docs/examples/mbs-Rb87_5s12_5p12_F11_q1-sech-2pi.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hyperfine Structure: Sech Pulse 2π, q=1 — Self-Induced Transparency\n",
    "\n",
    "$^{87}\\mathrm{Rb}$ driven on the $5S_{1/2} F=1 \\rightarrow 5p_{1/2} F=1$ transition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from maxwellbloch import hyperfine\n",
    "\n",
    "Rb87_5s12_F1 = hyperfine.LevelF(I=1.5, J=0.5, F=1)\n",
    "Rb87_5s12_F2 = hyperfine.LevelF(I=1.5, J=0.5, F=2) # Needed for decay\n",
    "\n",
    "Rb87_5p12_F1 = hyperfine.LevelF(I=1.5, J=0.5, F=1)\n",
    "\n",
    "atom1e = hyperfine.Atom1e(element='Rb', isotope='87')\n",
    "\n",
    "atom1e.add_F_level(Rb87_5s12_F1)\n",
    "atom1e.add_F_level(Rb87_5s12_F2)\n",
    "atom1e.add_F_level(Rb87_5p12_F1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "NUM_STATES = atom1e.get_num_mF_levels()\n",
    "print(NUM_STATES)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ENERGIES = atom1e.get_energies()\n",
    "print(ENERGIES)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Tune to be on resonance with the F1 -> F1 transition\n",
    "DETUNING = 0\n",
    "print(DETUNING)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "FIELD_CHANNELS = atom1e.get_coupled_levels(F_level_idxs_a=(0,), F_level_idxs_b=(2,))\n",
    "print(FIELD_CHANNELS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "q = 1 # Field polarisation\n",
    "FIELD_FACTORS = atom1e.get_clebsch_hf_factors(F_level_idxs_a=(0,), F_level_idxs_b=(2,), q=q)\n",
    "print(FIELD_FACTORS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "strength_factor = np.sum(FIELD_FACTORS**2)\n",
    "print(strength_factor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1/6 is the strength factor S_11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "hf_factor = np.max(FIELD_FACTORS)\n",
    "print(hf_factor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "DECAY_CHANNELS = atom1e.get_coupled_levels(F_level_idxs_a=(0,1), F_level_idxs_b=(2,))\n",
    "print(DECAY_CHANNELS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "DECAY_FACTORS = atom1e.get_decay_factors(F_level_idxs_a=(0, 1), F_level_idxs_b=(2,))\n",
    "print(DECAY_FACTORS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "INITIAL_STATE = (\n",
    "    [1.0/3.0]*3 + # s12_F1\n",
    "    [0.0/5.0]*5 + # s12_F2\n",
    "    [0.0]*3) # p12_F1    \n",
    "print(INITIAL_STATE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sech_fwhm_conv = 1./2.6339157938\n",
    "WIDTH = 1.0*sech_fwhm_conv # [τ]\n",
    "print('WIDTH', WIDTH)\n",
    "\n",
    "n = 2.0 # For a pulse area of nπ    \n",
    "AMPL = n/WIDTH/(2*np.pi) # Pulse amplitude [2π Γ]\n",
    "\n",
    "AMPL *= 1/hf_factor\n",
    "\n",
    "print('ampl', AMPL)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mb_solve_json = \"\"\"\n",
    "{{\n",
    "  \"atom\": {{\n",
    "    \"decays\": [\n",
    "      {{\n",
    "        \"channels\": {decay_channels},\n",
    "        \"rate\": 0.0,\n",
    "        \"factors\": {decay_factors}\n",
    "      }}\n",
    "    ],\n",
    "    \"energies\": {energies},\n",
    "    \"fields\": [\n",
    "      {{\n",
    "        \"coupled_levels\": {field_channels},\n",
    "        \"factors\": {field_factors},\n",
    "        \"detuning\": {detuning},\n",
    "        \"detuning_positive\": true,\n",
    "        \"label\": \"probe\",\n",
    "        \"rabi_freq\": 1.0,\n",
    "        \"rabi_freq_t_args\": {{\n",
    "          \"ampl\": {ampl},\n",
    "          \"centre\": 0.0,\n",
    "          \"width\": {width}\n",
    "        }},\n",
    "        \"rabi_freq_t_func\": \"sech\"\n",
    "      }}\n",
    "    ],\n",
    "    \"num_states\": {num_states},\n",
    "    \"initial_state\": {initial_state}\n",
    "  }},\n",
    "  \"t_min\": -2.0,\n",
    "  \"t_max\": 10.0,\n",
    "  \"t_steps\": 100,\n",
    "  \"z_min\": -0.5,\n",
    "  \"z_max\": 1.5,\n",
    "  \"z_steps\": 100,\n",
    "  \"z_steps_inner\": 1,\n",
    "  \"num_density_z_func\": \"square\",\n",
    "  \"num_density_z_args\": {{\n",
    "    \"on\": 0.0,\n",
    "    \"off\": 1.0,\n",
    "    \"ampl\": 1.0\n",
    "  }},\n",
    "  \"interaction_strengths\": [\n",
    "    5.0e2\n",
    "  ],\n",
    "  \"velocity_classes\": null,\n",
    "  \"method\": \"mesolve\",\n",
    "  \"opts\": {{\n",
    "    \"method\": \"bdf\", \n",
    "    \"atol\": 1e-8, \n",
    "    \"rtol\": 1e-6,\n",
    "    \"nsteps\": 1e2\n",
    "  }},\n",
    "  \"savefile\": \"mbs-Rb87_5s12_5p12_F11_q1-sech-2pi\"\n",
    "}}\n",
    "\"\"\".format(num_states=NUM_STATES, energies=ENERGIES, initial_state=INITIAL_STATE, \n",
    "           detuning=DETUNING, field_channels=FIELD_CHANNELS, field_factors=list(FIELD_FACTORS), \n",
    "           decay_channels=DECAY_CHANNELS, decay_factors=list(DECAY_FACTORS),\n",
    "           ampl=AMPL, width=WIDTH)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from maxwellbloch import mb_solve\n",
    "mbs = mb_solve.MBSolve().from_json_str(mb_solve_json)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%time Omegas_zt, states_zt = mbs.mbsolve(recalc=True, pbar_chunk_size=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "\n",
    "sns.set_style('darkgrid')\n",
    "\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig = plt.figure(1, figsize=(16, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "# cmap_range = np.linspace(0.0, 12, 11)\n",
    "cf = ax.contourf(mbs.tlist, mbs.zlist, \n",
    "                 np.abs(mbs.Omegas_zt[0]/(2*np.pi)),\n",
    "#                  cmap_range,\n",
    "                 cmap=plt.cm.Blues\n",
    "                )\n",
    "ax.set_title('Rabi Frequency ($\\Gamma / 2\\pi $)')\n",
    "ax.set_xlabel('Time ($1/\\Gamma$)')\n",
    "ax.set_ylabel('Distance ($L$)')\n",
    "ax.grid(alpha=0.5)\n",
    "ax.set_axisbelow(False)\n",
    "for y in [0.0, 1.0]:\n",
    "    ax.axhline(y, c='grey', lw=1.0, ls='dotted')\n",
    "plt.colorbar(cf);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig = plt.figure(1, figsize=(16, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "# cmap_range = np.linspace(0.0, 1.0e-3, 11)\n",
    "cf = ax.contourf(mbs.tlist, mbs.zlist, \n",
    "                 np.abs(mbs.populations_field(0, upper=False)),\n",
    "#                  cmap_range, \n",
    "                 cmap=plt.cm.Reds\n",
    "                )\n",
    "ax.set_title('Rabi Frequency ($\\Gamma / 2\\pi $)')\n",
    "ax.set_xlabel('Time ($1/\\Gamma$)')\n",
    "ax.set_ylabel('Distance ($L$)')\n",
    "for y in [0.0, 1.0]:\n",
    "    ax.axhline(y, c='grey', lw=1.0, ls='dotted')\n",
    "plt.colorbar(cf);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig = plt.figure(1, figsize=(16, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "# cmap_range = np.linspace(0.0, 1.0e-3, 11)\n",
    "cf = ax.contourf(mbs.tlist, mbs.zlist, \n",
    "                 np.imag(mbs.coherences_field(0)),\n",
    "#                  cmap_range, \n",
    "                 cmap=plt.cm.Greens\n",
    "                )\n",
    "ax.set_title('Rabi Frequency ($\\Gamma / 2\\pi $)')\n",
    "ax.set_xlabel('Time ($1/\\Gamma$)')\n",
    "ax.set_ylabel('Distance ($L$)')\n",
    "for y in [0.0, 1.0]:\n",
    "    ax.axhline(y, c='grey', lw=1.0, ls='dotted')\n",
    "plt.colorbar(cf);"
   ]
  }
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