Differential AC-Stark shift calculation on the S to P Transition of Beryllium at 1050 nm

be-shift.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip3 install atomphys\n",
    "# see https://github.com/mgrau/atomphys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from atomphys import Atom\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from math import pi as π\n",
    "\n",
    "# This example uses pint, it has to be installed\n",
    "try:\n",
    "    import pint\n",
    "except ImportError:\n",
    "    print('This example makes extensive use of the pint module. If it is not installed several code blocks will error')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Magnesium"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fetch the NIST transition data for Mg+\n",
    "Mg = Atom('Mg+')\n",
    "units = Mg.units\n",
    "c = units.c\n",
    "ε_0 = units.ε_0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "State(3S1/2, 2S1/2: 0 Ry)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Mg('S1/2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.00857300074692271 Hz cm<sup>2</sup> h/V<sup>2</sup>"
      ],
      "text/latex": [
       "$0.00857300074692271\\ \\frac{\\mathrm{Hz} \\cdot \\mathrm{cm}^{2} \\cdot \\mathrm{h}}{\\mathrm{V}^{2}}$"
      ],
      "text/plain": [
       "0.00857300074692271 <Unit('centimeter ** 2 * hertz * planck_constant / volt ** 2')>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate the static polarizability for the ground state\n",
    "Mg('S1/2').α().to('h Hz/(V/cm)^2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.73 Hz·cm²·h/W\n"
     ]
    }
   ],
   "source": [
    "# calculate the dynamic polarizability for the ground state at 1064 nm\n",
    "α0 = Mg('S1/2').α(λ=1064 * units.nm)\n",
    "print((α0/(2*c*ε_0)).to('h Hz/(W/cm^2)'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Beryllium"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fetch the NIST transition data for Mg+\n",
    "Be = Atom('Be+')\n",
    "units = Be.units\n",
    "c = units.c\n",
    "ε_0 = units.ε_0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "State(2S1/2, 2S1/2: 0 Ry)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Be('S1/2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.006008741924243778 Hz cm<sup>2</sup> h/V<sup>2</sup>"
      ],
      "text/latex": [
       "$0.006008741924243778\\ \\frac{\\mathrm{Hz} \\cdot \\mathrm{cm}^{2} \\cdot \\mathrm{h}}{\\mathrm{V}^{2}}$"
      ],
      "text/plain": [
       "0.006008741924243778 <Unit('centimeter ** 2 * hertz * planck_constant / volt ** 2')>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate the static polarizability for the ground state\n",
    "Be('S1/2').α().to('h Hz/(V/cm)^2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S1/2 = 1.24 Hz·cm²·h/W\n"
     ]
    }
   ],
   "source": [
    "# calculate the dynamic polarizability for the ground state at 1050 nm\n",
    "α0 = Be('S1/2').α(λ=1050 * units.nm)\n",
    "s = (α0/(2*c*ε_0)).to('h Hz/(W/cm^2)')\n",
    "print(f\"S1/2 = {s}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P1/2 = 0.0401 Hz·cm²·h/W\n"
     ]
    }
   ],
   "source": [
    "# calculate the dynamic polarizability for the ground state at 1050 nm\n",
    "α0 = Be('P1/2').α(λ=1050 * units.nm)\n",
    "p = (α0/(2*c*ε_0)).to('h Hz/(W/cm^2)')\n",
    "print(f\"P1/2 = {p}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "differential AC Stark shift = 1.2 Hz·cm²·h/W\n"
     ]
    }
   ],
   "source": [
    "diff = s - p\n",
    "print(f'differential AC Stark shift = {diff}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "w0 = 9 * units.um\n",
    "power = 1 * units.W\n",
    "intensity = 2 * power / (np.pi * w0 ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.7859503362562735 MW/cm<sup>2</sup>"
      ],
      "text/latex": [
       "$0.7859503362562735\\ \\frac{\\mathrm{MW}}{\\mathrm{cm}^{2}}$"
      ],
      "text/plain": [
       "0.7859503362562735 <Unit('megawatt / centimeter ** 2')>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "intensity.to(units.MW / (units.cm) ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "shift = intensity * diff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.9428513622351195 MHz h"
      ],
      "text/latex": [
       "$0.9428513622351195\\ \\mathrm{MHz} \\cdot \\mathrm{h}$"
      ],
      "text/plain": [
       "0.9428513622351195 <Unit('megahertz * planck_constant')>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shift.to(units.MHz * units.h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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