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{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"from scipy.special import erf\n",
"import qutip"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"b = [qutip.basis(2,m) for m in range(2)] #Define basis\n",
"tx = b[0]*b[1].dag()+b[1]*b[0].dag()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def f(t,args):\n",
" a = args['a']\n",
" b = args['b']\n",
" c = args['c']\n",
" return (erf((t-c+a/2)/b)-erf((t-c-a/2)/b))/2"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def solve_and_plot(t0):\n",
" t = np.linspace(0,14,200)+t0\n",
" args = {'a':5,'b':0.2,'c':5+t0}\n",
"\n",
" H = [[np.sqrt(5)*tx,f(t,args)]]\n",
" rho0 = b[0]*b[0].dag()\n",
" c_ops = []\n",
" obs_ops = [b[0]*b[0].dag(), b[1]*b[1].dag()]\n",
" output = qutip.mesolve(H, rho0, t, c_ops, obs_ops)\n",
"\n",
" plt.plot(t,f(t,args))\n",
" plt.plot(t,output.expect[1])\n",
" plt.ylim(0,1.2)\n",
" plt.xlim(t[0],t[-1])"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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ZYlH7N4g0ljDdDV4MsNZirTmcEPHTtarDI8aYPcD7gN9b76KHDx+mt3f5L71D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\nJ4UEERER8fS/AYNilxKFmjr9AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f045c441790>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"solve_and_plot(0)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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Y4Qbi3bkwzLFXQ7uhqQlSKVUSRKpJUe2GharALuDr/mPWWotXKbghx7f9JPAd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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f045c1febd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"solve_and_plot(2)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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NoE6CnEshQSQ54hESqtRJgOpu8hT2HSBBIUHOpZAgkhzRDwlVHG6A6m4X7XcS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\nl0KCiIiI5KWQICIiInkpJIiIiEhe/xcvcVZVm2+BUQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f045c5f5790>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"solve_and_plot(10)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python2",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.12"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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