{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "24450a95-b62d-4e10-ad2a-8d94dd7676ca",
   "metadata": {},
   "source": [
    "**The program for simulation of two-photon Rydberg excitation of 36D_{3/2} state in the external DC electric field. Supplemental material for the paper S.A.Spirin et al. Three-dimensional three-photon Stark spectroscopy of single Rydberg Rb atoms in an ultrahigh-vacuum glass cell with eight electrodes**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0817d908-5ebc-4ea1-b808-35d6b94a002a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x450 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final populations:\n",
      "P1 = 0.817242\n",
      "P2 = 0.003366\n",
      "P3 = 0.006065\n",
      "P4 = 0.173327\n",
      "P3 + P4 = 0.179392\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import qutip as qt\n",
    "import matplotlib.pyplot as plt\n",
    "import csv\n",
    "\n",
    "# ============================================================\n",
    "# Units\n",
    "# ============================================================\n",
    "MHz = 2 * np.pi * 1e6   # 1 MHz in angular-frequency units\n",
    "\n",
    "\n",
    "# ============================================================\n",
    "# Basis and operators for 4-level system\n",
    "#\n",
    "# Indices:\n",
    "# |1> -> 0\n",
    "# |2> -> 1\n",
    "# |3> -> 2\n",
    "# |4> -> 3\n",
    "#\n",
    "# Couplings:\n",
    "# |1> <-> |2>\n",
    "# |2> <-> |3>\n",
    "# |2> <-> |4>\n",
    "# ============================================================\n",
    "def four_level_ops():\n",
    "    N = 4\n",
    "    kets = [qt.basis(N, i) for i in range(N)]\n",
    "    P = [k * k.dag() for k in kets]\n",
    "\n",
    "    # spontaneous decay lowering operators\n",
    "    s21 = kets[0] * kets[1].dag()   # |1><2|\n",
    "    s32 = kets[1] * kets[2].dag()   # |2><3|\n",
    "    s42 = kets[1] * kets[3].dag()   # |2><4|\n",
    "\n",
    "    # coherent coupling operators\n",
    "    x12 = kets[0] * kets[1].dag() + kets[1] * kets[0].dag()\n",
    "    x23 = kets[1] * kets[2].dag() + kets[2] * kets[1].dag()\n",
    "    x24 = kets[1] * kets[3].dag() + kets[3] * kets[1].dag()\n",
    "\n",
    "    return kets, P, s21, s32, s42, x12, x23, x24\n",
    "\n",
    "\n",
    "# ============================================================\n",
    "# Hamiltonian in the rotating-wave approximation\n",
    "#\n",
    "# Detunings:\n",
    "# Delta12 : laser driving |1> <-> |2>\n",
    "# Delta23 : laser driving |2> <-> |3>\n",
    "# Delta24 : laser driving |2> <-> |4>\n",
    "#\n",
    "# In the rotating frame:\n",
    "# E2 -> -Delta12\n",
    "# E3 -> -(Delta12 + Delta23)\n",
    "# E4 -> -(Delta12 + Delta24)\n",
    "# ============================================================\n",
    "def branching_hamiltonian(Omega12, Omega23, Omega24,\n",
    "                          Delta12, Delta23, Delta24):\n",
    "    _, P, _, _, _, x12, x23, x24 = four_level_ops()\n",
    "\n",
    "    H_det = (\n",
    "        -Delta12 * P[1]-Delta23 * P[2]-Delta24 * P[3]\n",
    "    )\n",
    "\n",
    "    H_drive = (\n",
    "        0.5 * Omega12 * x12\n",
    "        + 0.5 * Omega23 * x23\n",
    "        + 0.5 * Omega24 * x24\n",
    "    )\n",
    "\n",
    "    return H_det + H_drive\n",
    "\n",
    "\n",
    "# ============================================================\n",
    "# Collapse operators\n",
    "#\n",
    "# Lifetimes:\n",
    "# tau2 : |2> -> |1|\n",
    "# tau3 : |3> -> |2|\n",
    "# tau4 : |4> -> |2|\n",
    "#\n",
    "# Laser linewidth dephasing:\n",
    "# gammaL12, gammaL23, gammaL24\n",
    "# ============================================================\n",
    "def collapse_operators(tau2=np.inf, tau3=np.inf, tau4=np.inf,\n",
    "                       gammaL12=0.0, gammaL23=0.0, gammaL24=0.0):\n",
    "    _, P, s21, s32, s42, _, _, _ = four_level_ops()\n",
    "    c_ops = []\n",
    "\n",
    "    # spontaneous decay\n",
    "    if np.isfinite(tau2) and tau2 > 0:\n",
    "        c_ops.append(np.sqrt(1.0 / tau2) * s21)\n",
    "\n",
    "    if np.isfinite(tau3) and tau3 > 0:\n",
    "        c_ops.append(np.sqrt(1.0 / tau3) * s32)\n",
    "\n",
    "    if np.isfinite(tau4) and tau4 > 0:\n",
    "        c_ops.append(np.sqrt(1.0 / tau4) * s42)\n",
    "\n",
    "    # laser-linewidth dephasing\n",
    "    if gammaL12 > 0:\n",
    "        c_ops.append(np.sqrt(gammaL12 / 2.0) * (P[1] - P[0]))\n",
    "\n",
    "    if gammaL23 > 0:\n",
    "        c_ops.append(np.sqrt(gammaL23 / 2.0) * (P[2] - P[1]))\n",
    "\n",
    "    if gammaL24 > 0:\n",
    "        c_ops.append(np.sqrt(gammaL24 / 2.0) * (P[3] - P[1]))\n",
    "\n",
    "    return c_ops\n",
    "\n",
    "\n",
    "# ============================================================\n",
    "# Solver options for stiff systems\n",
    "# ============================================================\n",
    "def make_solver_options(Omega12, Omega23, Omega24,\n",
    "                        tau2=np.inf, tau3=np.inf, tau4=np.inf,\n",
    "                        gammaL12=0.0, gammaL23=0.0, gammaL24=0.0):\n",
    "    rates = [\n",
    "        abs(Omega12), abs(Omega23), abs(Omega24),\n",
    "        gammaL12, gammaL23, gammaL24\n",
    "    ]\n",
    "\n",
    "    if np.isfinite(tau2) and tau2 > 0:\n",
    "        rates.append(1.0 / tau2)\n",
    "    if np.isfinite(tau3) and tau3 > 0:\n",
    "        rates.append(1.0 / tau3)\n",
    "    if np.isfinite(tau4) and tau4 > 0:\n",
    "        rates.append(1.0 / tau4)\n",
    "\n",
    "    fastest_rate = max(rates) if max(rates) > 0 else 1.0\n",
    "    max_step = 0.05 / fastest_rate\n",
    "\n",
    "    return {\n",
    "        \"method\": \"bdf\",\n",
    "        \"nsteps\": 500000,\n",
    "        \"atol\": 1e-8,\n",
    "        \"rtol\": 1e-6,\n",
    "        \"max_step\": max_step\n",
    "    }\n",
    "\n",
    "\n",
    "# ============================================================\n",
    "# Final populations only\n",
    "#\n",
    "# Returns:\n",
    "#   pops = [P1, P2, P3, P4]\n",
    "#   P34  = P3 + P4\n",
    "#   rhoT = final density matrix\n",
    "# ============================================================\n",
    "def final_populations(T,\n",
    "                      Omega12, Omega23, Omega24,\n",
    "                      Delta12, Delta23, Delta24,\n",
    "                      tau2=np.inf, tau3=np.inf, tau4=np.inf,\n",
    "                      gammaL12=0.0, gammaL23=0.0, gammaL24=0.0,\n",
    "                      rho0=None):\n",
    "    kets, P, *_ = four_level_ops()\n",
    "\n",
    "    if rho0 is None:\n",
    "        rho0 = qt.ket2dm(kets[0])\n",
    "\n",
    "    H = branching_hamiltonian(\n",
    "        Omega12, Omega23, Omega24,\n",
    "        Delta12, Delta23, Delta24\n",
    "    )\n",
    "\n",
    "    c_ops = collapse_operators(\n",
    "        tau2=tau2, tau3=tau3, tau4=tau4,\n",
    "        gammaL12=gammaL12, gammaL23=gammaL23, gammaL24=gammaL24\n",
    "    )\n",
    "\n",
    "    opts = make_solver_options(\n",
    "        Omega12, Omega23, Omega24,\n",
    "        tau2=tau2, tau3=tau3, tau4=tau4,\n",
    "        gammaL12=gammaL12, gammaL23=gammaL23, gammaL24=gammaL24\n",
    "    )\n",
    "\n",
    "    result = qt.mesolve(H, rho0, [0.0, T], c_ops, e_ops=[], options=opts)\n",
    "\n",
    "    rhoT = result.states[-1]\n",
    "    pops = np.array([qt.expect(Pi, rhoT) for Pi in P], dtype=float)\n",
    "    P34 = pops[2] + pops[3]\n",
    "\n",
    "    return pops, P34, rhoT\n",
    "\n",
    "\n",
    "# ============================================================\n",
    "# Simultaneous scan of detunings for states 3 and 4\n",
    "#\n",
    "# Common scan variable:\n",
    "#   Delta_scan\n",
    "#\n",
    "# Actual detunings:\n",
    "#   Delta23 = Delta_scan + delta3_offset\n",
    "#   Delta24 = Delta_scan + delta4_offset\n",
    "# ============================================================\n",
    "def excitation_spectrum_upper_scan(scan_values,\n",
    "                                   T,\n",
    "                                   Omega12, Omega23, Omega24,\n",
    "                                   Delta12,\n",
    "                                   delta3_offset=0.0,\n",
    "                                   delta4_offset=0.0,\n",
    "                                   tau2=np.inf, tau3=np.inf, tau4=np.inf,\n",
    "                                   gammaL12=0.0, gammaL23=0.0, gammaL24=0.0,\n",
    "                                   rho0=None):\n",
    "    all_pops = np.zeros((len(scan_values), 4), dtype=float)\n",
    "    spectrum = np.zeros(len(scan_values), dtype=float)\n",
    "    Delta23_values = np.zeros(len(scan_values), dtype=float)\n",
    "    Delta24_values = np.zeros(len(scan_values), dtype=float)\n",
    "\n",
    "    for i, Delta_scan in enumerate(scan_values):\n",
    "        Delta23 = Delta_scan + delta3_offset\n",
    "        Delta24 = Delta_scan + delta4_offset\n",
    "\n",
    "        pops, P34, _ = final_populations(\n",
    "            T=T,\n",
    "            Omega12=Omega12, Omega23=Omega23, Omega24=Omega24,\n",
    "            Delta12=Delta12, Delta23=Delta23, Delta24=Delta24,\n",
    "            tau2=tau2, tau3=tau3, tau4=tau4,\n",
    "            gammaL12=gammaL12, gammaL23=gammaL23, gammaL24=gammaL24,\n",
    "            rho0=rho0\n",
    "        )\n",
    "\n",
    "        all_pops[i, :] = pops\n",
    "        spectrum[i] = P34\n",
    "        Delta23_values[i] = Delta23\n",
    "        Delta24_values[i] = Delta24\n",
    "\n",
    "    return spectrum, all_pops, Delta23_values, Delta24_values\n",
    "\n",
    "\n",
    "def save_spectrum_csv(filename,\n",
    "                      scan_values,\n",
    "                      Delta23_values,\n",
    "                      Delta24_values,\n",
    "                      all_pops,\n",
    "                      spectrum,\n",
    "                      detuning_unit=MHz):\n",
    "    \"\"\"\n",
    "    Save scan results to a CSV file.\n",
    "\n",
    "    Columns:\n",
    "      scan_value, Delta23, Delta24, P1, P2, P3, P4, P34\n",
    "\n",
    "    Detunings are saved in units of detuning_unit.\n",
    "    For example, if detuning_unit = MHz, values are saved in MHz/(2*pi).\n",
    "    \"\"\"\n",
    "    with open(filename, mode=\"w\", newline=\"\") as f:\n",
    "        writer = csv.writer(f)\n",
    "        writer.writerow([\n",
    "            \"scan_value\",\n",
    "            \"Delta23\",\n",
    "            \"Delta24\",\n",
    "            \"P1\",\n",
    "            \"P2\",\n",
    "            \"P3\",\n",
    "            \"P4\",\n",
    "            \"P34\"\n",
    "        ])\n",
    "\n",
    "        for i in range(len(scan_values)):\n",
    "            P1, P2, P3, P4 = all_pops[i]\n",
    "            P34 = spectrum[i]\n",
    "            writer.writerow([\n",
    "                scan_values[i] / detuning_unit,\n",
    "                Delta23_values[i] / detuning_unit,\n",
    "                Delta24_values[i] / detuning_unit,\n",
    "                P1,\n",
    "                P2,\n",
    "                P3,\n",
    "                P4,\n",
    "                P34\n",
    "            ])\n",
    "\n",
    "# ============================================================\n",
    "# Example\n",
    "# ============================================================\n",
    "if __name__ == \"__main__\":\n",
    "    # Fixed interaction time\n",
    "    T = 1.0e-7\n",
    "\n",
    "    # Rabi frequencies\n",
    "    Omega12 =100.0 * MHz\n",
    "    Omega23 =86.0 * MHz\n",
    "    Omega24 =50.0 * MHz\n",
    "\n",
    "    # Lower transition detuning\n",
    "    Delta12 = 1000.0 * MHz\n",
    "      \n",
    "    Ex=0.0\n",
    "    Ey=2.5\n",
    "    Ez=0.0\n",
    "    alpha12=0.545\n",
    "    alpha32=8.416\n",
    "    # Offsets of upper transitions relative to common scan\n",
    "    delta3_offset = alpha32*(Ey**2+Ex**2+Ez**2)* MHz\n",
    "    delta4_offset = alpha12*(Ey**2+Ex**2+Ez**2)* MHz\n",
    "\n",
    "    # Lifetimes\n",
    "    tau2 = 26e-9\n",
    "    tau3 = 29e-6\n",
    "    tau4 = 29e-6\n",
    "\n",
    "    # Laser linewidth dephasing\n",
    "    gammaL12 = 0.0 * MHz\n",
    "    gammaL23 = 0.0 * MHz\n",
    "    gammaL24 = 0.0 * MHz\n",
    "\n",
    "    # Common scan of upper detunings\n",
    "    detuning_scan = np.linspace(-80* MHz-delta4_offset,20*MHz- delta4_offset, 321)\n",
    "\n",
    "    P34_spectrum, all_pops, Delta23_vals, Delta24_vals = excitation_spectrum_upper_scan(\n",
    "        scan_values=detuning_scan,\n",
    "        T=T,\n",
    "        Omega12=Omega12,\n",
    "        Omega23=Omega23,\n",
    "        Omega24=Omega24,\n",
    "        Delta12=Delta12,\n",
    "        delta3_offset=delta3_offset,\n",
    "        delta4_offset=delta4_offset,\n",
    "        tau2=tau2, tau3=tau3, tau4=tau4,\n",
    "        gammaL12=gammaL12, gammaL23=gammaL23, gammaL24=gammaL24\n",
    "    )\n",
    "\n",
    "    plt.figure(figsize=(7, 4.5))\n",
    "    plt.plot(detuning_scan / MHz, P34_spectrum, lw=2, label=r\"$P_3(T)+P_4(T)$\")\n",
    "    plt.xlabel(r'Common upper detuning scan / $(2\\pi\\ \\mathrm{MHz})$')\n",
    "    plt.ylabel(r'Final population')\n",
    "    plt.title('Four-level excitation spectrum')\n",
    "    plt.grid(True, alpha=0.3)\n",
    "    plt.legend()\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "\n",
    "    # Example endpoint at one scan value\n",
    "    Delta_scan0 = 0.0 * MHz\n",
    "    Delta23_0 = Delta_scan0 + delta3_offset\n",
    "    Delta24_0 = Delta_scan0 + delta4_offset\n",
    "\n",
    "    pops_res, P34_res, rhoT_res = final_populations(\n",
    "        T=T,\n",
    "        Omega12=Omega12, Omega23=Omega23, Omega24=Omega24,\n",
    "        Delta12=Delta12, Delta23=Delta23_0, Delta24=Delta24_0,\n",
    "        tau2=tau2, tau3=tau3, tau4=tau4,\n",
    "        gammaL12=gammaL12, gammaL23=gammaL23, gammaL24=gammaL24\n",
    "    )\n",
    "\n",
    "    print(\"Final populations:\")\n",
    "    print(f\"P1 = {pops_res[0]:.6f}\")\n",
    "    print(f\"P2 = {pops_res[1]:.6f}\")\n",
    "    print(f\"P3 = {pops_res[2]:.6f}\")\n",
    "    print(f\"P4 = {pops_res[3]:.6f}\")\n",
    "    print(f\"P3 + P4 = {P34_res:.6f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "86a71ff4-5012-4919-8716-f2533fd9d49c",
   "metadata": {},
   "outputs": [],
   "source": [
    "save_spectrum_csv(\n",
    "        filename=\"spectrum_scan.csv\",\n",
    "        scan_values=detuning_scan,\n",
    "        Delta23_values=Delta23_vals,\n",
    "        Delta24_values=Delta24_vals,\n",
    "        all_pops=all_pops,\n",
    "        spectrum=P34_spectrum,\n",
    "        detuning_unit=MHz\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "04ccaa54-e4a9-43c1-a073-b14ec4c8d7fe",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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