{ "cells": [ { "attachments": {}, "cell_type": "markdown", "id": "a5775784", "metadata": {}, "source": [ "# Simulating a Raman transition with constant lasers\n", "To present the features of the package, we show the simulation of a theoretically well understood transition that takes advantage of a detuning: the Raman transition. Here, we will simulate the system with constant lasers. For laser pulses see the second tutorial. \\\n", "Feel free to change parameters and play around to compare the simulation results with the theory." ] }, { "cell_type": "code", "execution_count": 2, "id": "f926d78a", "metadata": {}, "outputs": [], "source": [ "from atomcalc import Level, Laser, Decay, System, plot_pulse" ] }, { "attachments": {}, "cell_type": "markdown", "id": "f5b1ee93", "metadata": {}, "source": [ "We define the energy levels, the decay channels (here we assume no decay), the laser parameters, and the system. \\\n", "`Delta` is the detuning at `level3` and `delta` is the detuning at `level2` in angular frequency. The `Omega` are the Rabi frequencies of the corresponding lasers in angular frequency. \\\n", "The `detuning` argument of the laser is the detuning of the laser as an angular frequency. \\\n", "Using the `draw` function we can look at a sketch of the system." ] }, { "cell_type": "code", "execution_count": 3, "id": "428a7ee6", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "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", "# Alternatively: decay = Decay([0],[[level3,level1]]). It needs at least one entry.\n", "\n", "# define parameters\n", "Delta = 20\n", "delta = 0\n", "Omega1 = 1\n", "Omega2 = 1\n", "\n", "# define lasers (sort level couples from low to high energy.)\n", "laser1 = Laser(Omega1, Delta, [level1,level3])\n", "laser2 = Laser(Omega2, Delta-delta, [level2,level3])\n", "\n", "# define system (sort levels by energy in ascending order. The order of the lasers should not matter.)\n", "system = System([level1,level2,level3], [laser1,laser2], decay)\n", "\n", "# draw the system in matplotlib\n", "system.draw()" ] }, { "attachments": {}, "cell_type": "markdown", "id": "6f0d4e65", "metadata": {}, "source": [ "Now, we can simulate the time evolution of the level population. \\\n", "Note that a laser only affects the one specific transition that it is assigned to." ] }, { "cell_type": "code", "execution_count": 4, "id": "44bc3c0c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Hamiltonian in the rotating frame: Quantum object: dims = [[3], [3]], shape = (3, 3), type = oper, isherm = True\n", "Qobj data =\n", "[[ 0. 0. 0.5]\n", " [ 0. 0. 0.5]\n", " [ 0.5 0.5 20. ]]\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": [ "0.999536989981741" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# calculate and show the time evolution\n", "system.simulate([1,0,0], 1, 300, Diagonalization=True)" ] } ], "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 }