{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-02-09T09:55:27.183895900Z",
     "start_time": "2024-02-09T09:55:26.111399Z"
    },
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "from qutip import *\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as animation\n",
    "from IPython.display import HTML"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Wigner functions of mixed states\n",
    "\n",
    "Here, we will explore the Wigner quasiprobability distributions of \"mixed states\" (or, more accurately, of mixed ensembles)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Cat state vs. mixture of coherent states"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First: a reminder of what the Wigner function of two coherent states at $x=0$ with opposite momentum look like: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-02-09T09:55:29.587462500Z",
     "start_time": "2024-02-09T09:55:28.407444800Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N=30\n",
    "rho1 = coherent_dm(N,3j)\n",
    "rho2 = coherent_dm(N,-3j)\n",
    "\n",
    "fig,ax = plt.subplots(1,2, figsize=(12,6))\n",
    "plot_wigner(rho1, fig=fig, ax=ax[0])\n",
    "ax[0].set_title(r\"Coherent state $\\alpha = 3i$\")\n",
    "plot_wigner(rho2, fig=fig, ax=ax[1])\n",
    "ax[1].set_title(r\"Coherent state $\\alpha = -3i$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's compare a cat state and a mixed state. \n",
    "\n",
    "```{admonition} Reminder\n",
    "A cat state is a superposition of the wave functions: \n",
    "\n",
    "$$\n",
    "|{\\rm cat}\\rangle =  \\tfrac{1}{\\sqrt{2}}|\\alpha\\rangle +  \\tfrac{1}{\\sqrt{2}}|-\\alpha\\rangle\n",
    "$$\n",
    "\n",
    "whereas a 50/50 \"mixed\" state is defined by the sum of the density matrices:\n",
    "\n",
    "$$\n",
    "\\rho_{mix} = \\tfrac{1}{2}\\rho_\\alpha + \\tfrac{1}{2}\\rho_{-\\alpha}\n",
    "$$\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-09-27T19:14:21.106755Z",
     "start_time": "2021-09-27T19:14:20.304066Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N=30\n",
    "rho1 = coherent_dm(N,3j)\n",
    "rho2 = coherent_dm(N,-3j)\n",
    "mixed = rho1 + rho2\n",
    "\n",
    "psi1 = coherent(N,3j)\n",
    "psi2 = coherent(N,-3j)\n",
    "cat = psi1 + psi2\n",
    "\n",
    "fig,ax = plt.subplots(1,2, figsize=(12,6))\n",
    "plot_wigner(cat, fig=fig, ax=ax[0])\n",
    "ax[0].set_title(r\"Wigner function of a cat state of $\\alpha$ and $-\\alpha$\")\n",
    "plot_wigner(mixed, fig=fig, ax=ax[1])\n",
    "ax[1].set_title(r\"Wigner function of a mixed state of $\\alpha$ and $-\\alpha$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the difference? The \"fringes\" are gone! Similar to the coherences in the off-diagonal entries of the density matrix, the fringes of the cat state above are an indication of the \"coherence\" of the quantum superposition. \n",
    "\n",
    "Without this \"coherence\", the two \"wave packets\" do not interfere, as you can see if we plot $|\\psi(x)|^2$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-09-27T19:14:23.424857Z",
     "start_time": "2021-09-27T19:14:21.109501Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A hack to calculate the probability distribution\n",
    "x = np.linspace(-7.5,7.5,500)\n",
    "wigner_mixed = wigner(mixed,x,x)\n",
    "wigner_cat = wigner(cat,x,x)\n",
    "\n",
    "prob_mixed = np.sum(wigner_mixed,axis=0)\n",
    "prob_cat = np.sum(wigner_cat,axis=0)\n",
    "\n",
    "# Now the plot\n",
    "fig,ax = plt.subplots(1,2, figsize=(12,4))\n",
    "ax[0].plot(x,prob_cat)\n",
    "ax[0].set_title(\"Cat state\")\n",
    "ax[1].plot(x,prob_mixed)\n",
    "ax[1].set_title(\"Mixed state\")\n",
    "ax[0].set_yticks([])\n",
    "ax[1].set_yticks([])\n",
    "ax[0].axhline(0,ls=':', c='grey')\n",
    "ax[1].axhline(0,ls=':', c='grey')\n",
    "ax[0].set_xlabel(\"$x$\")\n",
    "ax[1].set_xlabel(\"$x$\")\n",
    "ax[0].set_ylabel(r\"$|\\psi(x)|^2$\")\n",
    "ax[1].set_ylabel(r\"$|\\psi(x)|^2$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course, the proper interpretation of the lack of interference is, of course, that in the experiment there are not two wave-packets, but instead just one, and then we repeat the experiment over and over again, each time with only  one coherent  state of either $\\alpha$ or $-\\alpha$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example:  Superposition vs. mixture of 0 and 1 photons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-09-27T19:14:24.161198Z",
     "start_time": "2021-09-27T19:14:23.427537Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N=30\n",
    "rho1 = fock_dm(N,0)\n",
    "rho2 = fock_dm(N,1)\n",
    "mixed = rho1 + rho2\n",
    "\n",
    "psi1 = fock(N,0)\n",
    "psi2 = fock(N,1)\n",
    "sup = psi1 + psi2\n",
    "\n",
    "fig,ax = plt.subplots(1,2, figsize=(12,6))\n",
    "plot_wigner(sup, fig=fig, ax=ax[0])\n",
    "ax[0].set_title(\"Superposition of 0 and 1 photons\")\n",
    "plot_wigner(mixed, fig=fig, ax=ax[1])\n",
    "ax[1].set_title(\"Mixed state of 0 and 1 photons\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now the \"wave function\" of the photon. \n",
    "\n",
    "```{admonition} Reminder: What is the \"wave function\" of a photon?\n",
    ":class: tip\n",
    "A classical electromagnetic wave is a standing wave whose electric field oscillates in time: for  example, for a given mode, we may have at a given fixed position in space an electric field with the following component in the z-direction:\n",
    "\n",
    "$$\n",
    "\\vec{E}(t)\\cdot \\hat{z} = E_z(t) = E_0 \\cos(\\omega t)\n",
    "$$\n",
    "\n",
    "where $\\hat{z}$ is a unit vector in the $z$ direction. Note the similarity to the mass-on-a-spring, which oscillates in position: \n",
    "\n",
    "$$\n",
    "x(t) = x_0 \\cos(\\omega t)\n",
    "$$\n",
    "\n",
    "In the mass-spring harmonic oscillator, we have a momentum $p(t)$ that oscillates out of phase with the position:\n",
    "\n",
    "$$\n",
    "p(t) = p_0 \\sin(\\omega t)\n",
    "$$\n",
    "\n",
    "In electromagnetism, there is also a magnetic field that also oscillates out of phase with the electric field :\n",
    "\n",
    "$$\n",
    "B_y(t) = B_0 \\sin(\\omega t)\n",
    "$$\n",
    "\n",
    "*(Note that if the $E_z$ above belongs to a wave propagating in the $x$ direction, then the magnetic field points in the $y$ direction...)*\n",
    "\n",
    "The mapping from the mass-spring harmonic oscillator to the photon harmonic oscillator in this case is then: \n",
    "\n",
    "* position $\\rightarrow$ electric field\n",
    "* momentum $\\rightarrow$ magnetic field\n",
    "```\n",
    "\n",
    "Using this logic, for a photon, one can interpret the axes of the Wigner plots above as:\n",
    "\n",
    "* Real part of $\\alpha$ $\\rightarrow$  $E_z$\n",
    "* Imaginary part of $\\alpha$ $\\rightarrow$  $B_y$\n",
    "\n",
    "The probability distributions of position $|\\psi(x)|^2$ and momentum $|\\phi(p)|^2$ are then replaced with probability  distributions of $E_z$ and $B_y$: \n",
    "\n",
    "* $|\\psi(x)|^2 \\rightarrow |\\psi(E_z)|^2$\n",
    "* $|\\phi(p)|^2 \\rightarrow |\\phi(B_y)|^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-09-27T19:14:26.723404Z",
     "start_time": "2021-09-27T19:14:24.163505Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A hack to calculate the probability distribution\n",
    "x = np.linspace(-7.5,7.5,500)\n",
    "wigner_mixed = wigner(mixed,x,x)\n",
    "wigner_sup = wigner(sup,x,x)\n",
    "\n",
    "prob_mixed = np.sum(wigner_mixed,axis=0)\n",
    "prob_cat = np.sum(wigner_sup,axis=0)\n",
    "\n",
    "# Now the plot\n",
    "fig,ax = plt.subplots(1,2, figsize=(12,4))\n",
    "ax[0].plot(x,prob_cat)\n",
    "ax[0].set_ylabel(r\"$|\\psi(E_z)|^2$\")\n",
    "ax[0].set_title(\"Superposition of 0 and 1 photons\")\n",
    "ax[1].plot(x,prob_mixed)\n",
    "ax[1].set_ylabel(r\"Probability density of measuring $E_z$\")\n",
    "ax[1].set_title(r\"Mixture of 0 and 1 photons\")\n",
    "ax[0].set_yticks([])\n",
    "ax[1].set_yticks([])\n",
    "ax[0].set_xlabel(\"$E_z$\")\n",
    "ax[1].set_xlabel(\"$E_z$\")\n",
    "ax[0].axhline(0,ls=':', c='grey')\n",
    "ax[1].axhline(0,ls=':', c='grey')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Demonstration: Thermal state of a harmonic oscillator (or a large spin)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Probability distributions for different temperatures:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_imgc6ba6f60c7354b72be0afd23a1455989\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_sliderc6ba6f60c7354b72be0afd23a1455989\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"animc6ba6f60c7354b72be0afd23a1455989.set_frame(parseInt(this.value));\">\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"animc6ba6f60c7354b72be0afd23a1455989.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"animc6ba6f60c7354b72be0afd23a1455989.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"animc6ba6f60c7354b72be0afd23a1455989.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"animc6ba6f60c7354b72be0afd23a1455989.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"animc6ba6f60c7354b72be0afd23a1455989.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"animc6ba6f60c7354b72be0afd23a1455989.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"animc6ba6f60c7354b72be0afd23a1455989.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"animc6ba6f60c7354b72be0afd23a1455989.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"animc6ba6f60c7354b72be0afd23a1455989.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_selectc6ba6f60c7354b72be0afd23a1455989\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_c6ba6f60c7354b72be0afd23a1455989\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_c6ba6f60c7354b72be0afd23a1455989\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_c6ba6f60c7354b72be0afd23a1455989\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_c6ba6f60c7354b72be0afd23a1455989\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_c6ba6f60c7354b72be0afd23a1455989\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_c6ba6f60c7354b72be0afd23a1455989\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_imgc6ba6f60c7354b72be0afd23a1455989\";\n",
       "    var slider_id = \"_anim_sliderc6ba6f60c7354b72be0afd23a1455989\";\n",
       "    var loop_select_id = \"_anim_loop_selectc6ba6f60c7354b72be0afd23a1455989\";\n",
       "    var frames = new Array(10);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAoAAAAHgCAYAAAA10dzkAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        animc6ba6f60c7354b72be0afd23a1455989 = new Animation(frames, img_id, slider_id, 200.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 30\n",
    "Ntemp  = 10\n",
    "Npts = 100\n",
    "\n",
    "Px = np.zeros([Npts,Ntemp])\n",
    "T = np.linspace(0,5,Ntemp)\n",
    "\n",
    "alpha_max = 7.5\n",
    "x = np.linspace(-alpha_max,alpha_max,Npts)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "line, = ax.plot(x, Px[:,0])\n",
    "\n",
    "def update(i):\n",
    "    wig = wigner(thermal_dm(N,T[i]),x,x)\n",
    "    line.set_ydata(np.sum(wig,axis=0))\n",
    "\n",
    "plt.ylabel(\"Probability density\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.title(\"Thermal occupation from 0 to 5 quanta\")\n",
    "plt.ylim(-0.25, 4)  # Set the y-axis limits\n",
    "\n",
    "anim = animation.FuncAnimation(fig, update, frames=Ntemp)\n",
    "plt.close(fig)\n",
    "\n",
    "HTML(anim.to_jshtml())\n"
   ]
  }
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