{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "from qutip import *\n", "from pylab import *\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Setup the Standard Problem" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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StIpdfF3YyTNPuClwHZAIfKOqG0Wkv6qOCWCM58iZM6eePHkyWMObDKZpUzh4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\n8cwjciIKCwujRcZDDz1Ebm5u9CJ1zz77LC1btmTt2rUAFYqRxo0bc+W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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define atomic states. Use ordering from paper\n", "ustate = basis(3, 0)\n", "excited = basis(3, 1)\n", "ground = basis(3, 2)\n", "\n", "# Set where to truncate Fock state for cavity\n", "N = 5\n", "\n", "# Create the atomic operators needed for the Hamiltonian\n", "sigma_ge = tensor(qeye(N), ground * excited.dag()) # |g>u, 4/9 e->g\n", "c_op_list.append(np.sqrt(5 * gamma / 9) * sigma_ue)\n", "c_op_list.append(np.sqrt(4 * gamma / 9) * sigma_ge)\n", "\n", "# Define time vector\n", "t = np.linspace(-15, 15, 100)\n", "# Define pump strength as a function of time\n", "wp = lambda t: 9 * exp(-(t / 5) ** 2)\n", "\n", "# Set up the time varying Hamiltonian\n", "g = 5\n", "H0 = -g * (sigma_ge.dag() * a + a.dag() * sigma_ge)\n", "H1 = (sigma_ue.dag() + sigma_ue)\n", "\n", "H = [H0,[-H1, '9*exp(-(t / 5)** 2)']]\n", "\n", "\n", "# Define initial state\n", "psi0 = tensor(basis(N, 0), ustate)\n", "\n", "# Define states onto which to project (same as in paper)\n", "state_GG = tensor(basis(N, 1), ground)\n", "sigma_GG = state_GG * state_GG.dag()\n", "state_UU = tensor(basis(N, 0), ustate)\n", "sigma_UU = state_UU * state_UU.dag()\n", "\n", "output = mesolve(H, psi0, t, c_op_list,\n", " [ada, sigma_UU, sigma_GG])\n", "\n", "exp_ada, exp_uu, exp_gg = (output.expect[0], output.expect[1],\n", " output.expect[2])\n", "\n", "# Plot the results\n", "figure(figsize=(8,8))\n", "subplot(211)\n", "plot(t, wp(t), 'k')\n", "ylabel('Control Field, $\\Omega_\\mathrm{p}$ [MHz]')\n", "ax = twinx()\n", "plot(t, kappa * exp_ada, 'b')\n", "ylabel('Cavity emission rate, $1/\\mu s$')\n", "for tl in ax.get_yticklabels():\n", " tl.set_color('b')\n", "\n", "subplot(212)\n", "plot(t, exp_uu, 'k-', label='$P{\\mathrm{uu}}$')\n", "plot(t, exp_gg, 'k:', label='$P{\\mathrm{gg}}$')\n", "ylabel('Population')\n", "xlabel('Time [$\\mu s$]')\n", "legend()\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Generate Some Random Noise for Gaussian" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "func = lambda t: 9*exp(-(t / 5)** 2)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "rnd_func = lambda t: func(t)+(0.05*func(t))*np.random.randn(t.shape[0])" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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bMx8H8u0CXTkSNUoTrn5w+thPJooDYY90hRBGIcQ7QogXohkQ0XgFa+VncQnc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\nXSIiohhh0iUiIoqR/w/SR4I610AJcgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure(figsize=(8,6))\n", "plot(t,func(t),lw=4)\n", "plot(t, rnd_func(t),'mo')\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Use QuTiP's Cubic_Spline to Interpolate" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "S = Cubic_Spline(t[0], t[-1], rnd_func(np.linspace(t[0],t[-1],1000)))" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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sBXD3LpxzbzUyLFnhamHy4P3a9xEI6ie5mGh0Y9IlArB+7yGYM/YodexaHllm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\nJF09vi/O1FS/gKw5RnfobExuAFOSJiU9RXewbr4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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure(figsize=(8,6))\n", "plot(t,func(t),lw=4)\n", "plot(t, rnd_func(t),'o')\n", "plot(t, S(t),'-',lw=4)\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Solve for Evolution with Noisy Gaussian via Interpolation" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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4MRw/Dhs3uhRYMXHDDTewcuVKqlSpQteuXXn55ZfJzs52OyxjvBGRs4ea58hX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\nbt26MXXqVN544w1effVV+6F8GuXLwz/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H2+NQ2h4HaVscStvjUNoeB2lbRC/uqioRERGp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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define atomic states. Use ordering from paper\n", "ustate = basis(3, 0)\n", "excited = basis(3, 1)\n", "ground = basis(3, 2)\n", "\n", "# Set where to truncate Fock state for cavity\n", "N = 2\n", "\n", "# Create the atomic operators needed for the Hamiltonian\n", "sigma_ge = tensor(qeye(N), ground * excited.dag()) # |g>u, 4/9 e->g\n", "c_op_list.append(np.sqrt(5 * gamma / 9) * sigma_ue)\n", "c_op_list.append(np.sqrt(4 * gamma / 9) * sigma_ge)\n", "\n", "# Define time vector\n", "t = np.linspace(-15, 15, 100)\n", "# Define pump strength as a function of time\n", "wp = lambda t: 9 * exp(-(t / 5) ** 2)\n", "\n", "# Set up the time varying Hamiltonian\n", "g = 5\n", "H0 = -g * (sigma_ge.dag() * a + a.dag() * sigma_ge)\n", "H1 = (sigma_ue.dag() + sigma_ue)\n", "\n", "# Hamiltonian with interpolation 'S' as time-dependence\n", "H = [H0,[-H1, S]]\n", "\n", "# Define initial state\n", "psi0 = tensor(basis(N, 0), ustate)\n", "\n", "# Define states onto which to project (same as in paper)\n", "state_GG = tensor(basis(N, 1), ground)\n", "sigma_GG = state_GG * state_GG.dag()\n", "state_UU = tensor(basis(N, 0), ustate)\n", "sigma_UU = state_UU * state_UU.dag()\n", "\n", "output = mesolve(H, psi0, t, c_op_list,\n", " [ada, sigma_UU, sigma_GG])\n", "\n", "exp_ada, exp_uu, exp_gg = (output.expect[0], output.expect[1],\n", " output.expect[2])\n", "\n", "# Plot the results\n", "figure(figsize=(8,8))\n", "subplot(211)\n", "plot(t, S(t), 'k')\n", "ylabel('Control Field, $\\Omega_\\mathrm{p}$ [MHz]')\n", "ax = twinx()\n", "plot(t, kappa * exp_ada, 'b')\n", "ylabel('Cavity emission rate, $1/\\mu s$')\n", "for tl in ax.get_yticklabels():\n", " tl.set_color('b')\n", "\n", "subplot(212)\n", "plot(t, exp_uu, 'k-', label='$P{\\mathrm{uu}}$')\n", "plot(t, exp_gg, 'k:', label='$P{\\mathrm{gg}}$')\n", "ylabel('Population')\n", "xlabel('Time [$\\mu s$]')\n", "legend()\n", "show()" ] }, { "cell_type": "code", "execution_count": 9, "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 23:01:13 2017 MDT
" ], "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from qutip.ipynbtools import version_table\n", "version_table()" ] } ], "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": 2 }