{ "cells": [ { "cell_type": "markdown", "id": "b1d6f273-c243-4417-8f4a-59cf1673e19c", "metadata": {}, "source": [ "**The program for simulation of three-photon Rydberg excitation of 37P_{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": "d5b566e5-800b-48bc-926e-c7ef2b152478", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import qutip as qt\n", "from scipy.sparse.linalg import expm_multiply\n", "\n", "def basis5(i):\n", " \"\"\"\n", " Returns |i> for i=0..4 in a 5-level Hilbert space.\n", " Convention:\n", " 0 -> |1>\n", " 1 -> |2>\n", " 2 -> |3>\n", " 3 -> |4>\n", " 4 -> |5>\n", " \"\"\"\n", " return qt.basis(5, i)\n", "\n", "\n", "def projector(i):\n", " \"\"\"\n", " Returns |i> <-> |2> with Omega12, Delta12\n", " |2> <-> |3> with Omega23, Delta23\n", " |3> <-> |4> with Omega34, Delta34\n", " |3> <-> |5> with Omega35, Delta35\n", "\n", " Basis:\n", " 0 -> |1>\n", " 1 -> |2>\n", " 2 -> |3>\n", " 3 -> |4>\n", " 4 -> |5>\n", "\n", " All parameters should be in consistent angular-frequency units.\n", " \"\"\"\n", "\n", " P2 = projector(1)\n", " P3 = projector(2)\n", " P4 = projector(3)\n", " P5 = projector(4)\n", "\n", " s12 = transition(0, 1)\n", " s21 = transition(1, 0)\n", "\n", " s23 = transition(1, 2)\n", " s32 = transition(2, 1)\n", "\n", " s34 = transition(2, 3)\n", " s43 = transition(3, 2)\n", "\n", " s35 = transition(2, 4)\n", " s53 = transition(4, 2)\n", "\n", " H_detuning = (\n", " -Delta12 * P2\n", " -Delta23 * P3\n", " -Delta34 * P4\n", " -Delta35 * P5\n", " )\n", "\n", " H_coupling = (\n", " 0.5 * Omega12 * (s12 + s21)\n", " + 0.5 * Omega23 * (s23 + s32)\n", " + 0.5 * Omega34 * (s34 + s43)\n", " + 0.5 * Omega35 * (s35 + s53)\n", " )\n", "\n", " return H_detuning + H_coupling\n", "\n", "\n", "# ============================================================\n", "# Collapse operators\n", "# ============================================================\n", "\n", "def collapse_operators(gamma21, gamma32, gamma43, gamma53,\n", " laser_lw12=0.0, laser_lw23=0.0,\n", " laser_lw34=0.0, laser_lw35=0.0):\n", " \"\"\"\n", " Spontaneous decay:\n", " gamma21: |2> -> |1>\n", " gamma32: |3> -> |2>\n", " gamma43: |4> -> |3>\n", " gamma53: |5> -> |3>\n", "\n", " Laser linewidth / dephasing:\n", " laser_lw12 dephases |1><2|\n", " laser_lw23 dephases |2><3|\n", " laser_lw34 dephases |3><4|\n", " laser_lw35 dephases |3><5|\n", " \"\"\"\n", " c_ops = []\n", "\n", " # Spontaneous decay\n", " if gamma21 > 0:\n", " c_ops.append(np.sqrt(gamma21) * transition(0, 1)) # |1><2|\n", "\n", " if gamma32 > 0:\n", " c_ops.append(np.sqrt(gamma32) * transition(1, 2)) # |2><3|\n", "\n", " if gamma43 > 0:\n", " c_ops.append(np.sqrt(gamma43) * transition(2, 3)) # |3><4|\n", "\n", " if gamma53 > 0:\n", " c_ops.append(np.sqrt(gamma53) * transition(2, 4)) # |3><5|\n", "\n", " # Laser linewidth as pure dephasing\n", " if laser_lw12 > 0:\n", " c_ops.append(linewidth_dephasing_op(0, 1, laser_lw12))\n", "\n", " if laser_lw23 > 0:\n", " c_ops.append(linewidth_dephasing_op(1, 2, laser_lw23))\n", "\n", " if laser_lw34 > 0:\n", " c_ops.append(linewidth_dephasing_op(2, 3, laser_lw34))\n", "\n", " if laser_lw35 > 0:\n", " c_ops.append(linewidth_dephasing_op(2, 4, laser_lw35))\n", "\n", " return c_ops\n", "\n", "\n", "\n", "def qobj_to_csr(qobj):\n", " \"\"\"\n", " Convert a QuTiP Qobj to a SciPy CSR sparse matrix\n", " for both QuTiP 4 and QuTiP 5 style backends.\n", " \"\"\"\n", " data = qobj.data\n", " if hasattr(data, \"as_scipy\"): # QuTiP 5\n", " return data.as_scipy().tocsr()\n", " return data.tocsr() # QuTiP 4\n", "\n", "\n", "def simultaneous_upper_detuning_spectrum_fast(\n", " scan_values,\n", " Delta34_start,\n", " Delta35_start,\n", " Omega12=0.0, Omega23=0.0, Omega34=0.0, Omega35=0.0,\n", " Delta12=0.0, Delta23=0.0,\n", " gamma21=0.0, gamma32=0.0, gamma43=0.0, gamma53=0.0,\n", " laser_lw12=0.0, laser_lw23=0.0, laser_lw34=0.0, laser_lw35=0.0,\n", " t_final=1.0\n", "):\n", " \"\"\"\n", " High-performance excitation spectrum for simultaneous scan of Delta34 and Delta35.\n", "\n", " For each scan value s:\n", " Delta34 = Delta34_start + s\n", " Delta35 = Delta35_start + s\n", "\n", " Uses direct Liouvillian propagation:\n", " rho(t) = exp(L t) rho(0)\n", "\n", " No unnecessary time grid is used.\n", "\n", " Returns\n", " -------\n", " Delta34_vals : np.ndarray\n", " Delta35_vals : np.ndarray\n", " P4_vals : np.ndarray\n", " P5_vals : np.ndarray\n", " P_upper_vals : np.ndarray\n", " \"\"\"\n", "\n", " scan_values = np.asarray(scan_values, dtype=float)\n", "\n", " # --------------------------------------------------------\n", " # Initial state |1><1|\n", " # --------------------------------------------------------\n", " rho0 = projector(0)\n", " rho0_vec = qt.operator_to_vector(rho0).full().ravel()\n", "\n", " # --------------------------------------------------------\n", " # Collapse operators (constant for all scan points)\n", " # --------------------------------------------------------\n", " c_ops = collapse_operators(\n", " gamma21, gamma32, gamma43, gamma53,\n", " laser_lw12, laser_lw23, laser_lw34, laser_lw35\n", " )\n", "\n", " # --------------------------------------------------------\n", " # Build Hamiltonian in a split form:\n", " #\n", " # H = H_base + Delta34 * (-|4><4|) + Delta35 * (-|5><5|)\n", " #\n", " # where H_base already contains:\n", " # Delta12, Delta23, couplings, and the common lower detuning structure\n", " # but with Delta34 = Delta35 = 0\n", " # --------------------------------------------------------\n", " H_base = five_level_hamiltonian(\n", " Omega12, Omega23, Omega34, Omega35,\n", " Delta12, Delta23, 0.0, 0.0\n", " )\n", "\n", " P4 = projector(3) # |4><4|\n", " P5 = projector(4) # |5><5|\n", "\n", " # Liouvillian pieces\n", " L_base = qt.liouvillian(H_base, c_ops)\n", " L_d34 = qt.liouvillian(-P4, [])\n", " L_d35 = qt.liouvillian(-P5, [])\n", "\n", " # Since both detunings are scanned with the same scan variable s:\n", " #\n", " # Delta34 = Delta34_start + s\n", " # Delta35 = Delta35_start + s\n", " #\n", " # then:\n", " #\n", " # L(s) = L_offset + s * L_scan\n", " # --------------------------------------------------------\n", " L_offset = L_base + Delta34_start * L_d34 + Delta35_start * L_d35\n", " L_scan = L_d34 + L_d35\n", "\n", " L_offset_csr = qobj_to_csr(L_offset)\n", " L_scan_csr = qobj_to_csr(L_scan)\n", "\n", " # --------------------------------------------------------\n", " # Diagonal population indices in vectorized density matrix\n", " # QuTiP vectorization is column-stacking.\n", " # For N=5, diagonal rho_ii is at index i*(N+1)\n", " # --------------------------------------------------------\n", " N = 5\n", " idx_p4 = 3 * (N + 1) # rho_44\n", " idx_p5 = 4 * (N + 1) # rho_55\n", "\n", " Delta34_vals = Delta34_start + scan_values\n", " Delta35_vals = Delta35_start + scan_values\n", "\n", " P4_vals = np.empty(len(scan_values), dtype=float)\n", " P5_vals = np.empty(len(scan_values), dtype=float)\n", " P_upper_vals = np.empty(len(scan_values), dtype=float)\n", "\n", " # --------------------------------------------------------\n", " # Main scan loop\n", " # --------------------------------------------------------\n", " for k, s in enumerate(scan_values):\n", " L_current = L_offset_csr + s * L_scan_csr\n", "\n", " # Propagate only to final time, no intermediate time steps\n", " rho_t_vec = expm_multiply(L_current * t_final, rho0_vec)\n", " rho_t_vec = np.asarray(rho_t_vec).ravel()\n", "\n", " p4 = np.real(rho_t_vec[idx_p4])\n", " p5 = np.real(rho_t_vec[idx_p5])\n", "\n", " # Small numerical cleanup\n", " if p4 < 0 and abs(p4) < 1e-14:\n", " p4 = 0.0\n", " if p5 < 0 and abs(p5) < 1e-14:\n", " p5 = 0.0\n", "\n", " P4_vals[k] = p4\n", " P5_vals[k] = p5\n", " P_upper_vals[k] = p4 + p5\n", "\n", " return Delta34_vals, Delta35_vals, P4_vals, P5_vals, P_upper_vals" ] }, { "cell_type": "code", "execution_count": 3, "id": "37dac4ce-c6dc-4469-9902-8cd4079b5413", "metadata": {}, "outputs": [], "source": [ "def save_simultaneous_spectrum_csv(\n", " filename,\n", " scan_values,\n", " Delta34_vals,\n", " Delta35_vals,\n", " P4_vals,\n", " P5_vals,\n", " P_upper_vals,\n", " freq_unit_scale=2.0 * np.pi\n", "):\n", " \"\"\"\n", " Save simultaneous scan spectrum data to CSV.\n", "\n", " Parameters\n", " ----------\n", " filename : str\n", " Output CSV filename.\n", " scan_values : array\n", " Common scan variable in angular frequency units.\n", " Delta34_vals : array\n", " Scanned Delta34 values in angular frequency units.\n", " Delta35_vals : array\n", " Scanned Delta35 values in angular frequency units.\n", " P4_vals, P5_vals, P_upper_vals : array\n", " Excitation probabilities.\n", " freq_unit_scale : float\n", " Scale factor for converting angular frequency to plotted units.\n", " Default: 2*pi*1e6, so output detunings are in MHz.\n", " \"\"\"\n", "\n", " data = np.column_stack([\n", " scan_values / freq_unit_scale,\n", " Delta34_vals / freq_unit_scale,\n", " Delta35_vals / freq_unit_scale,\n", " P4_vals,\n", " P5_vals,\n", " P_upper_vals\n", " ])\n", "\n", " header = (\n", " \"scan_variable_MHz,\"\n", " \"Delta34_MHz,\"\n", " \"Delta35_MHz,\"\n", " \"P4,\"\n", " \"P5,\"\n", " \"P4_plus_P5\"\n", " )\n", "\n", " np.savetxt(\n", " filename,\n", " data,\n", " delimiter=\",\",\n", " header=header,\n", " comments=\"\"\n", " )\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "abb02e48-3e58-493f-9214-518841ebc792", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "if __name__ == \"__main__\":\n", " import matplotlib.pyplot as plt\n", "\n", " MHz = 2.0 * np.pi \n", " # Fixed interaction time\n", " t_final = 0.1\n", " # Rabi frequencies\n", " Omega12 = 100.0 * MHz\n", " Omega23 = 2000.0 * MHz\n", " Omega34 = 86.0 * MHz\n", " Omega35 = 50.0 * MHz\n", "\n", " # Lower detunings\n", " Delta12 = 10.0 * MHz\n", " Delta23 = -200.0 * MHz\n", "\n", " \n", " Ex=0\n", " Ey=2.5\n", " Ez=0\n", " alpha32=16.24\n", " alpha12=19.4\n", " # Upper detuning starting values\n", " Delta34_start = alpha32*(Ey**2+Ex**2+Ez**2)* MHz\n", " Delta35_start = alpha12*(Ey**2+Ex**2+Ez**2)* MHz\n", "\n", " # Decay rates\n", " tau2 = 26e-3\n", " tau3 = 46e-3\n", " tau4 = 43\n", " tau5 = 43\n", "\n", " gamma21 = 1.0 / tau2\n", " gamma32 = 1.0 / tau3\n", " gamma43 = 1.0 / tau4\n", " gamma53 = 1.0 / tau5\n", "\n", " # Laser linewidths\n", " laser_lw12 = 0.3 * MHz\n", " laser_lw23 = 0.3 * MHz\n", " laser_lw34 = 0.3 * MHz\n", " laser_lw35 = 0.3 * MHz\n", "\n", " \n", "\n", " # Common simultaneous scan\n", " scan_values = np.linspace(-45* MHz-Delta34_start,45*MHz- Delta34_start, 161)\n", "\n", " Delta34_vals, Delta35_vals, P4_vals, P5_vals, P_upper_vals = \\\n", " simultaneous_upper_detuning_spectrum_fast(\n", " scan_values=scan_values,\n", " Delta34_start=Delta34_start,\n", " Delta35_start=Delta35_start,\n", " Omega12=Omega12,\n", " Omega23=Omega23,\n", " Omega34=Omega34,\n", " Omega35=Omega35,\n", " Delta12=Delta12,\n", " Delta23=Delta23,\n", " gamma21=gamma21,\n", " gamma32=gamma32,\n", " gamma43=gamma43,\n", " gamma53=gamma53,\n", " laser_lw12=laser_lw12,\n", " laser_lw23=laser_lw23,\n", " laser_lw34=laser_lw34,\n", " laser_lw35=laser_lw35,\n", " t_final=t_final\n", " )\n", "\n", " plt.figure(figsize=(8, 5))\n", " plt.plot(-scan_values / MHz, P4_vals, label=r\"$P_4$\", lw=2)\n", " plt.plot(-scan_values / MHz, P5_vals, label=r\"$P_5$\", lw=2)\n", " plt.plot(-scan_values / MHz, P_upper_vals, \"--\", label=r\"$P_4 + P_5$\", lw=2)\n", " plt.xlabel(r\"Common scan variable $\\delta / 2\\pi$ (MHz)\")\n", " plt.ylabel(r\"Excitation probability at $t_{\\mathrm{final}}$\")\n", " plt.title(\"Optimized simultaneous excitation spectrum\")\n", " plt.legend()\n", " plt.tight_layout()\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 18, "id": "192f1e20-c025-46bc-94d7-d5beef7f119c", "metadata": {}, "outputs": [], "source": [ "save_simultaneous_spectrum_csv(\n", " filename=\"simultaneous_excitation_spectrum.csv\",\n", " scan_values=scan_values,\n", " Delta34_vals=Delta34_vals,\n", " Delta35_vals=Delta35_vals,\n", " P4_vals=P4_vals,\n", " P5_vals=P5_vals,\n", " P_upper_vals=P_upper_vals)" ] }, { "cell_type": "code", "execution_count": null, "id": "d722cae8-b2ce-45c6-8222-da1dfba27923", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.13.9" } }, "nbformat": 4, "nbformat_minor": 5 }