{ "metadata": { "name": "", "signature": "sha256:59ccc374555ac85bca77e028ec2093a5f59e12103bb8e976e55ff78fb6db9d41" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lecture 10: Cavity-QED in the dispersive regime\n", "\n", "Author: J. R. Johansson (robert@riken.jp), http://dml.riken.jp/~rob/\n", "\n", "The latest version of this [IPython notebook](http://ipython.org/ipython-doc/dev/interactive/htmlnotebook.html) lecture is available at [http://github.com/jrjohansson/qutip-lectures](http://github.com/jrjohansson/qutip-lectures).\n", "\n", "The other notebooks in this lecture series are indexed at [http://jrjohansson.github.com](http://jrjohansson.github.com)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "from qutip import *" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction\n", "\n", "A qubit-resonator system can described by the Hamiltonian\n", "\n", "$\\displaystyle H = \\omega_r a^\\dagger a - \\frac{1}{2} \\omega_q \\sigma_z + g (a^\\dagger + a) \\sigma_x$\n", "\n", "where $\\omega_r$ and $\\omega_q$ are the the bare frequencies of the resonator and qubit, respectively, and where $g$ is the dipole interaction strength. \n", "\n", "The dispersive regime occurs when the resonator and qubit is far off resonance, $\\Delta \\gg g$, where $\\Delta = \\omega_r-\\omega_q$ is the detuning between the resonator and the qubit (for example $\\omega_r \\gg \\omega_q$).\n", "\n", "In the dispersive regime the system can be described by an effective Hamiltonian on the form\n", "\n", "$\\displaystyle H = \\omega_r a^\\dagger a - \\frac{1}{2}\\omega_q \\sigma_z + \\chi (a^\\dagger a + 1/2) \\sigma_z$\n", "\n", "where $\\chi = g^2/\\Delta$ . We can view the last term as a correction of the resonator frequency that depends on the qubit state, or a correction to the qubit frequency that depends on the resonator state.\n", "\n", "In a beautiful experiment by D. I. Schuster et al., the dispersive regime was used to resolving the photon number states of a microwave resonator by monitoring a qubit that was coupled to the resonator. This notebook shows how to simulate this kind of system numerically in QuTiP.\n", "\n", "### References\n", "\n", " * [D. I. Schuster et al., Resolving photon number states in a superconducting circuit, Nature 445, 515 (2007)](http://dx.doi.org/10.1038/nature05461)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Parameters" ] }, { "cell_type": "code", "collapsed": false, "input": [ "N = 20\n", "\n", "wr = 2.0 * 2 * pi # resonator frequency\n", "wq = 3.0 * 2 * pi # qubit frequency\n", "chi = 0.025 * 2 * pi # parameter in the dispersive hamiltonian\n", "\n", "delta = abs(wr - wq) # detuning\n", "g = sqrt(delta * chi) # coupling strength that is consistent with chi" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "# compare detuning and g, the first should be much larger than the second\n", "delta/(2*pi), g/(2*pi)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 4, "text": [ "(1.0, 0.15811388300841897)" ] } ], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "# cavity operators\n", "a = tensor(destroy(N), qeye(2))\n", "nc = a.dag() * a\n", "xc = a + a.dag()\n", "\n", "# atomic operators\n", "sm = tensor(qeye(N), destroy(2))\n", "sz = tensor(qeye(N), sigmaz())\n", "sx = tensor(qeye(N), sigmax())\n", "nq = sm.dag() * sm\n", "xq = sm + sm.dag()\n", "\n", "I = tensor(qeye(N), qeye(2))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "# dispersive hamiltonian\n", "H = wr * (a.dag() * a + I/2.0) + (wq / 2.0) * sz + chi * (a.dag() * a + I/2) * sz" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Try different initial state of the resonator, and see how the spectrum further down in the notebook reflects the photon distribution chosen here." ] }, { "cell_type": "code", "collapsed": false, "input": [ "#psi0 = tensor(coherent(N, sqrt(6)), (basis(2,0)+basis(2,1)).unit())" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "#psi0 = tensor(thermal_dm(N, 3), ket2dm(basis(2,0)+basis(2,1))).unit()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "psi0 = tensor(coherent(N, sqrt(4)), (basis(2,0)+basis(2,1)).unit())" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Time evolution" ] }, { "cell_type": "code", "collapsed": false, "input": [ "tlist = np.linspace(0, 250, 1000)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "res = mesolve(H, psi0, tlist, [], [], options=Odeoptions(nsteps=5000))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Excitation numbers\n", "\n", "We can see that the systems do not exchange any energy, because of they are off resonance with each other." ] }, { "cell_type": "code", "collapsed": false, "input": [ "nc_list = expect(nc, res.states)\n", "nq_list = expect(nq, res.states)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(1, 1, sharex=True, figsize=(12,4))\n", "\n", "ax.plot(tlist, nc_list, 'r', linewidth=2, label=\"cavity\")\n", "ax.plot(tlist, nq_list, 'b--', linewidth=2, label=\"qubit\")\n", "ax.set_ylim(0, 7)\n", "ax.set_ylabel(\"n\", fontsize=16)\n", "ax.set_xlabel(\"Time (ns)\", fontsize=16)\n", "ax.legend()\n", "\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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JAAAAhavKUuwbNmzIfvvtl+bm5px88sn5xje+kZNPPvn9gizFDgAAVEmHW4p9v/32S5I0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\nAOEKAACgAMIVAABAAYQrAACAAvwv2rD9/B2J1EoAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Resonator quadrature" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, the quadratures of the resonator are oscillating rapidly." ] }, { "cell_type": "code", "collapsed": false, "input": [ "xc_list = expect(xc, res.states)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(1, 1, sharex=True, figsize=(12,4))\n", "\n", "ax.plot(tlist, xc_list, 'r', linewidth=2, label=\"cavity\")\n", "ax.set_ylabel(\"x\", fontsize=16)\n", "ax.set_xlabel(\"Time (ns)\", fontsize=16)\n", "ax.legend()\n", "\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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7BYB580RZTjO5fFlMCZTp7Fnghx/ktklERMa7cAHYsAFo2BCoUgWoVg3o0wfYvVt3ZObX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\njb5n1tg3ZpKrpKQkNTU1qaWlRW63W2fPnlVaWtpIh4W/1Of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"text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Correlation function for the resonator" ] }, { "cell_type": "code", "collapsed": false, "input": [ "tlist = np.linspace(0, 1000, 10000)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "code", "collapsed": false, "input": [ "corr_vec = correlation(H, psi0, None, tlist, [], a.dag(), a)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 17 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(1, 1, sharex=True, figsize=(12,4))\n", "\n", "ax.plot(tlist, real(corr_vec), 'r', linewidth=2, label=\"resonator\")\n", "ax.set_ylabel(\"correlation\", fontsize=16)\n", "ax.set_xlabel(\"Time (ns)\", fontsize=16)\n", "ax.legend()\n", "ax.set_xlim(0,50)\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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obn6ur6l6dJXvIyo3KrsvuQlFjnztDQ3pdp5WKJ/b9vbS+TOLmqqss5Yo5aqp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HZcN8F8pPybDu5tJo5dSiZU4i7JkgvXOP/84n3i6/MtOXH5fEw/f5uJc9nxqTq2dWKKX7cQAE4/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\n7a9QaYEEQYRhxozoR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"text": [ "" ] } ], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Spectrum of the resonator" ] }, { "cell_type": "code", "collapsed": false, "input": [ "w, S = spectrum_correlation_fft(tlist, corr_vec)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 19 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(figsize=(9,3))\n", "ax.plot(w / (2 * pi), abs(S))\n", "ax.set_xlabel(r'$\\omega$', fontsize=18)\n", "ax.set_xlim(wr/(2*pi)-.5, wr/(2*pi)+.5);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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K8jUgGzduJDMzk5UrV9Ld3Q1Ae3s7LpcrVMflchEIBC4qdzqdBAKBy+i2iIwFCiAiYlWc\nlZ1KS0t5+umnAXjqqad47LHHqKqqCkuHysrKQs9zcnLIyckJy/uKSPjZEQ7OXV+ii1BFxj6v14vX\n6x1VXUsBJDExMfT84Ycf5p577gGCIxttbW2hbX6/H5fLhdPpxO/3Dyp3Op1Dvvf5AURExjaNgIjI\n+S4cOCgvL79kXUtTMB0dHaHnr7zySugOmYKCArZs2UJfXx+tra34fD48Hg9JSUkkJCTQ0NCAaZps\n2rSJwsJCK02LyBiiACIiVo04AlJcXMzu3bvp6upi+vTplJeX4/V6aW5uxjAMZsyYwUsvvQSA2+2m\nqKgIt9tNXFwclZWVGJ98h3ZlZSUrVqygt7eX/Px88vLyIntkIhJxug1XRKwyzKFuZ4kSwzCGvLtG\nRMamAwcgPR2eeAK+973ItHHyJEydCiUl8KtfRaYNEYmM4T7XtRKqiFimlVBFxCoFEBGxTNeAiIhV\nCiAiYpkCiIhYpQAiIpYpgIiIVQogImKZ7oIREasUQETEMl2EKiJWKYCIiGXnQoGmYETks1IAERHL\ndA2IiFilACIiltn5ZXQKICKxRQFERCzTCIiIWKUAIiKW2XkXjC5CFYktCiAiYplGQETEKgUQEbFM\nAURErFIAERHLFEBExCoFEBGxTAuRiYhVIwaQhx56CIfDQUZGRqjs+PHj5ObmMnPmTBYuXEh3d3do\n2/r160lNTSUtLY36+vpQeWNjIxkZGaSmprJ69eowH4aIRINGQETEqhEDyIMPPkhdXd2gsoqKCnJz\nczl8+DALFiygoqICgJaWFrZu3UpLSwt1dXWsWrUK85O/GqWlpVRVVeHz+fD5fBe9p4iMP/ouGBGx\nasQAcscddzBt2rRBZdu3b6ekpASAkpISampqAKitraW4uJj4+HiSk5NJSUmhoaGBjo4Oenp68Hg8\nACxfvjy0j4iMXxoBERGrLF0D0tnZicPhAMDhcNDZ2QlAe3s7LpcrVM/lchEIBC4qdzqdBAKBy+m3\niIwBCiAiYlXc5b6BYRgYhhGOvgBQVlYWep6Tk0NOTk7Y3ltEwksXoYrI+bxeL16vd1R1LQUQh8PB\n0aNHSUpKoqOjg8TERCA4stHW1haq5/f7cblcOJ1O/H7/oHKn0znke58fQERkbNN3wYjI+S4cOCgv\nL79kXUtTMAUFBVRXVwNQXV1NYWFhqHzLli309fXR2tqKz+fD4/GQlJREQkICDQ0NmKbJpk2bQvuI\nyPilKRgRsWrEEZDi4mJ2795NV1cX06dP59lnn2XdunUUFRVRVVVFcnIy27ZtA8DtdlNUVITb7SYu\nLo7KysrQ9ExlZSUrVqygt7eX/Px88vLyIntkIhJxCiAiYpVhmmPn19owDMZQd0RkBK+/Drm5sHw5\nfDIoGnZ//SvMmgVf/zrs3BmZNkQkMob7XNdKqCJimS5CFRGrFEBExDJNwYiIVQogImKZHXeoKICI\nxCYFEBGxTCMgImKVAoiIWKYAIiJWKYCIiGV2fhmdLkIViS0KICJimZ0jIGfORK4NEbGfAoiIWGbn\nCMjHH0euDRGxnwKIiFh2Lhz090e2jSuvhL6+yLUhIvZTABERy0wT4uIiOzoxMACf+5xGQERijQKI\niFhmmsFwEMnRCdOEq67SCIhIrFEAERHL7AgHdoQcEbGfAoiIWHYuHERyesSONkTEfgogImKZpmBE\nxCoFEBGx7Fw4sGMERAFEJLZcVgBJTk5mzpw5ZGdn4/F4ADh+/Di5ubnMnDmThQsX0t3dHaq/fv16\nUlNTSUtLo76+/vJ6LiJRZ9cISHx88G6Ys2cj146I2OuyAohhGHi9Xpqamti7dy8AFRUV5Obmcvjw\nYRYsWEBFRQUALS0tbN26lZaWFurq6li1ahUDWltZZFyzawTEMLQWiEisuewpGPOCNZi3b99OSUkJ\nACUlJdTU1ABQW1tLcXEx8fHxJCcnk5KSEgotIjI+2TUCYhiahhGJNZc9AnLnnXcyd+5cfv7znwPQ\n2dmJw+EAwOFw0NnZCUB7ezsulyu0r8vlIhAIXE7zIhJl/f1wzTX2BJArr9SdMCKxJO5ydt6zZw83\n3XQTx44dIzc3l7S0tEHbDcPAMIxL7j/UtrKystDznJwccnJyLqeLIhJBH34I118f2WDQ3x+8BkQj\nICJjn9frxev1jqruZQWQm266CYAbb7yRe++9l7179+JwODh69ChJSUl0dHSQmJgIgNPppK2tLbSv\n3+/H6XRe9J7nBxARGdtOnYLrrotsMPjwQ5gyRdeAiIwHFw4clJeXX7Ku5SmY06dP09PTA8CHH35I\nfX09GRkZFBQUUF1dDUB1dTWFhYUAFBQUsGXLFvr6+mhtbcXn84XunBGR8enUKUhICE6RnDkTuTau\nuUZTMCKxxvIISGdnJ/feey8AZ86c4f7772fhwoXMnTuXoqIiqqqqSE5OZtu2bQC43W6Kiopwu93E\nxcVRWVk57PSMiIx9p07BjTd+OjoRd1ljqpduY8oUTcGIxBrDvPA2ligyDOOiu2pEZOxatQrS0+HJ\nJ+G992DatPC3sWFD8L3ffBN+8hPQwKnI+DHc57pWQhURy86NTkTy+gw72hAR+ymAiIhl567PiOT0\niB1tiIj9FEBExLLz71CJ1AWi59q49lo4cSIybYiI/RRARMSyc9MjkyfD6dORbSMxEY4di0wbImI/\nBRARsexcOLjxRujqilwb11wTDCD/93+RaUNE7KcAIiKWdXUFFyJLTIRPvnUh7M5NwSiAiMQWBRAR\nseTjj4MB5OabIxtA/v734O29CiAisSUCywaJyETQ1hYMH1dcAQ5H5MLB//4vfOEL0NsbuZAjIvZT\nABERS44cCQYDCI5OvPVW+Nv46CP44AO46SY4exYOHQp/GyISHZqCERFLWlpg5szg83/4B2htDX8b\nbW3gdMKkSTB9enAURHfCiMQGBRARsWTPHvjKV4LPMzNh3z4I9zcpHDoEKSnB54YRbOedd8LbhohE\nhwKIiHxm/f2waxd89avB10lJEB8fHLEIpz174LbbPn29aBH84Q/hbUNEokMBREQ+s9ra4PTLjBmf\nln3ta1BfH952du6EO+749PU//zNs2xZcG0RExjcFEBH5THp64PHH4YknBpcvXQqbNoWvnQMHgiMq\nX/vap2UpKcFRkH/7t/C1IyLRoQAiIqPW3g533hkMAfn5g7cVFoLfHxwduVwDA/Av/wJr1kDcBffq\nvfgivP46PP108M4YERmfbA0gdXV1pKWlkZqayg9+8AM7m7aV1+uNdhfkAjon1p09C42N8J3vwJw5\ncM89sHHjxfXi42HzZnjkEdi7d/j3HO58nDkDjz4a/G6Z73zn4u1Tp8Jf/hK8PiQzE376Uy1QFg76\nHRlbJsL5sC2AnD17lm9/+9vU1dXR0tLCyy+/zMGDB+1q3lYT4R/OeKNzcmmmCSdPwnvvBYPDq6/C\nCy8EQ8CiRXDDDXD//cHl0N95B7773eAdKUO57Tb4z/+Ef/qnYHgIBIauN9T5OHMmOHpy663g88Er\nrwS/ZXcoSUnBUZAf/SgYRlJS4EtfCvazrAx+/Wv4n/+Bv/41uFqrRkpGpt+RsWUinA/bFiLbu3cv\nKSkpJCcnA3DfffdRW1vLrFmz7OqCTADn3wZ6/vOBgeAHnGkGnw/1c7htVupezvudORN89Pd/+vyz\nvu7vD66bcfr0pR8ffgjHj8PnPhcMGuceX/xi8EN94ULweIILjY1WQQE0N8Nzz0F6OrjdwemaW2+F\nf/xHSEgI1uvvD17n8c47wRDxxz8G21y3DhYvDq79MRzDCAakRYuCAePAAXj3Xfjb3+BPfwquoHrs\nWDCAnDgBn/98sO1rrhn6cdVVwVGcK6/89Of5zy/8GRcX7OMVV1z8c6iy0dY1jOg8ROxmWwAJBAJM\nnz499NrlctHQ0HBRvdmzgz8v9UFy4ToD4awXrvc+eTL4v8Bo9uFy6o2nPgzn/D+qpgnf+96nf+Av\n/DlUmZU64aobHx/8gIuLG/x8NK+vvnrw8wsfkycPfn3ddcEP33C6+Wb48Y/hBz8I3q772mvwzDPB\nYOJyBS9k/Y//CK6kOnducOTk3/89uKCZFVdcEZwemjNn6O1nzgSDVk9PMHQN9fj4Y+jrCwajvr7g\n4/TpwWXnbzt7NvgYGBj8c6iyS/0cquxcILXrcb5nn7UeXC4MMZfaFs59YrnNri7YutX6/peqP9pt\n4Sofjm0BxBhF7zIzM9m3LzaieE9PebS7MOFd+Md1YKCcgYHo9EU+9ely6uUcPAgHD4b37hmxzjTL\nw76YnFj397+P/8+RzMzMS26zLYA4nU7azlulqK2tDZfLNahOc3OzXd0RERGRKLLtItS5c+fi8/k4\ncuQIfX19bN26lYKCAruaFxERkTHEthGQuLg4XnzxRRYtWsTZs2dZuXKlLkAVERGZoAzT1IyfiIiI\n2EsroVr00EMP4XA4yMjIuGQdr9dLdnY26enp5OTk2Ne5CWqkc9LV1UVeXh5ZWVmkp6fzq1/9yt4O\nTjBtbW3Mnz+f2bNnk56ezgsvvDBkvUcffZTU1FQyMzNpamqyuZcTy2jOyW9+8xsyMzOZM2cOX/nK\nV9i/f38UejoxjPZ3BODtt98mLi6O3//+9zb2MMJMseQvf/mL+e6775rp6elDbv/ggw9Mt9tttrW1\nmaZpmseOHbOzexPSSOfkmWeeMdetW2eaZvB8XHfddWZ/f7+dXZxQOjo6zKamJtM0TbOnp8ecOXOm\n2dLSMqjOH/7wB/Ouu+4yTdM033rrLXPevHm293MiGc05efPNN83u7m7TNE1zx44dOicRNJrzYZqm\neebMGXP+/Pnm3Xffbf7ud7+zu5sRoxEQi+644w6mTZt2ye2//e1vWbJkSehOnxtuuMGurk1YI52T\nm266iZMnTwJw8uRJrr/+euIu/KIRCZukpCSysrIAmDJlCrNmzaK9vX1Qne3bt1NSUgLAvHnz6O7u\nprOz0/a+ThSjOSe33XYbU6dOBYLnxO/3297PiWI05wNg48aNLF26lBtvvNHuLkaUAkiE+Hw+jh8/\nzvz585k7dy6btNBB1D3yyCMcOHCAm2++mczMTDZs2BDtLk0YR44coampiXnz5g0qH2qBQn3g2eNS\n5+R8VVVV5F/4rYMSEcP9jtTW1lJaWgqMbk2t8UL//YuQ/v5+3n33XXbu3Mnp06e57bbbuPXWW0lN\nTY121yas73//+2RlZeH1evnb3/5Gbm4u+/bt49prr41212LaqVOnWLp0KRs2bGDKlCkXbTcvuA4+\nlv7AjlUjnROAXbt28Ytf/II9e/bY3LuJZ7jzsWbNGioqKjAMA9M0L/p9Gc8UQCJk+vTp3HDDDUye\nPJnJkyfz1a9+lX379imARNGbb77Jk08+CcAtt9zCjBkzOHToEHPnzo1yz2JXf38/S5YsYdmyZRQW\nFl60/cIFCv1+P06n084uTjgjnROA/fv388gjj1BXVzfstKZcvpHOR2NjI/fddx8QvJB+x44dxMfH\nx8Q6WpqCiZBvfOMbvPHGG5w9e5bTp0/T0NCA2+2OdrcmtLS0NF5//XUAOjs7OXToEF/84hej3KvY\nZZomK1euxO12s2bNmiHrFBQU8Otf/xqAt956i89//vM4HA47uzmhjOacvP/++yxevJjNmzeTkpJi\ncw8nltGcj/fee4/W1lZaW1tZunQpP/3pT2MifIBGQCwrLi5m9+7ddHV1MX36dMrLy+nv7wfgW9/6\nFmlpaeTl5TFnzhwmTZrEI488ogASYSOdkyeeeIIHH3yQzMxMBgYGeO6557juuuui3OvYtWfPHjZv\n3sycOXPIzs4GgtNg77//PhA8J/n5+fzxj38kJSWFa665hl/+8pfR7HLMG805efbZZ/nggw9C1xzE\nx8ezd+/eqPU5lo3mfMQyLUQmIiIittMUjIiIiNhOAURERERspwAiIiIitlMAEREREdspgIiIiIjt\nFEBERETEdgogIiIiYjsFEBEREbGdAoiIiIjYTgFEREREbKcAIiIiIrZTABERERHbKYCISMQdOnSI\nTZs2XXL7fffdx7Jly2zskYhEmwKIiERcdXU1999//yW3f+ELX+Ddd9+1sUciEm0KICISUQcPHiQr\nK4tJkz6YqXKmAAABO0lEQVT9c/Pqq68yMDAQev3d736X5OTkKPRORKJFAUREIurVV1/lnnvuCb0+\nffo0y5YtGxRA+vv7uf3226PRPRGJEgUQEYkov9/P5MmTQ6/37t1LTk4OcXFxobKf/exnLFmyJBrd\nE5EoUQARkYhqbW3lxIkTAJimSXV1NTk5OaHtu3fvZv/+/XzpS1+KUg9FJBriRq4iImJdcnIyixcv\nZvHixezYsQO/38+f//xn4uPjOXz4MDU1NezZsyfa3RQRm2kEREQiau3atRw7downn3ySW265hTff\nfJOsrCzWrVvH4cOH2blzJy6XK9rdFBGbGaZpmtHuhIiIiEwsGgERERER2ymAiIiIiO0UQERERMR2\nCiAiIiJiOwUQERERsZ0CiIiIiNhOAURERERspwAiIiIitlMAEREREdv9P82iM3AckVgSAAAAAElF\nTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 20 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we can see how the resonator peak is split and shiften up and down due to the superposition of 0 and 1 states of the qubit! We can also verify that the splitting is exactly $2\\chi$, as expected:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(figsize=(9,3))\n", "ax.plot((w-wr)/chi, abs(S))\n", "ax.set_xlabel(r'$(\\omega-\\omega_r)/\\chi$', fontsize=18)\n", "ax.set_xlim(-2,2);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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6En3UIVYkOihzIp4aNHNy+PBhtmzZwqxZs8jKygLMW4Uff/xxCgsLKS0tJSkpiddffx0A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\nffLSS+ZPYUj0UHA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Y98orr7B27VrsdjsHDhzos05NTQ0/+MEPhlUWEfEPBSciEayhoQGL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\nwYmIiIiEFAUnIiIiElL+P3HGGr67f05mAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Correlation function of the qubit" ] }, { "cell_type": "code", "collapsed": false, "input": [ "corr_vec = correlation(H, psi0, None, tlist, [], sx, sx)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 22 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(1, 1, sharex=True, figsize=(12,4))\n", "\n", "ax.plot(tlist, real(corr_vec), 'r', linewidth=2, label=\"qubit\")\n", "ax.set_ylabel(\"correlation\", fontsize=16)\n", "ax.set_xlabel(\"Time (ns)\", fontsize=16)\n", "ax.legend()\n", "ax.set_xlim(0,50)\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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CAH0cqaj9dNwHBLZr0SJgzBjgZz/L/XcQEkFRFbSora3F2WefjWeeeQbdu3fH3nvvjaOO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"text": [ "" ] } ], "prompt_number": 23 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Spectrum of the qubit\n", "\n", "The spectrum of the qubit has an interesting structure: from it one can see the photon distribution in the resonator mode!" ] }, { "cell_type": "code", "collapsed": false, "input": [ "w, S = spectrum_correlation_fft(tlist, corr_vec)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 24 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(figsize=(9,3))\n", "ax.plot(w / (2 * pi), abs(S))\n", "ax.set_xlabel(r'$\\omega$', fontsize=18)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 25, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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k8XhUXl7ei7IBID0wnQFEF7FjUV9fL5fLpQsXLujChQt64IEHVFJSoqKiIlVUVGjJkiXK\ny8vTqlWrElUvAPQZBBX0RRGDxYQJE7Rz585LxnNycuT1euNWFACkot5cF4TAgEzBzpsAAMAyBAsA\n6AU6EUBHBAsASCEEFaQ7ggUApBCCBdIdwQIAYmT14k1CBPoiggUAALAMwQIAYhRr1yHCVQ6APo9g\nAQAW680UR+dzi4qkjz7qXT1AIhEsACBGVq+JiOX5du+WNm2y9nWBeIoaLA4fPtx+ufTx48fr5Zdf\nliQ1NjbK6XQqPz9fpaWl7dcUAYBM15vFmyzyRLqLGiyys7P10ksv6Q9/+IM+/PBDvfbaa9q7d6/c\nbrecTqf8fr9KSkrkdrsTUS8ApLzerLEIFyIuXOj58wGJFjVY2O12FRYWSpIGDhyosWPH6ujRo6qt\nrZXL5ZIkuVwu1dTUxLdSAEgTWRZPMhMskE669T//Q4cOadeuXSouLlYgEJBhGJIkwzAUCATiUiAA\npIrefCrE6i4GkKpiDhanTp3S3LlztWjRIn33u9/t8JjNZpONz1cBgCSCBTJbxMumB507d05z587V\nAw88oPLycklml6KhoUF2u1319fXKzc0Ne25VVVX7fYfDIYfD0euiASAZor3BBx/vTbBgjQVSic/n\nk8/n69Y5UYNFW1ubHn74YRUUFGjhwoXt42VlZfJ4PHrqqafk8XjaA0dnocECAPqyYCiIdXqkN1uE\nA4nQuSFQXV0d9ZyowWLLli1avny5Jk6cqKKiIknS888/r8rKSlVUVGjJkiXKy8vTqlWrel45AKSB\naGssInUWetOxIFggnUQNFlOnTtWFLv5avF6v5QUBQLrqbsci0nNEGwNSFTtvAkAPhAsRVnQswmGN\nBdIJwQIAeiDcQs1I3YberLEgWCCdECwAIEahQSBSxyI0CAQf7004YCoE6YRgAQA9EC4ohAsRwbHW\n1tielzUWSHcECwCIUbjuRLix0BARbiwo1q2/CRZIJwQLAOiBSB2L0BARqWMR67oL1lggnRAsAKAH\n6FgA4REsACCKWD9a2t2ORXdfH0gHBAsAiJHVayxiXajJVAjSCcECAKKItWMRLkRE6lhwrRD0RVGD\nxYIFC2QYhiZMmNA+1tjYKKfTqfz8fJWWlqqpqSmuRQJAKojWsTh3zvwaa7CINJ0S7TggVUUNFg89\n9JDWrl3bYcztdsvpdMrv96ukpERutztuBQJAsoXrWITbsyJcsAg3FhRrYKBjgXQSNVjceuutGjx4\ncIex2tpauVwuSZLL5VJNTU18qgOAFBKuY3H+/MWxWINFbzfNstmk3/0utnOBROvRGotAICDDMCRJ\nhmEoEAhYWhQAJNOTT14MBFLkNRahwSJ4P1qwCHdu59eKNrZ9e/jagWSLetn0aGw2m2wRLttXVVXV\nft/hcMjhcPT2JQEgrl56SXr8cSkvr+tjWlrMr9FCRKRgEWvHItJCUSCefD6ffD5ft87pUbAwDEMN\nDQ2y2+2qr69Xbm5ul8eGBgsASBfRFmoGg0VPpkIidSxi3Y2zN/tiALHq3BCorq6Oek6PpkLKysrk\n8XgkSR6PR+Xl5T15GgBIC8EAEPoG/+23HR+TYg8WwfvhgkWs3Ylw5wKpIGqwmD9/vqZMmaJ9+/Zp\n+PDhWrp0qSorK7V+/Xrl5+drw4YNqqysTEStAJAwoSEiXLDoTcci3LlBsX4ElY4FUlXUqZAVK1aE\nHfd6vZYXAwCpIlqw6G7HIvS4SMEi1o20CBZIVey8CQBhhL6ZB9/EY+1YhBs7c+biWLhQ0vm1QoXr\nYhAskKoIFgAQRk+mQpqbO36VLgaLU6cinxtExwLpjmABACHC7VkR61TIyZPm19OnL46dPWt+DRcs\nQo/r/FrhagpFsECqIlgAQIhwu2KGdiCCvvnG/No5WFx1VccQcfKkNHBg+GBx4sTFsUgfQWUqBOmE\nYAEAIYJv4qFv5sFQELob5/Hjl46dPCkNHXppsOg8Fi5YBMdCny8o3N4WfNwUqYpgAQAhwu2KGZzi\nCE5/SGawyMrq2M0IBKSRI6MHi7Nnpf79pdALQ4ebMgnq1+/Ssc4di2HDpE7XiwSSgmABACHCBYvg\nm33wzV+SPv9cmjChY9fh6FEpP7/j2omvvpJuuEE6duziWFOTdP31Hc8NhpYvv7y0pliCxdGjErsA\nIBUQLAAgRLhg0dBgfg0NFvv3Szfd1LHr8Pnn0o03mmEi6OhRafJkqbHx4kdOjx+Xxo2Tjhy5+HrB\nMBLumo7huhjh1liE1gckC8ECAEIEpzZC37j9fvNrsKvQ0iLt2CFNn36x69DaKn3yifT3f28GkeBa\nicOHpeuuk4YPlz77zBxrbDQ7Fjk5F8eamqSrrzaDSFBwIWlotyMoXLAI3SsDSBaCBQCEaGw0vwbf\nuC9ckH77W7PrEOwIrFkjjR0rjRp1cRHn1q1mWBgyRLLbzW6EZIaNggJpzBhpzx5z7OBB89gbb5Tq\n6syx48eliRPNMHHokDkWDArhpkfCLd4M9+kVINF6FSzWrl2rMWPG6IYbbtCPf/xjq2pCnHT30reI\nP34nqcXn82nbNvN+a6v5Rr1woTR4sFRaak5XNDZK//7v0n/8h9mJCHYcli2T7rrLvD96tPTxx9Kf\n/2wGheuuk2bOlNatMx/fv99c5Dl3rrR8uTkWCJih5I47pL9c41HHj5sfVd27V/r66461fvHFpfV3\nngp5773wUyvphL+R9NPjYNHa2qrHHntMa9eu1aeffqoVK1Zo7969VtYGi/EHmnr4nSReW5s5ffHn\nP0vbtkm/+5355v6jH0n//M8+/du/mcctW2YuxGxokN5+W7rmGnMNRUWFVFYmzZpljn37rdl1+NWv\npH/5F/PcGTPMhZSrVpnH2WxSeblUU2OGhQ8/lG65Rbr7bjOAeL3Svn1mIHnmGen1180uyfHj5hTK\nggVmCNm//+LPsX27eQvVOURMm6b2nydd8TeSfqJehKwrdXV1GjVqlPLy8iRJ99xzj95++22NHTu2\nw3GdU3ZQuJ3kkvVYptRz/LjZgrXyOXtzbjr9t4tXrQ0N0kcfdX1uX761tl68nT/fs/udx1pazOmD\ns2fNW/B+6NdvvzW7AFdfbd5ycqS//mvzkxvjx0u/+IX5/eLF0gcfSH/zN+bv47rrpH/9V8nplH7y\nE3PMZjOnM2bONLsYQ4aY42Vl0pQp5sdRN20yx66/Xrr9djNoDBtmhhJJ+p//kf7xH81zf/QjacQI\nqbbWfI5p08zOxn//t/maf/u30p13muf97/+aYWXAAPM5JbPev/s7s+bJk82xX/1Kqq42f9YhQ6TH\nHzcXjj7+uPnfYfBgc32HzWb+3NnZkW/nz5s/V1aW+WmVrKzw+2wgc/U4WBw9elTDhw9v/37YsGHa\nunXrJcfl53f9HJH+x5joxzKhnqYm8x8sq1+vN+emy3+7eD0WCJhvBpHO7au3fv3MW//+4e9fdln0\nY4L3g1+/8x3p8svNcy+/vOP94Ne/+ivzzTCcqirzDfiKK6R58y6GCskMEJIZPEI//jlzpjnl8OST\nF8cKCswgkZ1tfiQ16L/+ywwov/jFxbHSUmn+fOnFF6XbbjPHiovNLsbEidKzz5qv9/TT0j/9k/QP\n/2Aec++95nm7dklvvmmOffmluY6jrs7slkjSf/6nuZD000/Nx7/80gw2S5eae2wcPy7t3m0eO368\neWzw1tLS8ftz58yfKTQYtrV1/H0Gg4bN1vX9SI91Pq6pSfq//+vec4T+zUW7351je3M/lV4n3mxt\nbdH+P1V4b731ltauXavFixdLkpYvX66tW7fqlVdeaT9m1KhROnDggDWVAgCApBo5cqT2h87JhdHj\njsW1116rw4cPt39/+PBhDRs2rMMx0V4cAAD0LT1evDlp0iT96U9/0qFDh9TS0qI333xTZWVlVtYG\nAADSTI87Fv3799err76q2267Ta2trXr44YcvWbgJAAAyS4/XWAAAAHQWl5032TgrtSxYsECGYWhC\n6PJ0JM3hw4c1ffp0jRs3TuPHj9fLL7+c7JIy3tmzZ1VcXKzCwkIVFBTo6aefTnZJkLlfUlFRkWYF\nP0+LpMrLy9PEiRNVVFSkW265pcvjLO9YtLa2avTo0fJ6vbr22ms1efJkrVixgmmSJNq8ebMGDhyo\nBx98UB9//HGyy8l4DQ0NamhoUGFhoU6dOqWbb75ZNTU1/I0kWXNzswYMGKDz589r6tSpevHFFzV1\n6tRkl5XRfvrTn2rHjh06efKkaiN9Vh4JMWLECO3YsUM5OTkRj7O8YxG6cVZ2dnb7xllInltvvVWD\nBw9Odhn4C7vdrsLCQknSwIEDNXbsWH0Rbn9mJNSAAQMkSS0tLWptbY36jyfi68iRI1qzZo0eeeQR\nMWOfOmL5XVgeLMJtnHU09HJ9ANodOnRIu3btUnFxcbJLyXgXLlxQYWGhDMPQ9OnTVVBQkOySMtoT\nTzyhF154QVld7WaGhLPZbJo5c6YmTZrUvodVOJb/xmyJ3N4LSGOnTp3SvHnztGjRIg0cODDZ5WS8\nrKws7d69W0eOHNF7773HNSqSaPXq1crNzVVRURHdihSyZcsW7dq1S++8845ee+01bd68OexxlgeL\nWDbOAjLduXPnNHfuXN1///0qLy9PdjkIMWjQIN1xxx3a3vkKX0iY999/X7W1tRoxYoTmz5+vDRs2\n6MEHH0x2WRlv6NChkqQhQ4Zo9uzZqqurC3uc5cGCjbOAyNra2vTwww+roKBACxcuTHY5kHTs2DE1\nNTVJks6cOaP169erqKgoyVVlrueee06HDx/WwYMHtXLlSs2YMUO//OUvk11WRmtubtbJkyclSadP\nn9a6deu6/KSh5cEidOOsgoIC3X333ax2T7L58+drypQp8vv9Gj58uJYuXZrskjLali1btHz5cm3c\nuFFFRUUqKirS2rVrk11WRquvr9eMGTNUWFio4uJizZo1SyUlJckuC3/BFHvyBQIB3Xrrre1/I3fe\neadKS0vDHssGWQAAwDIstwUAAJYhWAAAAMsQLAAAgGUIFgAAwDIECwAAYBmCBQAAsAzBAgAAWIZg\nAQAALEOwAAAAliFYAAAAyxAsAACAZQgWAADAMgQLAN2yb98+LVu2rMvH77nnHt1///0JrAhAKiFY\nAOgWj8ej++67r8vHr7/+eu3cuTOBFQFIJQQLADHbu3evCgsLlZV18Z+O1atX68KFC+3fP/PMM8rL\ny0tCdQBSAcECQMxWr16tWbNmtX/f3Nys+++/v0OwOHfunKZOnZqM8gCkAIIFgJgdOXJEl19+efv3\ndXV1cjgc6t+/f/vYz3/+c82dOzcZ5QFIAQQLADE7ePCgTpw4IUlqa2uTx+ORw+Fof3zTpk3as2eP\nRo8enaQKASRb/+iHAIApLy9Pc+bM0Zw5c/TOO+/oyJEj2rBhg7Kzs+X3+1VTU6MtW7Yku0wASUTH\nAkDMnnzySX311Vf64Q9/qJEjR+r9999XYWGhKisr5ff79e6772rYsGHJLhNAEtna2trakl0EAADo\nG+hYAAAAyxAsAACAZQgWAADAMgQLAABgGYIFAACwDMECAABYhmABAAAsQ7AAAACWIVgAAADL/D9P\noYL4uGTDnQAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 25 }, { "cell_type": "markdown", "metadata": {}, "source": [ "It's a bit clearer if we shift the spectrum and scale it with $2\\chi$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(figsize=(9,3))\n", "ax.plot((w - wq - chi) / (2 * chi), abs(S))\n", "ax.set_xlabel(r'$(\\omega - \\omega_q - \\chi)/2\\chi$', fontsize=18)\n", "ax.set_xlim(-.5, N);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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GThccIYOVDCIi/wuZkBEMhADatFEbMsLD1QYADpcQEYWOkAkZwfDzKqpDgOoQ49oGwOES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\nxRdrrouLa/l8iVO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"text": [ "" ] } ], "prompt_number": 26 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compare to the cavity fock state distribution:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "rho_cavity = ptrace(res.states[-1], 0)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 27 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(1, 1, figsize=(9,3))\n", "\n", "axes.bar(arange(0, N)-.4, real(rho_cavity.diag()), color=\"blue\", alpha=0.6)\n", "axes.set_ylim(0, 1)\n", "axes.set_xlim(-0.5, N)\n", "axes.set_xticks(arange(0, N))\n", "axes.set_xlabel('Fock number', fontsize=12)\n", "axes.set_ylabel('Occupation probability', fontsize=12);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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eHi4aGxuFEELcvn1b1viPW7lypfjDH/7Q6/hd9fGrX/1KZGZmCiGEyMjIEGFh\nYbLGDwoKEmfOnBFCCLFnzx6xbt26XsfvDYMdSXl8AzkTExPNBnJyCg0NhaWlpawxHzdq1CgEBAQA\nAIYOHQovLy+UlpbK2seQIUMAAI2NjWhpaYGVlZWs8YG2lVoZGRlYsmQJhI5mF3UVFwDu3r2Ls2fP\nYvHixQDarrEyNzfXSV8nT56Ei4tLuz2D5PDcc8/BxMQEdXV1aG5uRl1dXaer53rr6tWrCAkJweDB\ng/HMM8/gV7/6FY4cOaJ13M4+Y49v/LhgwQL893//t6zxPT094e7u3uuYUvqYNGkSjIzafv2GhISg\nuLhY1vjDhg3TPK+trYW1tXWv43fVBwC8+eab2Lp1q1axu4sv5+e6sz4++ugjrF69GiYmJgCAESNG\nyBr/ESEEDh06hDlz5vQ6fld92NraakbiampqtPpcdxY/Ly8PoaGhAIDw8HD85S9/6XX83jDYIqWz\nzeFKSkr6MSPtFBQU4NKlSwgJCZE1bmtrKwICAmBjY4MXX3wR3t7essYHgBUrVuDdd9/V/FKWm0Kh\nQHh4OIKCgrB7927Z4+fn52PEiBFYtGgRxowZg6VLl6Kurk72fgDg008/xdy5c2WPa2VlhZUrV8LB\nwQF2dnawsLBAeHi4bPF9fX1x9uxZVFVVoa6uDl9++aVWX7zdeXwnahsbG1RUVOikn76yZ88eTJs2\nTfa4a9asgYODA/bt24e33npL9vjp6elQqVTw9/eXPfYj27dvh1qtRnR0tFbTel3Jy8vDmTNn8MIL\nLyAsLAwXLlyQvQ8AOHv2LGxsbODi4iJ77M2bN2s+26tWrcI777wja3wfHx/NH/iHDx/WeurwaRls\nkaJQKPo7BdnU1tZi1qxZeP/99zF06FBZYxsZGeHy5csoLi7GmTNnZL+R1BdffIGRI0ciMDBQZ6Md\nf/vb33Dp0iUcO3YMH374Ic6ePStr/ObmZly8eBFvvPEGLl68CDMzM2zevFnWPoC20ay//vWvePXV\nV2WPffPmTWzbtg0FBQUoLS1FbW0tDh48KFt8T09PxMfH46WXXsLUqVMRGBios6L0cQqF4mf9WU9K\nSoKpqalOCtOkpCQUFhZi4cKFWLFihayx6+rqsGnTJiQmJmqOyf35jo2NRX5+Pi5fvgxbW1usXLlS\n1vhA22e7uroa586dw7vvvovXXntN9j4AIC0tTSf/xwAQHR2NDz74AIWFhXjvvfc0I75y2bNnD3bu\n3ImgoCDJARn8AAAI/0lEQVTU1tbC1NRU1vg9MdgiRcoGcj8HTU1NmDlzJubNm4dXXnlFZ/2Ym5vj\n17/+tex/SXzzzTf4/PPP4eTkhDlz5iArKwtRUVGy9mFrawugbah2+vTpyMnJkTW+SqWCSqVCcHAw\nAGDWrFmyXFD5pGPHjuH555/Xasi5KxcuXMAvfvELDB8+HMbGxpgxYwa++eYbWftYvHgxLly4gNOn\nT8PCwgIeHh6yxn/ExsYG5eXlAICysjKMHDlSJ/3o2scff4yMjAxZi8XOzJ07V6uLKTtz8+ZNFBQU\nQK1Ww8nJCcXFxXj++edx+/Zt2foYOXKkpghdsmSJ7J9roO2zPWPGDABAcHAwjIyMcOfOHVn7aG5u\nxtGjRzF79mxZ4z6Sk5OD6dOnA2j73ST3v5OHhweOHz+OCxcuIDIyUiejQd0x2CJFygZy+k4Igejo\naHh7e2P58uWyx6+srNQModbX1+Orr77S+urzJ23atAlFRUXIz8/Hp59+igkTJmg27ZNDXV2d5mrz\nBw8e4MSJE7Kvtho1ahTs7e1x/fp1AG3Xjfj4+MjaB9D215a2c9Zd8fT0xLlz51BfXw8hBE6ePCn7\n1N6jL6jCwkIcPXpUZ385RkREYN++fQCAffv26bR419XoX2ZmJt59912kp6dj8ODBssfPy8vTPE9P\nT5f9c+3n54eKigrk5+cjPz8fKpUKFy9elLVgLCv7572Tjh49qpNVlK+88gqysrIAANevX0djYyOG\nDx8uax8nT56El5cX7OzsZI37iKurK06fPg0AyMrKkvV6KgD46aefALRdGrBx40bExsbKGr9HfXqZ\nbh/LyMgQ7u7uwsXFRWzatEn2+JGRkcLW1laYmpoKlUol9uzZI2v8s2fPCoVCIdRqtQgICBABAQHi\n2LFjssW/cuWKCAwMFGq1Wvj5+YmtW7fKFrsz2dnZsq/uuXXrllCr1UKtVgsfHx+d/D8LIcTly5dF\nUFCQ8Pf3F9OnT5d9dU9tba0YPnx4u1UZctuyZYvw9vYWvr6+IioqSrOiQS6hoaHC29tbqNVqkZWV\nJUvMR58xExMTzWfszp07YuLEicLNzU1MmjRJVFdXyxY/JSVFHD16VKhUKjF48GBhY2MjpkyZIus5\npKSkCFdXV+Hg4KD5XMfGxsoaf+bMmcLX11eo1WoxY8YMUVFRIcs5dPW7zsnJSavVPZ2dw/z584Wf\nn5/w9/cXv/3tb0V5ebns59DY2CjmzZsnfH19xZgxY8TXX38ta3whhFi4cKHYtWuXVrk/2cfjn4fz\n58+LsWPHCrVaLV544QVx8eJF2eKnpKSI999/X7i7uwt3d3exevVqWc7jaXAzNyIiItJLBjvdQ0RE\nRD9vLFKIiIhIL7FIISIiIr3EIoWIiIj0EosUIiIi0kssUoiIiEgvsUghIlmFhYUhJSWlv9PowNHR\nEadOnervNIjoKbBIIRrgHB0dMWTIEAwbNgzDhg3Dc889p9l2vjf09X46+poXEXWNRQrRAKdQKPDF\nF1/g/v37uH//Pu7du4dRo0b1d1p6q7m5ub9TIBowWKQQUacaGhqwfPlyKJVKKJVKrFixAo2NjZr3\n09PTERAQAHNzc7i6uuLEiRMdYpSVlcHf3x/Jycmd9uHo6Ijk5GSo1WpYWFggMjISDQ0NANpuwBca\nGtquvZGREW7dugUAWLhwId544w1MmzYNw4YNQ2hoKMrLy/Ef//EfsLS0hJeXFy5fvtzu53NycuDj\n4wMrKyssXrxY0xfQdsfugIAAWFpaYvz48fjuu+/a5bl161b4+/tj2LBhaG1tfcp/TSLqDRYpRNTp\njfSSkpKQk5OD3Nxc5ObmIicnBxs3bgTQ9mW/YMECJCcn4+7duzhz5gxGjx7d7ufz8/MRFhaGZcuW\nYeXKlZ32q1AocPjwYRw/fhz5+fm4cuUKPv74Y8l5Hz58GElJSaisrISpqSleeOEFBAcHo6qqCrNm\nzcKbb77Z7hw/+eQTnDhxAjdv3sT169c153Pp0iVER0dj9+7dqKqqQkxMDCIiItDU1KT5+U8//RTH\njh1DTU0NjIz4q5OoL/CTRjTACSHwyiuvwNLSEpaWlppb1x88eBDr16+HtbU1rK2t8fbbbyM1NRUA\nkJKSgujoaEycOBEAYGdnBw8PD03M77//HhMmTMCGDRuwZMmSbvtftmwZRo0aBUtLS7z88ssdRj+6\nolAoMGPGDAQGBmLQoEGYPn06zMzMMG/ePCgUCrz22mu4dOlSu/ZxcXFQKpWwtLTEmjVrkJaWBgD4\n05/+hJiYGAQHB0OhUCAqKgqDBg3CuXPnND+7bNkyKJVKDBo0SOK/LBFpi0UK0QCnUCiQnp6O6upq\nVFdX48iRIwDapmoeHx1xcHBAaWkpAKC4uBguLi6dxhNC4ODBg1CpVJg5c2aP/T9+/cuzzz6L2tpa\nybmPHDlS83zw4MHtXncWy97eXvP88fP58ccfkZycrCnULC0tUVxcrHn/yZ8lor7BIoWIOmVnZ4eC\nggLN68LCQiiVSgBtX9g3btzo9OcUCgUSExMxfPhwzJ07t9fXb5iZmaGurk7zWpsVR48UFha2e/7o\nfBwcHLBmzRpNoVZdXY3a2lrMnj1b054rg4j6HosUIurUnDlzsHHjRlRWVqKyshIbNmzAvHnzAADR\n0dHYu3cvsrKy0NraipKSEly7dk3zsyYmJjh8+DAePHiAqKioTq956Ylarcb333+P3NxcPHz4EAkJ\nCe3ef9qYQgh8+OGHKCkpQVVVFZKSkjRFyNKlS/HHP/4ROTk5EELgwYMH+PLLL59qVIeI5McihYg6\ntXbtWgQFBcHf3x/+/v4ICgrC2rVrAQDBwcHYu3cvVqxYAQsLC4SFhbUbpQDaCpUjR46goqIC0dHR\nkoqKx/cycXd3x/r16xEeHg4PDw+Ehoa2G814ct+TzvZBefL9119/HS+99BJcXFzg5uamOZ/nn38e\nu3fvRlxcHKysrODm5ob9+/dz9ISonylEb/7EISIiItIxjqQQERGRXmKRQkRERHqJRQoRERHpJRYp\nREREpJdYpBAREZFeYpFCREREeolFChEREeklFilERESkl/4/BUjllcwgljMAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 28 }, { "cell_type": "markdown", "metadata": {}, "source": [ "And if we look at the cavity wigner function we can see that after interacting dispersively with the qubit, the cavity is no longer in a coherent state, but in a superposition of coherent states." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(1, 1, figsize=(6,6))\n", "\n", "xvec = np.linspace(-5,5,200)\n", "W = wigner(rho_cavity, xvec, xvec)\n", "wlim = abs(W).max()\n", "\n", "axes.contourf(xvec, xvec, W, 100, norm=mpl.colors.Normalize(-wlim,wlim), cmap=plt.get_cmap('RdBu'))\n", "axes.set_xlabel(r'Im $\\alpha$', fontsize=18)\n", "axes.set_ylabel(r'Re $\\alpha$', fontsize=18);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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hPOHo22YaSY1GmuVEC3mpnCYF57FGFV1eR4XSt985S6GH9O1LUkbVeoINW+rIdp1mOiqp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\nbW1zC9o/obDNXyg6oy+SgTxe9WMVbcdMl8lJYcrRQl8pqy+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"text": [ "" ] } ], "prompt_number": 30 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Software versions" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from qutip.ipynbtools import version_table\n", "version_table()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
SoftwareVersion
QuTiP3.0.0.dev-5a88aa8
matplotlib1.3.1
Numpy1.8.1
Cython0.20.1post0
Python3.4.1 (default, Jun 9 2014, 17:34:49) \n", "[GCC 4.8.3]
IPython2.0.0
SciPy0.13.3
OSposix [linux]
Thu Jun 26 14:20:38 2014 JST
" ], "metadata": {}, "output_type": "pyout", "prompt_number": 31, "text": [ "" ] } ], "prompt_number": 31 } ], "metadata": {} } ] }