{ "cells": [ { "attachments": {}, "cell_type": "markdown", "id": "f763377a", "metadata": {}, "source": [ "# Simulating a Raman transition with laser pulses\n", "This tutorial builds on the first tutorial. \\\n", "We simulate the same system as in the first tutorial but with a time-dependent Rabi frequency of both lasers." ] }, { "cell_type": "code", "execution_count": 2, "id": "87f4c012", "metadata": {}, "outputs": [], "source": [ "from atomcalc import Level, Laser, Decay, System, plot_pulse\n", "import numpy as np" ] }, { "attachments": {}, "cell_type": "markdown", "id": "2581debe", "metadata": {}, "source": [ "We use the same parameters as in the first tutorial." ] }, { "cell_type": "code", "execution_count": 3, "id": "02efbfb2", "metadata": {}, "outputs": [], "source": [ "# define level objects\n", "level1 = Level(0)\n", "level2 = Level(20)\n", "level3 = Level(100)\n", "\n", "# define decay object\n", "decay = Decay([0,0],[[level3,level1],[level3,level2]]) # no decay\n", "\n", "# define parameters\n", "Delta = 20\n", "delta = 0\n", "Omega1 = 1\n", "Omega2 = 1" ] }, { "attachments": {}, "cell_type": "markdown", "id": "ce3faaf5", "metadata": {}, "source": [ "We define the pulses as functions depending on t. Here, we define gaussian pulses. \\\n", "`plot_pulse` is just a little function to draw the pulse with matplotlib." ] }, { "cell_type": "code", "execution_count": 4, "id": "a31b4102", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def pulse_1(t):\n", " return Omega1 * np.exp(-0.5 * ((t - 150) / (50)) ** 2)\n", "\n", "def pulse_2(t):\n", " return Omega2 * np.exp(-0.5 * ((t - 150) / (50)) ** 2)\n", "\n", "plot_pulse(pulse_1, range(0, 300, 1))" ] }, { "cell_type": "code", "execution_count": 5, "id": "99c51042", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# System\n", "laser1 = Laser(Omega1, Delta, [level1, level3], pulse=pulse_1)\n", "laser2 = Laser(Omega2, Delta - delta, [level2, level3], pulse=pulse_2)\n", "system = System([level1, level2, level3], [laser1, laser2], decay)\n", "system.draw()\n" ] }, { "attachments": {}, "cell_type": "markdown", "id": "6c19a5ce", "metadata": {}, "source": [ "The Trotter intervals determine how the pulse is discretized. In my master thesis this is explained in detail in the method and the appendix section. An excerpt is shown following this tutorial \\\n", "A Trotter interval is a time interval in which the pulse is assumed to be constant. \\\n", "A Trotter step is the distance in time where the population of the levels is calculated. \\\n", "In this example we calculate the population for every 3 time units and the pulse is assumed to be constant over time intervals of 6 time units." ] }, { "cell_type": "code", "execution_count": 6, "id": "d7045681", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Hamiltonian in the rotating frame: [[ 0.+0.j 0.+0.j 0.+0.j]\n", " [ 0.+0.j 0.+0.j 0.+0.j]\n", " [ 0.+0.j 0.+0.j 20.+0.j]]\n", "One trotterinterval has size 6.0.\n", "One trotter step has size 3.0.\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Maximum population of level 2:\n" ] }, { "data": { "text/plain": [ "0.7997789543219783" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# calculate and show the time evolution\n", "system.simulate([1, 0, 0],1,300,Diagonalization=True,Trotterintervals=50,points_per_TI=2)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "3c922a46", "metadata": {}, "source": [ "## Trotter decomposition (excerpt of my master thesis)\n", "\n", "\n", "\n", "\n", "This Figure shows the Trotter decomposition of a timeline and visualizes the parameters of the sourcecode. The illustration is done with `number_TI = 5` and `points_per_TI = 2`. The time discretization `td` defines the Trotter intervals where the respective Liouvillian `L[n]` is constant. The `trotter_step` defines the points in time where the density matrix is calculated.\n", "\n", "For every Trotter interval the respective Liouvillian is constant and for every `trotter_step` a density matrix is calculated. There are two conditions for the code to work: The number of Trotter intervals `number_TI` must be chosen so that the Trotter intervals have integer time. Additionally, `points_per_TI` must be chosen so that `trotter_step` is integer. Together that means $\\frac{\\texttt{maxtime}}{\\texttt{number\\_TI}\\cdot \\texttt{points\\_per\\_TI}}$ has to be an integer. In the illustrated example this would be fulfilled for `maxtime = 10`, for example." ] } ], "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": "3.9.12" } }, "nbformat": 4, "nbformat_minor": 5 }