rol\u0119. Model ten doskonale przybli\u017ca drgania mod\u00f3w optycznych i mikrofalowych w osrodkach liniowych. Zastosowania optyki kwantowej zwi\u0105zane z generowaniem na przyk\u0142ad stan\u00f3w \u015bcie\u015bnionych (squeezed) wymaga jednak wykorzystania osrodk\u00f3w nieliniowych. Bodaj najlepiej znanym przyk\u0142adem teakiego osrodka jest osrodek Kerra, w kt\u00f3rym mody optyczne opisuje hamiltonian \n", "\n", "$H=a^\\dagger a+ \\alpha (a^\\dagger a^\\dagger + aa)$\n", "\n", "Naszym celem jest przprowadzenie znalizy graficznej (wizualizacji) wp\u0142ywu nielionow\u015bci (poprzez amplitud\u0119 $\\alpha$) na wybrane w\u0142asno\u015bci oscylatora nielionwego. Jako punkt odniesienia przyjmiemy osylator harmoniczny\n", "\n", "$H_0=a^\\dagger a$\n", "\n", "Rozpoczniemy od zaimportowania niezbednych narz\u0119dzi:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from qutip import *\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from matplotlib 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": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Przestrze\u0144 Hilberta oscylatora harmonicznego, bed\u0105ca w istocie aren\u0105 dla reprezentacji algebry Heisenberga-Weyla\n", "\n", "$[a,a^\\dagger]=1$\n", "\n", "jest niesko\u0144czenie wymiarowa. \n", "W obliczeniach wykorzystujemy obciet\u0105 przestrze\u0144 stan\u00f3w. Obci\u0119cie ograniczamy do wymiaru $N$ okreslonego poni\u017cej: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "N=10" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dalej okre\u015blamy stopie\u0144 nieliniowo\u015bci naszego oscylatora" ] }, { "cell_type": "code", "collapsed": false, "input": [ "x=1.0" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "i jego hamiltonian" ] }, { "cell_type": "code", "collapsed": false, "input": [ "H=num(N)+x*(create(N)*create(N)+destroy(N)*destroy(N))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "A tak\u017ce odpowiadaj\u0105cy mu model harmoniczny:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "H0=num(N)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Na wst\u0119pie skupimy si\u0119 na zagadnieniou stacjonarnym:\n", "\n", "$H|\\psi_n\\rangle=E_n|\\psi_n\\rangle$\n", "\n", "Do znalezienia widm obu oscylator\u00f3w wykorzystamy funkcj\u0119 eigenstates():" ] }, { "cell_type": "code", "collapsed": false, "input": [ "kk=H.eigenstates(sort='low')\n", "E=kk[0] # warto\u015bci w\u0142asne\n", "W=kk[1] # wektory w\u0142asne" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Oczywi\u015bcie obliczenia numeryczne dla oscylatora harmionicznego s\u0105 zbedne, jednak dla og\u00f3lno\u015bci rozwa\u017ca\u0144 oraz jako test funkcji eigenstates() przprowadzimy je mimo to:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "kk0=H0.eigenstates(sort='low')\n", "E0=kk0[0] # warto\u015bci w\u0142asne\n", "W0=kk0[1] # wektory w\u0142asne" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Najprostsza wizualizacja zamieszczona poni\u017cej pozwala zauwa\u017cy\u0107 znacz\u0105cy wp\u0142yw nieliowo\u015bci na widmo oscylatora. Wszelkie odst\u0119pstwa od zale\u017cnosci liniowej na poni\u017cszym wykrsie s\u0105 interpretowane jako efekt indukowany nieliniowo\u015bci\u0105:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot(E0,E, '.')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Wp\u0142yw nieliowo\u015bci na stany stacjonarne (wektory w\u0142asne hamiltonianu) okreslimy przy uzyciu _fidelity_ \n", "\n", "$F(\\rho,\\sigma)=\\mbox{Tr}[\\sqrt{\\sqrt{\\rho}\\sigma\\sqrt{\\rho}}]$\n", "\n", "policzonej dla stan\u00f3w w\u0142asnych $|\\psi_n\\rangle$ oraz $|\\psi_n^0\\rangle$.\n", "\n", "Oczywi\u015bcie w tym przypadku $F$ redukuje si\u0119 do iloczynu skalarnego \n", "\n", "$F=\\langle\\psi_n|\\psi_n^0\\rangle$, \n", "\n", "my jednak wykorzystamy w obliczeniach funkcj\u0119 fidelity():" ] }, { "cell_type": "code", "collapsed": false, "input": [ "nlist=linspace(0,N-1,N)\n", "fidlist=zeros(len(nlist))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "for i1 in xrange(len(nlist)):\n", " a=ket2dm(W[i1])\n", " b=ket2dm(W0[i1])\n", " fidlist[i1]=fidelity(a,b)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Uyskane wyniki nakre\u015blimy:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot(nlist,fidlist, '--', linewidth=7)\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Niezwykle ciekawym jest wp\u0142yw nieliowo\u015bci na nieklasyczne w\u0142asono\u015bci stan\u00f3w stacjonarnych. Wp\u0142yw ten prezentujemy za pomoc\u0105 funkcji Wignera. \n", "\n", "Funcja Wignera jest jedn\u0105 z najcz\u0119\u015bciej wykorzystywanych funkcji w optyce kwantowej. Tutaj zdefiniujemy j\u0105 jedynie dla stan\u00f3w czystych $|\\psi\\rangle$ poprzez jedn\u0105 z jej w\u0142asno\u015bci, kt\u00f3re mo\u017cna otrzyma\u0107 z og\u00f3lnej definicji:\n", "\n", "$ W(\\alpha)=\\frac{2}{\\pi}\\sum_{n=0}^\\infty \\langle \\psi|D(\\alpha)|n\\rangle\\langle n|D^\\dagger(\\alpha)|\\psi\\rangle $\n", "\n", "gdzie operator przesuni\u0119cia $ D $dany jest wzorem:\n", "\n", "$ D(\\alpha) = \\exp(\\alpha a^\\dagger -\\alpha^* a )$\n", "\n", "Podstawow\u0105 cech\u0105 funkcji Wignera, kt\u00f3r\u0105 wykorzystamy jest to, \u017ce przyjmuje ona warto\u015bci ujemne dla stan\u00f3w, kt\u00f3re nale\u017c\u0105 do grupy \"nieklasycznych\"\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "rho=ket2dm(W[1]) #stan, dla kt\u00f3rego funkcja Wignera zostanie nakre\u015blona\n", "xvec = linspace(-5,5,200)\n", "X, Y = meshgrid(xvec, xvec)\n", "W = wigner(rho, xvec, xvec)\n", "fig = figure()\n", "ax = Axes3D(fig, azim=-62, elev=25)\n", "ax.plot_surface(X, Y, W, rstride=2, cstride=2, cmap=cm.jet, lw=.1)\n", "ax.set_xlim3d(-6, 6)\n", "ax.set_ylim3d(-6, 6)\n", "ax.set_zlim3d(0, 0.4)\n", "title('Funkcja Wignera')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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lmdHRURKJRF/LnokJOpPJOGuL3RzXTLYG6yEms0gkQjQaJRaLkUgkSKVSpFIp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WRrKcKxJvk4JtzPsN4yj7kZkbzFpPRCwKgUkw4yio0Io2oRuWPiQUJ1scnBC5uUF+rEYYKMROzH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\ncccdd+D3+3nggQdYuHDhZJv1J4sQgpKSEs466yzOOuuTJAXHcejq6soL4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"text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "W nastepnym kroku naszych rozwa\u017ca\u0144 przejdziemy do badania zagadnienia niestacjonarnego. Zadamy pytanie o wp\u0142yw nieliniowosci na ewolucj\u0119 w czasie wybranych stan\u00f3w pocz\u0105tkowych:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "psi0=ket2dm(basis(N,0))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 13 }, { "cell_type": "code", "collapsed": false, "input": [ "tlist=linspace(0.0, 1.0, 5.0)\n", "qlist=zeros(len(tlist))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Bedziemy por\u00f3wnywac ewolucj\u0105 harmoniczn\u0105 (dla $H_0$) z ewolucj\u0105 generowana przez osrodek nieliniowy $H$: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "qq=mesolve(H, psi0, tlist, [], [])\n", "qq0=mesolve(H0, psi0, tlist, [], [])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Jako mier\u0119 wp\u0142ywu nieliowosci ponownie wykorzystamy fidelity:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "for i1 in xrange(len(tlist)):\n", " a=qq.states[i1]\n", " b=qq0.states[i1]\n", " qlist[i1]=fidelity(a,b)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Uzyskany wynik nakre\u015blimy:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot(tlist,qlist, '--', linewidth=7)\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Zadania\n", "------\n", "1. Zwizualiziwac wp\u0142yw nieliniowio\u015bci na odleg\u0142o\u015bc miedzy stanami stacjonarnymi osyclatora nieliniowego i oscylatora harmonicznego uzywaj\u0105c \"trace distance\"\n", "2. Wykre\u015blic fidelity w ewolucji czasowej innego warunku poczatkowego\n", "3. Powt\u00f3rzy\u0107 analiz\u0119 dla przypadku $H=a^\\dagger a+\\alpha\\cos(a+a^\\dagger))$" ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 17 } ], "metadata": {} } ] }