{ "cells": [ { "cell_type": "markdown", "id": "ed66967b", "metadata": {}, "source": [ "# Driven dynamics with TLS\n", "\n", "Here, we demonstrate the socket-free TLS workflow using the `maxwelllink.LaserDrivenSimulation` electromagnetic solver. By resonantly coupling one cosine driving field to a two-level system (TLS), we aim to monitor the driven population dynamics of the TLS." ] }, { "cell_type": "markdown", "id": "26a64100", "metadata": {}, "source": [ "## 1. Defining Molecule\n", "\n", "We first create a `Molecule` instance using the non-socket mode, i.e., we directly initialize the TLS within the `Molecule` class:" ] }, { "cell_type": "code", "execution_count": 1, "id": "eb90582c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[Init Molecule] Operating in non-socket mode, using driver: tls\n" ] } ], "source": [ "import numpy as np\n", "import maxwelllink as mxl\n", "\n", "frequency_au = 1.0\n", "mu12 = 1\n", "\n", "molecule = mxl.Molecule(\n", " driver=\"tls\",\n", " driver_kwargs={\n", " \"omega\": frequency_au,\n", " \"mu12\": mu12,\n", " \"orientation\": 2,\n", " \"pe_initial\": 0e-3,\n", " }\n", ")" ] }, { "cell_type": "markdown", "id": "9404431e", "metadata": {}, "source": [ "## 2. Defining the driven field\n", "\n", "Then, we create a `LaserDrivenSimulation` instance which defines the parameters for a custom driven field. The pre-defined `molecule` is also attached to this class for coupled light-matter simulations.\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "efeaa956", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "init TLSModel with dt = 0.100000 a.u., molecule ID = 0\n", "[LaserDriven] Completed 1000/20000.0 [5.0%] steps, time/step: 7.49e-05 seconds, remaining time: 1.42 seconds.\n", "[LaserDriven] Completed 2000/20000.0 [10.0%] steps, time/step: 6.84e-05 seconds, remaining time: 1.29 seconds.\n", "[LaserDriven] Completed 3000/20000.0 [15.0%] steps, time/step: 6.60e-05 seconds, remaining time: 1.19 seconds.\n", "[LaserDriven] Completed 4000/20000.0 [20.0%] steps, time/step: 8.24e-05 seconds, remaining time: 1.17 seconds.\n", "[LaserDriven] Completed 5000/20000.0 [25.0%] steps, time/step: 8.32e-05 seconds, remaining time: 1.12 seconds.\n", "[LaserDriven] Completed 6000/20000.0 [30.0%] steps, time/step: 6.35e-05 seconds, remaining time: 1.02 seconds.\n", "[LaserDriven] Completed 7000/20000.0 [35.0%] steps, time/step: 5.97e-05 seconds, remaining time: 0.92 seconds.\n", "[LaserDriven] Completed 8000/20000.0 [40.0%] steps, time/step: 6.63e-05 seconds, remaining time: 0.85 seconds.\n", "[LaserDriven] Completed 9000/20000.0 [45.0%] steps, time/step: 5.97e-05 seconds, remaining time: 0.76 seconds.\n", "[LaserDriven] Completed 10000/20000.0 [50.0%] steps, time/step: 5.81e-05 seconds, remaining time: 0.68 seconds.\n", "[LaserDriven] Completed 11000/20000.0 [55.0%] steps, time/step: 5.82e-05 seconds, remaining time: 0.61 seconds.\n", "[LaserDriven] Completed 12000/20000.0 [60.0%] steps, time/step: 6.72e-05 seconds, remaining time: 0.54 seconds.\n", "[LaserDriven] Completed 13000/20000.0 [65.0%] steps, time/step: 7.82e-05 seconds, remaining time: 0.48 seconds.\n", "[LaserDriven] Completed 14000/20000.0 [70.0%] steps, time/step: 6.13e-05 seconds, remaining time: 0.41 seconds.\n", "[LaserDriven] Completed 15000/20000.0 [75.0%] steps, time/step: 5.84e-05 seconds, remaining time: 0.34 seconds.\n", "[LaserDriven] Completed 16000/20000.0 [80.0%] steps, time/step: 7.86e-05 seconds, remaining time: 0.27 seconds.\n", "[LaserDriven] Completed 17000/20000.0 [85.0%] steps, time/step: 8.04e-05 seconds, remaining time: 0.21 seconds.\n", "[LaserDriven] Completed 18000/20000.0 [90.0%] steps, time/step: 5.81e-05 seconds, remaining time: 0.14 seconds.\n", "[LaserDriven] Completed 19000/20000.0 [95.0%] steps, time/step: 7.13e-05 seconds, remaining time: 0.07 seconds.\n", "[LaserDriven] Completed 20000/20000.0 [100.0%] steps, time/step: 8.34e-05 seconds, remaining time: 0.00 seconds.\n" ] } ], "source": [ "\n", "from maxwelllink.tools import cosine_drive\n", "\n", "dt_au = 1e-1\n", "total_steps = 2e4\n", "\n", "# you are encouraged to try different field parameters\n", "omega_au_field = frequency_au * 1.0\n", "amplitude_au = 1e-2\n", "\n", "sim = mxl.LaserDrivenSimulation(\n", " molecules=[molecule],\n", " coupling_axis=\"z\",\n", " drive=cosine_drive(omega_au=omega_au_field, amplitude_au=amplitude_au),\n", " dt_au=dt_au,\n", " record_history=True,\n", ")\n", "\n", "sim.run(steps=total_steps)" ] }, { "cell_type": "markdown", "id": "6448af65", "metadata": {}, "source": [ "## 3. Retrieve simulation observables\n", "\n", "After the simulation, we can retrieve the TLS trajectory from `molecule.extra`." ] }, { "cell_type": "code", "execution_count": null, "id": "7ff5617a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Collected 20000 TLS samples.\n" ] } ], "source": [ "# users can also use molecule.additional_data_history to access the time-resolved data recorded during the simulation, \n", "# population = np.array([entry[\"Pe\"] for entry in molecule.additional_data_history])\n", "# tls_time_au = np.array([entry[\"time_au\"] for entry in molecule.additional_data_history])\n", "# but here we demonstrate the use of molecule.extra which is more convenient for post-processing and plotting. \n", "population = molecule.extra[\"Pe\"]\n", "tls_time_au = molecule.extra[\"time_au\"]\n", "\n", "print(\n", " f\"Collected {population.size} TLS samples.\"\n", ")" ] }, { "cell_type": "markdown", "id": "535b133b", "metadata": {}, "source": [ "## 4. Inspect time-domain Rabi oscillations\n", "\n", "According to the analytical rotating wave approximation, under near resonance excitation, the excited-state population $P_{\\rm e}(t)$ obeys:\n", "\n", "$$\n", "P_{\\rm e}(t) = \\frac{\\Omega_0^2}{\\Omega_{\\rm R}^2} \\sin^2(\\frac{\\Omega_{\\rm R} t}{2}).\n", "$$\n", "where $\\Omega_0 \\equiv \\mu_{12} E_0$ and $\\Omega_{\\rm R} = \\sqrt{\\Delta^2 + \\Omega_0^2}$, with $\\Delta = \\omega_0 - \\omega_{\\rm {ph}}$ denoting the light-matter detuning.\n", "\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "4b159ffe", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "# analytical solution under RWA\n", "Omega_0 = mu12 * amplitude_au\n", "Omega_R = np.sqrt(Omega_0**2 + (omega_au_field - frequency_au) ** 2)\n", "population_analytical = Omega_0**2 / Omega_R**2 * np.sin(Omega_R * tls_time_au / 2) ** 2\n", "\n", "plt.figure(figsize=(7, 4))\n", "plt.plot(tls_time_au, population, label=\"TLS excited-state population\")\n", "plt.plot(tls_time_au, population_analytical, label=\"Analytical population\", linestyle=\"--\")\n", "plt.xlabel(\"time (a.u.)\")\n", "plt.ylabel(\"Pe\")\n", "plt.title(\"TLS population dynamics\")\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "mxl", "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" }, "title": "Single-Mode Cavity with TLS" }, "nbformat": 4, "nbformat_minor": 5 }