{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QuTiP example: Vacuum Rabi oscillations in the Jaynes-Cummings model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "J.R. Johansson and P.D. Nation\n", "\n", "This ipython notebook demonstrates how to simulate the quantum vacuum rabi oscillations in the Jaynes-Cumming model, using QuTiP: The Quantum Toolbox in Python.\n", "\n", "For more information about QuTiP see project web page: http://code.google.com/p/qutip/" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "from qutip import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction\n", "\n", "The Jaynes-Cumming model is the simplest possible model of quantum mechanical light-matter interaction, describing a single two-level atom interacting with a single electromagnetic cavity mode. The Hamiltonian for this system is (in dipole interaction form)\n", "\n", "$H = \\hbar \\omega_c a^\\dagger a + \\frac{1}{2}\\hbar\\omega_a\\sigma_z + \\hbar g(a^\\dagger + a)(\\sigma_- + \\sigma_+)$\n", "\n", "or with the rotating-wave approximation\n", "\n", "$H_{\\rm RWA} = \\hbar \\omega_c a^\\dagger a + \\frac{1}{2}\\hbar\\omega_a\\sigma_z + \\hbar g(a^\\dagger\\sigma_- + a\\sigma_+)$\n", "\n", "where $\\omega_c$ and $\\omega_a$ are the frequencies of the cavity and atom, respectively, and $g$ is the interaction strength." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem parameters\n", "\n", "\n", "Here we use units where $\\hbar = 1$: " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "wc = 1.0 * 2 * np.pi # cavity frequency\n", "wa = 1.0 * 2 * np.pi # atom frequency\n", "g = 0.05 * 2 * np.pi # coupling strength\n", "kappa = 0.005 # cavity dissipation rate\n", "gamma = 0.05 # atom dissipation rate\n", "N = 15 # number of cavity fock states\n", "n_th_a = 0.0 # temperature in frequency units\n", "use_rwa = True\n", "\n", "tlist = np.linspace(0,25,100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setup the operators, the Hamiltonian and initial state" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# intial state\n", "psi0 = tensor(basis(N,0), basis(2,1)) # start with an excited atom\n", "\n", "# operators\n", "a = tensor(destroy(N), qeye(2))\n", "sm = tensor(qeye(N), destroy(2))\n", "\n", "# Hamiltonian\n", "if use_rwa:\n", " H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() * sm + a * sm.dag())\n", "else:\n", " H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() + a) * (sm + sm.dag())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Create a list of collapse operators that describe the dissipation" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "c_op_list = []\n", "\n", "rate = kappa * (1 + n_th_a)\n", "if rate > 0.0:\n", " c_op_list.append(np.sqrt(rate) * a)\n", "\n", "rate = kappa * n_th_a\n", "if rate > 0.0:\n", " c_op_list.append(np.sqrt(rate) * a.dag())\n", "\n", "rate = gamma\n", "if rate > 0.0:\n", " c_op_list.append(np.sqrt(rate) * sm)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Evolve the system\n", "\n", "Here we evolve the system with the Lindblad master equation solver, and we request that the expectation values of the operators $a^\\dagger a$ and $\\sigma_+\\sigma_-$ are returned by the solver by passing the list [a.dag()*a, sm.dag()*sm] as the fifth argument to the solver." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "output = mesolve(H, psi0, tlist, c_op_list, [a.dag() * a, sm.dag() * sm])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualize the results\n", "\n", "Here we plot the excitation probabilities of the cavity and the atom (these expectation values were calculated by the mesolve above). We can clearly see how energy is being coherently transferred back and forth between the cavity and the atom." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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29LDBLP6o8XDO3bB1MRw093dI0zTXoJO6vfU/B3LSjDFSE1TX1vFdej5T40Lx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\noaWTojlcVEdTu+dV+jpSVEdtcwfXTxtG8pEQ6m698BPP+DB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KgK8Xzz6cSZCf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\nNDehB3VN0zRNcxN6UNc0TdM0N/H/AQyA46AXczBYAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8,5))\n", "ax.plot(tlist, output.expect[0], label=\"Cavity\")\n", "ax.plot(tlist, output.expect[1], label=\"Atom excited state\")\n", "ax.legend()\n", "ax.set_xlabel('Time')\n", "ax.set_ylabel('Occupation probability')\n", "ax.set_title('Vacuum Rabi oscillations');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Software version:" ] }, { "cell_type": "code", "execution_count": 10, "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 22:29:51 2017 MDT
" ], "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from qutip.ipynbtools import version_table\n", "\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": 1 }