{ "cells": [ { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# Spin Squeezing in presence of local and collective noise\n", "\n", "Notebook author: Nathan Shammah (nathan.shammah at gmail.com)\n", "\n", "Here we study the effect of collective and local processes on a spin squeezing Hamiltonian. \n", "\n", "We consider a system of $N$ two-level systems (TLSs) with identical frequency $\\omega_{0}$, which can de-excite incoherently or collectively at the rates $\\gamma_\\text{E}$ and $\\gamma_\\text{CE}$,\n", "\n", "\\begin{eqnarray}\n", "\\dot{\\rho} &=&-i\\lbrack -i\\Lambda\\left(J_{+}^2-J_{-}^2\\right),\\rho \\rbrack\n", "+\\frac{\\gamma_\\text {CE}}{2}\\mathcal{L}_{J_{-}}[\\rho]\n", "+\\frac{\\gamma_\\text{E}}{2}\\sum_{n=1}^{N}\\mathcal{L}_{J_{-,n}}[\\rho]\n", "\\end{eqnarray}\n", "\n", "We study the time evolution of the spin squeezing parameter [1-4]\n", "\\begin{eqnarray}\n", "\\xi^2 &=& N\\langle\\Delta J_y^2\\rangle/\\left(\\langle J_z\\rangle^2+\\langle J_x\\rangle^2\\right)\n", "\\end{eqnarray}\n", "\n", "We assess how different dynamical conditions and initial states can be explored to optimize the spin squeezing of a given Dicke state [5-7]. This study can be generalized to other types of local and collective incoherent processes. A table grouping this processes is given below, \n", "\n", "\n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
 Keyword Rate $\\gamma_j$ Lindbladian $\\mathcal{L}[\\rho]$ $\\texttt{emission}$ $\\gamma_\\text{E}$ \\begin{eqnarray}\\mathcal{L}[\\rho]&=&\\sum_n^N \\left(J_{-,n}\\rho J_{+,n} - \\frac{1}{2}J_{+,n}J_{-,n}\\rho - \\frac{1}{2}\\rho J_{+,n}J_{-,n} \\right)\\end{eqnarray} $\\texttt{pumping}$ $\\gamma_\\text{P}$ \\begin{eqnarray}\\mathcal{L}[\\rho]&=&\\sum_n^N \\left(J_{+,n}\\rho J_{-,n} - \\frac{1}{2}J_{-,n}J_{+,n}\\rho - \\frac{1}{2}\\rho J_{-,n}J_{+,n} \\right)\\end{eqnarray} $\\texttt{dephasing}$ $\\gamma_\\text{D}$ \\begin{eqnarray}\\mathcal{L}[\\rho]&=&\\sum_n^N \\left(J_{z,n}\\rho J_{z,n} - \\frac{1}{2}J_{z,n}J_{z,n}\\rho - \\frac{1}{2}\\rho J_{z,n}J_{z,n} \\right)\\end{eqnarray} $\\texttt{collective}\\_\\texttt{emission}$ $\\gamma_\\text{CE}$ \\begin{eqnarray}\\mathcal{L}[\\rho]&=& J_{-}\\rho J_{+} - \\frac{1}{2}J_{+}J_{-}\\rho - \\frac{1}{2}\\rho J_{+}J_{-} \\end{eqnarray} $\\texttt{collective}\\_\\texttt{pumping}$ $\\gamma_\\text{CP}$ \\begin{eqnarray}\\mathcal{L}[\\rho]&=& J_{+}\\rho J_{-} - \\frac{1}{2}J_{-}J_{+}\\rho - \\frac{1}{2}\\rho J_{-}J_{+} \\end{eqnarray} $\\texttt{collective}\\_\\texttt{dephasing}$ $\\gamma_\\text{CD}$ \\begin{eqnarray}\\mathcal{L}[\\rho]&=& J_{z}\\rho J_{z} - \\frac{1}{2}J_{z}^2\\rho - \\frac{1}{2}\\rho J_{z}^2 \\end{eqnarray}
\n", "\n", "\n", "Note that in the table above and in $\\texttt{qutip.piqs}$ functions, the Lindbladian $\\mathcal{L}[\\rho]$ is written with a factor 1/2 with respect to $\\mathcal{L}_{A}[\\rho]$ reported in the LaTeX math equations, in order to have the Lindbladian and full Liouvillian matrix consistently defined by the rates $\\gamma_\\alpha$. \n", "\n", "Note also that the *local depolarizing channel* can be written in terms of this Lindbladians as\n", "\\begin{eqnarray}\n", "\\gamma_{Dep}\\sum_n^N\\left(\\mathcal{L}_{J_{x,n}}+\\mathcal{L}_{J_{y,n}}+\\mathcal{L}_{J_{z,n}}\\right)=\\gamma_{Dep}\\sum_n^N\\left(\\frac{1}{2}\\mathcal{L}_{J_{+,n}}+\\frac{1}{2}\\mathcal{L}_{J_{-,n}}+ \\mathcal{L}_{J_{z,n}}\\right).\n", "\\end{eqnarray}\n", "Similarly, the *collective depolarizing channel* reads\n", "\n", "\\begin{eqnarray}\n", "\\gamma_\\text{CDep}\\left(\\mathcal{L}_{J_{x}}+\\mathcal{L}_{J_{y}}+\\mathcal{L}_{J_{z}}\\right)=\\gamma_\\text{CDep}\\left(\n", "\\frac{1}{2}\\mathcal{L}_{J_{+}}+\\frac{1}{2}\\mathcal{L}_{J_{-}}+ \\mathcal{L}_{J_{z}}\\right).\n", "\\end{eqnarray}" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from time import clock\n", "from scipy.io import mmwrite\n", "import matplotlib.pyplot as plt\n", "from qutip import *\n", "from qutip.piqs import *\n", "from scipy.sparse import load_npz, save_npz" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def isdicke(N, j, m):\n", " \"\"\"\n", " Check if an element in a matrix is a valid element in the Dicke space.\n", " Dicke row: j value index. Dicke column: m value index. \n", " The function returns True if the element exists in the Dicke space and\n", " False otherwise.\n", "\n", " Parameters\n", " ----------\n", " N : int\n", " The number of two-level systems. \n", " j: float\n", " \"j\" index of the element in Dicke space which needs to be checked.\n", " m: float\n", " \"m\" index of the element in Dicke space which needs to be checked.\n", " \"\"\"\n", " dicke_row = j\n", " dicke_col = m\n", " \n", " rows = N + 1\n", " cols = 0\n", "\n", " if (N % 2) == 0:\n", " cols = int(N/2 + 1)\n", " else:\n", " cols = int(N/2 + 1/2)\n", "\n", " if (dicke_row > rows) or (dicke_row < 0):\n", " return (False)\n", "\n", " if (dicke_col > cols) or (dicke_col < 0):\n", " return (False)\n", "\n", " if (dicke_row < int(rows/2)) and (dicke_col > dicke_row):\n", " return False\n", "\n", " if (dicke_row >= int(rows/2)) and (rows - dicke_row <= dicke_col):\n", " return False\n", "\n", " else:\n", " return True\n", "\n", "def dicke_space(N):\n", " \"\"\"\n", " Generate a matrix to visualize the Dicke space.\n", " j is on the horizontal axis, increasing right to left.\n", " m is on the vertical axis, increasing bottom to top.\n", " It puts 1 in all allowed (j,m) values.\n", " It puts 0 in all not-allowed (j,m) values.\n", " Parameters\n", " ----------\n", " N : int\n", " The number of two-level systems.\n", " Returns\n", " ----------\n", " dicke_space : ndarray\n", " The matrix of all allowed (j,m) pairs.\n", "\n", " \"\"\" \n", " rows = N + 1\n", " cols = 0\n", "\n", " if (rows % 2) == 0:\n", " cols = int((rows/2))\n", "\n", " else:\n", " cols = int((rows + 1)/2)\n", "\n", " dicke_space = np.zeros((rows, cols), dtype = int)\n", "\n", " for (i, j) in np.ndindex(rows, cols):\n", " dicke_space[i, j] = isdicke(N, i, j)\n", "\n", " return (dicke_space)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "N = 20\n", "Hilbert space dim = (121, 121)\n", "Number of Dicke states = 121\n", "Liouvillian space dim = (14641, 14641)\n", "collective_emission = 0.2\n", "N = 20\n", "Hilbert space dim = (121, 121)\n", "Number of Dicke states = 121\n", "Liouvillian space dim = (14641, 14641)\n", "emission = 0.2\n" ] } ], "source": [ "## general parameters\n", "N = 20\n", "ntls = N\n", "nds = num_dicke_states(N)\n", "[jx, jy, jz] = jspin(N)\n", "jp = jspin(N, \"+\")\n", "jm = jspin(N, \"-\")\n", "jpjm = jp*jm\n", "\n", "Lambda = 1\n", "factor_l = 5\n", "\n", "#spin hamiltonian\n", "h = -1j*Lambda * (jp**2-jm**2)\n", "gCE = Lambda/factor_l\n", "gE = Lambda/factor_l\n", "\n", "# system with collective emission only\n", "system = Dicke(N=N)\n", "# system2 with local emission only\n", "system2 = Dicke(N=N)\n", "system.collective_emission = gCE\n", "system2.emission = gE\n", "system.hamiltonian = h\n", "system2.hamiltonian = h\n", "liouv = system.liouvillian() \n", "liouv2 = system2.liouvillian()\n", "\n", "print(system)\n", "print(system2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Time evolution of Spin Squuezing Parameter $\\xi^2= \\frac{N \\langle\\Delta J_y^2\\rangle}{\\langle J_z\\rangle^2}$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/nathanshammah/Downloads/Applications/lib/python3.6/site-packages/ipykernel_launcher.py:31: RuntimeWarning: invalid value encountered in true_divide\n", "/Users/nathanshammah/Downloads/Applications/lib/python3.6/site-packages/ipykernel_launcher.py:43: RuntimeWarning: invalid value encountered in true_divide\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "|j, m> = 0.0 0.0\n", "|j, m> = 1.0 1.0\n", "|j, m> = 2.0 2.0\n", "|j, m> = 3.0 3.0\n", "|j, m> = 4.0 4.0\n", "|j, m> = 5.0 5.0\n", "|j, m> = 6.0 6.0\n", "|j, m> = 7.0 7.0\n", "|j, m> = 8.0 8.0\n", "|j, m> = 9.0 9.0\n", "|j, m> = 10.0 10.0\n" ] } ], "source": [ "#set initial state for spins (Dicke basis)\n", "nt = 1001\n", "td0 = 1/(N*Lambda)\n", "tmax = 10 * td0\n", "t = np.linspace(0, tmax, nt)\n", "excited = dicke(N, N/2, N/2)\n", "load_file = False\n", "if load_file == False:\n", " # cycle over all states in Dicke space\n", " xi2_1_list = []\n", " xi2_2_list = []\n", " xi2_1_min_list = []\n", " xi2_2_min_list = []\n", "\n", " for j in j_vals(N):\n", " #for m in m_vals(j):\n", " m = j\n", " rho0 = dicke(N, j, m)\n", " #solve using qutip (Dicke basis)\n", " # Dissipative dynamics: Only collective emission \n", " result = mesolve(liouv, rho0, t, [], \n", " e_ops = [jz, jy, jy**2,jz**2, jx],\n", " options = Options(store_states=True))\n", " rhot = result.states\n", " jz_t = result.expect[0]\n", " jy_t = result.expect[1]\n", " jy2_t = result.expect[2]\n", " jz2_t = result.expect[3]\n", " jx_t = result.expect[4]\n", " Delta_jy = jy2_t - jy_t**2\n", " xi2_1 = N * Delta_jy / (jz_t**2+jx_t**2)\n", " # Dissipative dynamics: Only local emission \n", " result2 = mesolve(liouv2, rho0, t, [], \n", " e_ops = [jz, jy, jy**2,jz**2, jx],\n", " options = Options(store_states=True))\n", " rhot2 = result2.states\n", " jz_t2 = result2.expect[0]\n", " jy_t2 = result2.expect[1]\n", " jy2_t2 = result2.expect[2]\n", " jz2_t2 = result2.expect[3]\n", " jx_t2 = result2.expect[4]\n", " Delta_jy2 = jy2_t2 - jy_t2**2\n", " xi2_2 = N * Delta_jy2 / (jz_t2**2+jx_t2**2)\n", "\n", " xi2_1_min = np.min(xi2_1)\n", " xi2_2_min = np.min(xi2_2) \n", " xi2_1_list.append(xi2_1)\n", " xi2_2_list.append(xi2_2)\n", " xi2_1_min_list.append(xi2_1_min)\n", " xi2_2_min_list.append(xi2_2_min) \n", "\n", " print(\"|j, m> = \",j,m)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Visualization" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "label_size2 = 20\n", "lw = 3\n", "texplot = False\n", "# if texplot == True:\n", "# plt.rc('text', usetex = True)\n", "# plt.rc('xtick', labelsize=label_size) \n", "# plt.rc('ytick', labelsize=label_size)\n", "\n", "fig1 = plt.figure(figsize = (10,6))\n", "for xi2_1 in xi2_1_list:\n", " plt.plot(t*(N*Lambda), xi2_1, '-', label = r' $\\gamma_\\Downarrow=0.2$', linewidth = lw)\n", "for xi2_2 in xi2_2_list:\n", " plt.plot(t*(N*Lambda), xi2_2, '-.', label = r'$\\gamma_\\downarrow=0.2$')\n", "plt.plot(t*(N*Lambda), 1+0*t, '--k')\n", "plt.xlim([0,3])\n", "plt.ylim([0,8000.5])\n", "plt.ylim([0,2.5])\n", "plt.xlabel(r'$N \\Lambda t$', fontsize = label_size2)\n", "plt.ylabel(r'$\\xi^2$', fontsize = label_size2)\n", "#plt.legend(fontsize = label_size2*0.8)\n", "plt.title(r'Spin Squeezing Parameter, $N={}$'.format(N), fontsize = label_size2)\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/nathanshammah/Downloads/Applications/lib/python3.6/site-packages/ipykernel_launcher.py:15: RuntimeWarning: invalid value encountered in less\n", " from ipykernel import kernelapp as app\n", "/Users/nathanshammah/Downloads/Applications/lib/python3.6/site-packages/ipykernel_launcher.py:16: RuntimeWarning: invalid value encountered in less\n", " app.launch_new_instance()\n" ] } ], "source": [ "## Here we find for how long the spin-squeezing parameter, xi2, \n", "## is less than 1 (non-classical or \"quantum\" condition), in the two dynamics\n", "\n", "dt_quantum_xi1_list = []\n", "dt_quantum_xi2_list = []\n", "\n", "dt1_jm =[]\n", "dt2_jm =[]\n", "ds = dicke_space(N)\n", "i = 0\n", "for j in j_vals(N):\n", " #for m in m_vals(j):\n", " m = j\n", " rho0 = dicke(N, j, m)\n", " quantum_xi1 = xi2_1_list[i][xi2_1_list[i] < 1.0] \n", " quantum_xi2 = xi2_2_list[i][xi2_2_list[i] < 1.0]\n", "\n", " # first ensemble\n", " if len(quantum_xi1)>0:\n", " dt_quantum_xi1 = len(quantum_xi1)\n", " dt1_jm.append((dt_quantum_xi1, j, m))\n", "\n", " else:\n", " dt_quantum_xi1 = 0.0\n", "\n", " # second ensemble\n", " if len(quantum_xi2)>0:\n", " dt_quantum_xi2 = len(quantum_xi2)\n", " dt2_jm.append((dt_quantum_xi2, j, m))\n", " else:\n", " dt_quantum_xi2 = 0.0\n", "\n", " dt_quantum_xi1_list.append(dt_quantum_xi1)\n", " dt_quantum_xi2_list.append(dt_quantum_xi2)\n", "\n", " i = i+1" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "collective emission: (squeezing time, j, m)\n", "[(71, 5.0, 5.0), (92, 6.0, 6.0), (98, 7.0, 7.0), (100, 8.0, 8.0), (99, 9.0, 9.0), (96, 10.0, 10.0)]\n", "local emission: (squeezing time, j, m)\n", "[(25, 4.0, 4.0), (98, 5.0, 5.0), (112, 6.0, 6.0), (114, 7.0, 7.0), (113, 8.0, 8.0), (110, 9.0, 9.0), (106, 10.0, 10.0)]\n" ] } ], "source": [ "print(\"collective emission: (squeezing time, j, m)\")\n", "print(dt1_jm)\n", "print(\"local emission: (squeezing time, j, m)\")\n", "print(dt2_jm)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Visualization" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.rc('text', usetex = True)\n", "label_size = 20\n", "label_size2 = 20\n", "label_size3 = 20\n", "plt.rc('xtick', labelsize=label_size) \n", "plt.rc('ytick', labelsize=label_size)\n", "\n", "lw = 3\n", "i0 = -3\n", "i0s=2\n", "fig1 = plt.figure(figsize = (8,5))\n", "# excited state spin squeezing\n", "plt.plot(t*(N*Lambda), xi2_1_list[-1], 'k-', \n", " label = r'$|\\frac{N}{2},\\frac{N}{2}\\rangle$, $\\gamma_\\Downarrow=0.2\\Lambda$', \n", " linewidth = 0.8)\n", "plt.plot(t*(N*Lambda), xi2_2_list[-1], 'r--',\n", " label = r'$|\\frac{N}{2},\\frac{N}{2}\\rangle$, $\\gamma_\\downarrow=0.2\\Lambda$',\n", " linewidth = 0.8)\n", "# state with max time of spin squeezing\n", "\n", "plt.plot(t*(N*Lambda), xi2_1_list[i0], 'k-', \n", " label = r'$|j,j\\rangle$, $\\gamma_\\Downarrow=0.2\\Lambda$', \n", " linewidth = 0.8+0.4*i0s*lw)\n", "plt.plot(t*(N*Lambda), xi2_2_list[i0], 'r--',\n", " label = r'$|j,j\\rangle$, $\\gamma_\\downarrow=0.2\\Lambda$',\n", " linewidth = 0.8+0.4*i0s*lw)\n", "plt.plot(t*(N*Lambda), 1+0*t, '--k')\n", "\n", "plt.xlim([0,2.5])\n", "plt.yticks([0,1,2])\n", "plt.ylim([-1,2.])\n", "\n", "plt.xlabel(r'$N \\Lambda t$', fontsize = label_size3)\n", "plt.ylabel(r'$\\xi^2$', fontsize = label_size3)\n", "plt.legend(fontsize = label_size2*0.8, ncol=2)\n", "fname = 'figures/spin_squeezing_N_{}_states.pdf'.format(N)\n", "plt.title(r'Spin Squeezing Parameter, $N={}$'.format(N), fontsize = label_size2)\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plot shows the spin squeezing parameter for two different dynamics -- only collective de-excitation, black curves; only local de-excitation, red curves -- and for two different inital states, the maximally excited state (thin curves) and another Dicke state with longer squeezing time (thick curves). This study, performed in Refs. [5,6] for the maximally excited state has been extended to any Dicke state in Ref. [7]." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot the dt matrix in the Dicke space\n", "plt.rc('text', usetex = True)\n", "label_size = 20\n", "label_size2 = 20\n", "label_size3 = 20\n", "plt.rc('xtick', labelsize=label_size) \n", "plt.rc('ytick', labelsize=label_size)\n", "\n", "lw = 3\n", "i0 = 7\n", "i0s=2\n", "ratio_squeezing_local = 3\n", "fig1 = plt.figure(figsize = (6,8))\n", "ds = dicke_space(N)\n", "value_excited = 3\n", "ds[0,0]=value_excited\n", "ds[int(N/2-i0),int(N/2-i0)]=value_excited * ratio_squeezing_local\n", "plt.imshow(ds, cmap=\"inferno_r\")\n", "plt.xticks([])\n", "plt.yticks([])\n", "plt.xlabel(r\"$j$\", fontsize = label_size3)\n", "plt.ylabel(r\"$m$\", fontsize = label_size3)\n", "plt.title(r\"Dicke space $(j,m)$ for $N={}$\".format(N), fontsize = label_size3)\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Plot above shows the two initial states (darker dots) $|\\frac{N}{2},\\frac{N}{2}\\rangle$ (top edge of the Dicke triangle, red dot) and $|j,j\\rangle$, with $j=\\frac{N}{2}-3=7$ (black dot). A study of the Dicke triangle (dark yellow space) and state engineering is performed in Ref. [8] for different initial state. " ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "#### References\n", "\n", "[1] D. J. Wineland, J. J. Bollinger, W. M. Itano, F. L. Moore, and D. J. Heinzen, Spin squeezing and reduced quantum noise in spectroscopy, *Phys. Rev. A* **46**, R6797 (1992)\n", "\n", "[2] M. Kitagawa and M. Ueda, Squeezed spin states, *Phys. Rev. A* **47**, 5138 (1993)\n", "\n", "[3] J. Ma, X. Wang, C.-P. Sun, and F. Nori, Quantum spin squeezing, *Physics Reports* **509**, 89 (2011)\n", "\n", "[4] L. PezzeĚ€, A. Smerzi, M. K. Oberthaler, R. Schmied, and P. Treutlein, Quantum metrology with nonclassical states of atomic ensembles, *Reviews of Modern Physics*, in press (2018)\n", "\n", "[5] B. A. Chase and J. Geremia, Collective processes of an ensemble of spin-1 particles, *Phys. Rev. A* **78**,0521012 (2008)\n", "\n", "[6] B. Q. Baragiola, B. A. Chase, and J. Geremia, Collective uncertainty in partially polarized and partially deco- hered spin-1 systems, *Phys. Rev. A* **81**, 032104 (2010)\n", "\n", "[7] N. Shammah, S. Ahmed, N. Lambert, S. De Liberato, and F. Nori, \n", "Open quantum systems with local and collective incoherent processes: Efficient numerical simulation using permutational invariance https://arxiv.org/abs/1805.05129\n", "\n", "[8] N. Shammah, N. Lambert, F. Nori, and S. De Liberato, Superradiance with local phase-breaking effects, *Phys. Rev. A* **96**, 023863 (2017).\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "qutip.about()" ] } ], "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": "3.6.7" } }, "nbformat": 4, "nbformat_minor": 2 }