Updated_Lattice_Light_Shift_Calculations.ipynb

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   "source": [
    "# Light shift Calculations"
   ]
  },
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   "source": [
    "**These calculations come from the following paper:**  \n",
    "https://arxiv.org/pdf/physics/9902072v1.pdf  \n",
    "OPTICAL DIPOLE TRAPS FOR NEUTRAL ATOMS  \n",
    "Rudolf Grimm and Matthias Weidemu¨ller \n"
   ]
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   },
   "source": [
    "## Setup"
   ]
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   "source": [
    "### Imports"
   ]
  },
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   "source": [
    "import sys\n",
    "sys.path.append('..')"
   ]
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   "source": [
    "%config Completer.use_jedi = False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
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   "source": [
    "import Analysis_Python_Files.MarksConstants as mc"
   ]
  },
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       "            paths: {\n",
       "                'plotly': ['https://cdn.plot.ly/plotly-latest.min']\n",
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       "        require(['plotly'], function(Plotly) {\n",
       "            window._Plotly = Plotly;\n",
       "        });\n",
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       "        </script>\n",
       "        "
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   "source": [
    "import numpy as np \n",
    "from numpy import array as arr\n",
    "import pandas as pd\n",
    "import plotly.offline as pltly\n",
    "pltly.init_notebook_mode(connected=True)\n",
    "from plotly import graph_objs as go\n",
    "import math\n",
    "import scipy.optimize as opt\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.colors import ListedColormap\n",
    "import warnings \n",
    "warnings.filterwarnings('module')\n",
    "from datetime import datetime\n",
    "import uncertainties.unumpy\n",
    "import IPython\n",
    "import pandas as pd\n",
    "import pickle\n",
    "\n",
    "from matplotlib.pyplot import *\n",
    "from matplotlib import rcParams\n",
    "from matplotlib import style\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.dates as mdates\n",
    "%matplotlib inline\n",
    "\n",
    "# ## set matplotlib plot defaults :D\n",
    "# Style controls many default colors in matplotlib plots.\n",
    "# Change the following if you don't like dark backgrounds. Many other options.\n",
    "import matplotlib as mpl\n",
    "\n",
    "if False:\n",
    "    # My Dark Settings\n",
    "    style.use(['dark_background'])\n",
    "    c = '#0A0A0A'\n",
    "    mpl.rcParams['axes.facecolor'] = '#000000'\n",
    "    mpl.rcParams['figure.edgecolor'] = c\n",
    "    mpl.rcParams['figure.facecolor'] = c\n",
    "else:\n",
    "    # My Light Settings\n",
    "    style.use(['default'])\n",
    "    c = '#FFFFFF'\n",
    "    mpl.rcParams['axes.facecolor'] = c\n",
    "    mpl.rcParams['figure.edgecolor'] = c\n",
    "    mpl.rcParams['figure.facecolor'] = c  \n",
    "# the default cycling of colors in this mode isn't very good.\n",
    "#rcParams['axes.prop_cycle'] = (\"cycler('color', ['r','c','g','#FFFFFF','b']) + cycler('marker', ['o','v','<','>','^'])\")\n",
    "### General\n",
    "rcParams['figure.figsize'] = (25.0, 8.0)\n",
    "rcParams['axes.grid'] = True\n",
    "rcParams['axes.formatter.useoffset'] = False\n",
    "rcParams['grid.alpha'] = 0.15\n",
    "rcParams['axes.formatter.limits'] = (-3,3)\n",
    "rcParams['image.cmap'] = 'viridis'\n",
    "#rcParams['image.cmap'] = dark_viridis_cmap\n",
    "# to see all available options, decomment this line.\n",
    "# print(mpl.rcParams)\n",
    "rcParams['font.size'] = 14\n",
    "from matplotlib import cm\n",
    "viridis = cm.get_cmap('viridis', 256)\n",
    "dark_viridis = []\n",
    "bl = 0.15\n",
    "for i in range(256):\n",
    "    dark_viridis.append(list(viridis(i)))\n",
    "    dark_viridis[-1][0] = dark_viridis[-1][0] *(bl+(1-bl)*i/255)\n",
    "    dark_viridis[-1][1] = dark_viridis[-1][1] *(bl+(1-bl)*i/255)\n",
    "    dark_viridis[-1][2] = dark_viridis[-1][2] *(bl+(1-bl)*i/255)\n",
    "dark_viridis_cmap = ListedColormap(dark_viridis)"
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   "source": [
    "## Functions"
   ]
  },
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   "source": [
    "### powerFromFrequency(frequency, waist, lightWavelength, latticeWavelength)"
   ]
  },
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   "source": [
    "Assuming a gaussian beam and pi polarization, we have\n",
    "$$\n",
    "Power \\equiv P\\{\\omega_t\\} = -\\frac{(2\\pi)^2 mw_{\\text{beam}}^2\\omega_{\\text{t}}^2\\lambda^2}{8c^2\\bigg(2 \\frac{\\Gamma_{D2}}{\\omega_{D2}^3*\\Delta_{D2}} + \\frac{\\Gamma_{D1}}{\\omega_{D1}^3*\\Delta_{D1}}\\bigg)}\n",
    "$$"
   ]
  },
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      "C:\\Users\\wdwor\\Miniconda3\\lib\\site-packages\\ipykernel\\ipkernel.py:283: DeprecationWarning:\n",
      "\n",
      "`should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.\n",
      "\n"
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   "source": [
    "def powerFromFrequency(frequency, waist, lightWavelength, latticeWavelength):    \n",
    "    import numpy as np\n",
    "    ### constants\n",
    "    # in kg\n",
    "    mass = 1.443*10**(-25)\n",
    "    # in Hz\n",
    "    d1TransitionFrequency = 384.2*10**12\n",
    "    d2TransitionFrequency = 377.1*10**12\n",
    "    c = 2.998*10**8\n",
    "    # linewidth is equivalent to the \n",
    "    d1LineWidth = 36.1*10**6\n",
    "    d2LineWidth = 38.11*10**6\n",
    "    # from inputs & constants\n",
    "    detuningFromD1 = d1TransitionFrequency - c / lightWavelength\n",
    "    detuningFromD2 = d2TransitionFrequency - c / lightWavelength\n",
    "    # calculation\n",
    "    power = (((2*np.pi)**2 * mass * (waist**2) * (2*np.pi*frequency)**2*(latticeWavelength**2)) \n",
    "            / (8 * (c**2)* (2 * d2LineWidth/(d2TransitionFrequency**3*detuningFromD2) \n",
    "                                       + (d1LineWidth/(d1TransitionFrequency**3*detuningFromD1)))))\n",
    "    return power"
   ]
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   "source": [
    "print(powerFromFrequency(810, 1000, ))"
   ]
  },
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   "source": [
    "### trapFrequency(power, waist, lightWavelength, latticeWavelength)"
   ]
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   "source": [
    "We have\n",
    "$$\n",
    "\\text{trap frequency} \\equiv \\nu_t = \\frac{1}{\\lambda_t} \\sqrt{\\frac{2D}{m_{rb}}}= \\sqrt{\\frac{8 c^2  P}{\\lambda_t^2m_{rb}w_{waist}^2(2\\pi)^4}\\bigg(\\frac{2\\Gamma_{D2}}{\\nu_{D2}^3\\Delta_{D2}} + \\frac{\\Gamma_{D1}}{\\nu_{D1}^3\\Delta_{D1}}  \\bigg)}\n",
    "$$"
   ]
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   "source": [
    "def trapFrequency(power, waist, lightWavelength, latticeWavelength):\n",
    "    mass = 1.443*10**(-25)\n",
    "    depth = trapDepth(power, waist, lightWavelength)\n",
    "    frequency = (1 /  latticeWavelength) * np.sqrt(2*depth / mass)\n",
    "    return frequency\n",
    "\n"
   ]
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   "source": [
    "### trapDepth(power, waist, lightWavelength)"
   ]
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   "source": [
    "Assuming a Gaussian Beam, we have\n",
    "$$\n",
    "\\text{Depth} \\equiv D = \\frac{4 c^2  P}{w_{waist}^2(2\\pi)^4}\\bigg(\\frac{2\\Gamma_{D2}}{\\nu_{D2}^3\\Delta_{D2}} + \\frac{\\Gamma_{D1}}{\\nu_{D1}^3\\Delta_{D1}}  \\bigg)\n",
    "$$"
   ]
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   "source": [
    "def trapDepth(power, waist, lightWavelength):\n",
    "    \"\"\"\n",
    "    Assumes PI polarization (exchange 2->2+P and 1->1-P)\n",
    "    \"\"\"\n",
    "    # natural linewidth is equivalent to the decay rate\n",
    "    detuningFromD1 = mc.Rb87_D1LineFrequency - mc.c / lightWavelength\n",
    "    detuningFromD2 = mc.Rb87_D2LineFrequency - mc.c / lightWavelength\n",
    "    chi = (mc.Rb87_D1Gamma/(mc.Rb87_D1LineFrequency**3 * detuningFromD1) \n",
    "           + 2 * mc.Rb87_D2Gamma / (mc.Rb87_D2LineFrequency**3 * detuningFromD2))\n",
    "    depth = ((4 * mc.c**2 * power) / (waist**2 * (2*np.pi)**4)) * chi\n",
    "    return depth\n",
    "      "
   ]
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   "source": [
    "### scatterRate(power, waistAtTrap, lightWavelength)"
   ]
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   "source": [
    "$$\n",
    "\\text{Scattering Rate} \\equiv \\Gamma_{\\text{sc}} = \\frac{4c^2P}{\\hbar w^2(2\\pi)^5}\\bigg(\\frac{2 \\Gamma_{D2}^2}{\\Delta_{D2}^2 \\nu_{D2}^3}+\\frac{\\Gamma_{D1}^2}{\\Delta_{D2}^2 \\nu_{D2}^3}\\bigg)\n",
    "$$"
   ]
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   "source": [
    "def scatterRate(power, waist, lightWavelength):\n",
    "    # natural linewidth is equivalent to the decay rate\n",
    "    deltaD1 = mc.Rb87_D1LineFrequency - mc.c / lightWavelength\n",
    "    deltaD2 = mc.Rb87_D2LineFrequency - mc.c / lightWavelength\n",
    "    #print(deltaD2, deltaD1)\n",
    "    scatteringRate = (mc.c**2 * 4 * power / (mc.hbar * waist**2)*(2 * mc.pi)**(-5)\n",
    "                    * (2 * mc.Rb87_D2Gamma**2 / (deltaD2**2*mc.Rb87_D2LineFrequency**3) \n",
    "                       + mc.Rb87_D1Gamma**2 / (deltaD1**2*mc.Rb87_D1LineFrequency**3)))\n",
    "    return scatteringRate    "
   ]
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   "source": [
    "### Tweezer Depth"
   ]
  },
  {
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   "execution_count": 9,
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   "source": [
    "def tweezerDepth(power, waist, wavelength):\n",
    "    # from inputs & constants\n",
    "    deltaD1 = mc.Rb87_D1LineFrequency - mc.c / wavelength\n",
    "    deltaD2 = mc.Rb87_D2LineFrequency - mc.c / wavelength\n",
    "    # calculation\n",
    "    chi = (2 * mc.Rb87_D2Gamma / (deltaD2 * mc.Rb87_D2LineFrequency**3) \n",
    "           + mc.Rb87_D1Gamma / (deltaD1 * mc.Rb87_D1LineFrequency**3))\n",
    "    depth = mc.c**2 * power / ((2*np.pi)**4*waist**2) * chi\n",
    "    # in joules\n",
    "    return depth"
   ]
  },
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   "source": [
    "### Tweezer+Lattice Depth"
   ]
  },
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   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
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   "source": [
    "def latticeDepth(latticePower, latticeWaist, latticeLightWavelength,\n",
    "                 latticeTrapWavelength, z, latticePhase):\n",
    "    deltaD1Lattice = mc.Rb87_D1LineFrequency - mc.c / latticeLightWavelength\n",
    "    deltaD2Lattice = mc.Rb87_D2LineFrequency - mc.c / latticeLightWavelength\n",
    "    # calculation\n",
    "    chiLattice = (2 *  mc.Rb87_D2Gamma / (deltaD2Lattice * mc.Rb87_D2LineFrequency**3) \n",
    "                  +  mc.Rb87_D1Gamma / (deltaD1Lattice * mc.Rb87_D1LineFrequency**3))\n",
    "    commonFactor = mc.c**2/(2*np.pi)**4\n",
    "    latticeDepth = commonFactor * 4 * latticePower * chiLattice / latticeWaist**2 \\\n",
    "                    * (np.cos(2*np.pi / latticeTrapWavelength * z + latticePhase))**2\n",
    "    return latticeDepth\n",
    "    "
   ]
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   "source": [
    "latticeDepth(0.2, 5.985916001243852e-05, 850e-9, 850e-9, 0, 0)/mc.k_B*1e6"
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   "source": [
    "def tweezerPlusLatticeDepth(tweezerPower, tweezerWaist, tweezerWavelength, latticePower, latticeWaist, \n",
    "                            latticeLightWavelength, latticeTrapWavelength, z, latticePhase):\n",
    "    # from inputs & constants\n",
    "    deltaD1Tweezer = mc.Rb87_D1LineFrequency - mc.c / tweezerWavelength\n",
    "    deltaD2Tweezer = mc.Rb87_D2LineFrequency - mc.c / tweezerWavelength\n",
    "    deltaD1Lattice = mc.Rb87_D1LineFrequency - mc.c / latticeLightWavelength\n",
    "    deltaD2Lattice = mc.Rb87_D2LineFrequency - mc.c / latticeLightWavelength\n",
    "    # calculation\n",
    "    chiTweezer = (2 *  mc.Rb87_D2Gamma / (deltaD2Tweezer * mc.Rb87_D2LineFrequency**3) \n",
    "                  +  mc.Rb87_D1Gamma / (deltaD1Tweezer * mc.Rb87_D1LineFrequency**3))\n",
    "    chiLattice = (2 *  mc.Rb87_D2Gamma / (deltaD2Lattice * mc.Rb87_D2LineFrequency**3) \n",
    "                  +  mc.Rb87_D1Gamma / (deltaD1Lattice * mc.Rb87_D1LineFrequency**3))\n",
    "    \n",
    "    commonFactor = mc.c**2/(2*np.pi)**4\n",
    "    tweezerRayleighRange = np.pi * tweezerWaist**2 / tweezerWavelength\n",
    "    tweezerDynamicWaist = tweezerWaist * np.sqrt(1 + (z/tweezerRayleighRange)**2)\n",
    "    tweezerDepth = commonFactor * tweezerPower * chiTweezer / tweezerDynamicWaist**2\n",
    "    latticeDepth = commonFactor * 4 * latticePower * chiLattice / latticeWaist**2 \\\n",
    "                    * (np.cos(2*np.pi / latticeTrapWavelength * z + latticePhase))**2\n",
    "    return tweezerDepth + latticeDepth\n",
    "    "
   ]
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    "def tweezerPlusLatticeDepth(tweezerPower, tweezerWaist, tweezerWavelength, latticePower, latticeWaist, \n",
    "                            latticeLightWavelength, latticeTrapWavelength, z, latticePhase):\n",
    "    # from inputs & constants\n",
    "    deltaD1Tweezer = mc.Rb87_D1LineFrequency - mc.c / tweezerWavelength\n",
    "    deltaD2Tweezer = mc.Rb87_D2LineFrequency - mc.c / tweezerWavelength\n",
    "    deltaD1Lattice = mc.Rb87_D1LineFrequency - mc.c / latticeLightWavelength\n",
    "    deltaD2Lattice = mc.Rb87_D2LineFrequency - mc.c / latticeLightWavelength\n",
    "    # calculation\n",
    "    chiTweezer = (2 * mc.Rb87_D2Gamma / (deltaD2Tweezer * mc.Rb87_D2LineFrequency**3) \n",
    "                  + mc.Rb87_D1Gamma / (deltaD1Tweezer * mc.Rb87_D1LineFrequency**3))\n",
    "    chiLattice = (2 * mc.Rb87_D2Gamma / (deltaD2Lattice * mc.Rb87_D2LineFrequency**3) \n",
    "                  + mc.Rb87_D1Gamma / (deltaD1Lattice * mc.Rb87_D1LineFrequency**3))\n",
    "    \n",
    "    commonFactor = mc.c**2/(2*np.pi)**4\n",
    "    tweezerRayleighRange = np.pi * tweezerWaist**2 / tweezerWavelength\n",
    "    tweezerDynamicWaist = tweezerWaist * np.sqrt(1 + (z/tweezerRayleighRange)**2)\n",
    "    tweezerDepth = commonFactor * tweezerPower * chiTweezer / tweezerDynamicWaist**2\n",
    "    latticeDepth = commonFactor * 4 * latticePower * chiLattice / latticeWaist**2 \\\n",
    "                    * (np.cos(2*np.pi / latticeTrapWavelength * z + latticePhase))**2\n",
    "    return tweezerDepth + latticeDepth\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "wavelengthInc = 1\n",
    "depthProfile[wavelengthInc] = tweezerPlusLatticeDepth( tweezerPower, tweezerWaist, tweezerWavelength, powerEstimate,\n",
    "                                                       latticeWaist, lightWavelengths[wavelengthInc], \n",
    "                                                       latticeWavelengths[wavelengthInc], positions, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": "false",
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "source": [
    "### Tweezer Frequency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-04-26T13:46:59.818745",
     "start_time": "2017-04-26T13:46:59.663586"
    },
    "heading_collapsed": "false",
    "hidden": true,
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "def tweezerFrequency(power, waist, wavelength):\n",
    "    deltaD1 = mc.Rb87_D1LineFrequency - mc.c / wavelength\n",
    "    deltaD2 = mc.Rb87_D2LineFrequency - mc.c / wavelength\n",
    "    # calculation\n",
    "    chi = (2 * mc.Rb87_D2Gamma / (deltaD2 * mc.Rb87_D2LineFrequency**3) \n",
    "           + mc.Rb87_D1Gamma / (deltaD1 * mc.Rb87_D1LineFrequency**3))\n",
    "    nu_t = mc.c * wavelength / ((2 * np.pi)**4 * waist**3) * np.sqrt(8 * power * chi / mc.Rb87_M)\n",
    "    return nu_t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-04-26T13:46:59.949941",
     "start_time": "2017-04-26T13:46:59.821248"
    },
    "heading_collapsed": "false",
    "hidden": true,
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "121.72574108902138khz\n",
      "0.016760194444177024\n"
     ]
    }
   ],
   "source": [
    "intensity = 3.185 * 10**11 * 0.00715\n",
    "power = intensity * waist**2 * np.pi/2\n",
    "print(str(tweezerFrequency(power, 700e-9, 850e-9)*1e-3) + \"khz\")\n",
    "print(power)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": "false",
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "source": [
    "### Lattice + Tweezer freq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def latticeTweezerTrapFrequency(tweezerPower, tweezerWaist, tweezerLightWavelength, latticePower,\n",
    "                                latticeWaist, latticeLightWavelength, latticeWavelength):\n",
    "    deltaD1Tweezer = - mc.Rb87_D1LineFrequency + mc.c / tweezerLightWavelength\n",
    "    deltaD2Tweezer = - mc.Rb87_D2LineFrequency + mc.c / tweezerLightWavelength\n",
    "    deltaD1Lattice = - mc.Rb87_D1LineFrequency + mc.c / latticeLightWavelength\n",
    "    deltaD2Lattice = - mc.Rb87_D2LineFrequency + mc.c / latticeLightWavelength\n",
    "    # calculation\n",
    "    chiTweezer = (2 * mc.Rb87_D2Gamma / (deltaD2Tweezer * mc.Rb87_D2LineFrequency**3) \n",
    "                  + mc.Rb87_D1Gamma / (deltaD1Tweezer * mc.Rb87_D1LineFrequency**3))\n",
    "    chiLattice = (2 * mc.Rb87_D2Gamma / (deltaD2Lattice * mc.Rb87_D2LineFrequency**3) \n",
    "                  + mc.Rb87_D1Gamma / (deltaD1Lattice * mc.Rb87_D1LineFrequency**3))\n",
    "    omegat = np.sqrt(-(mc.c**2 / (mc.Rb87_M * (2 * np.pi)**3))\n",
    "                     * (chiLattice * 16 * np.pi * latticePower / (latticeWaist**2 * latticeWavelength**2)\n",
    "                     + chiTweezer * tweezerPower * tweezerLightWavelength**2/(np.pi**3*tweezerWaist**6)))\n",
    "    return omegat/(2*np.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-04-26T13:47:00.293836",
     "start_time": "2017-04-26T13:47:00.108205"
    },
    "heading_collapsed": "false",
    "hidden": true,
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "38589.20851788066\n",
      "65825.54272506153\n",
      "0.8155452374157985\n"
     ]
    }
   ],
   "source": [
    "intensity = 3.185 * 10**11 * 0.00715\n",
    "waist = 707*10**-9\n",
    "power = intensity * waist**2 * np.pi/2\n",
    "print(latticeTweezerTrapFrequency(power, waist, 850e-9,\n",
    "                                  0 * 1.4 * 0.8 * 0.8 * 0.9, \n",
    "                                  170e-6, 850e-9, 850e-9*np.sqrt(2)))\n",
    "print(trapFrequency(1.4*0.8*0.8*0.9, 170e-6, 850e-9, 850e-9 * np.sqrt(2)))\n",
    "print(powerFromFrequency(70000, 170e-6, 850e-9, 850e-9 * np.sqrt(2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": "false",
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "source": [
    "## Calculations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-04-26T13:47:00.295337",
     "start_time": "2017-04-26T19:46:50.053Z"
    },
    "heading_collapsed": "false",
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'h' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-19-9d465d3c0292>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m     33\u001b[0m \u001b[1;31m# second plot\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     34\u001b[0m \u001b[0max2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0max1\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtwinx\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 35\u001b[1;33m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlightWavelengths\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdepths\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m10\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mh\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'y'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmarker\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'o'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmarkevery\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mindex850\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mindex820\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'Lattice Trap Depth'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     36\u001b[0m \u001b[0max2\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mset_ylabel\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'Depth'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcolor\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'y'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     37\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mtl\u001b[0m \u001b[1;32min\u001b[0m \u001b[0max2\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_yticklabels\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'h' is not defined"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2500x800 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# in hertz\n",
    "desiredTrapFrequency = 75e3\n",
    "# waist is in meters\n",
    "trapWaist = 170e-6\n",
    "# (in meters) This is different from the wavelength because of the bowtie configuration.\n",
    "powerEstimate = 1.4 * 0.8 * 0.8 * 0.9\n",
    "# \n",
    "tweezerWavelength = 850*10**-9\n",
    "tweezerIntensity = 3.185 * 10**11 * 0.00715\n",
    "tweezerWaist = 707*10**-9\n",
    "tweezerPower = tweezerIntensity * tweezerWaist**2 * np.pi/2\n",
    "\n",
    "lightWavelengths = np.linspace(810*10**-9, 860*10**-9, 101)\n",
    "latticeWavelengths = np.sqrt(2) * lightWavelengths\n",
    "\n",
    "trapFrequencies = trapFrequency(powerEstimate, trapWaist, lightWavelengths, latticeWavelengths)\n",
    "totalTrapFrequencies = latticeTweezerTrapFrequency(power, waist, tweezerWavelength, powerEstimate, trapWaist, lightWavelengths, latticeWavelengths)\n",
    "depths = trapDepth(powerEstimate, trapWaist, lightWavelengths)\n",
    "scatterRates = scatterRate(powerEstimate, trapWaist, lightWavelengths)\n",
    "index850 = np.where(lightWavelengths==850*10**-9)[0][0]\n",
    "index820 = np.where(lightWavelengths==820*10**-9)[0][0]\n",
    "fig, ax1 = plt.subplots()\n",
    "plt.plot(lightWavelengths, scatterRates, 'r', marker='o', markevery=[index850, index820], label='Lattice Scattering Rate')\n",
    "ax1.set_ylabel('Scatter Rate (Hz)', color='r')\n",
    "for tl in ax1.get_yticklabels():\n",
    "    tl.set_color('r')\n",
    "ax1.grid(color='r')\n",
    "ax1.annotate(\"{:.1f}\".format(scatterRates[index850]),\n",
    "             xy=(lightWavelengths[index850], scatterRates[index850]+0.5), color='r')\n",
    "ax1.annotate(\"{:.1f}\".format(scatterRates[index820]),\n",
    "             xy=(lightWavelengths[index820], scatterRates[index820]+0.5), color='r')\n",
    "ax1.legend(loc=6)\n",
    "# second plot\n",
    "ax2 = ax1.twinx()\n",
    "plt.plot(lightWavelengths, depths*10**-3/h, 'y', marker='o', markevery=[index850, index820], label='Lattice Trap Depth')\n",
    "ax2.set_ylabel('Depth', color='y')\n",
    "for tl in ax2.get_yticklabels():\n",
    "    tl.set_color('y')\n",
    "ax2.set_yticks(np.arange(0,2200,500))\n",
    "ax2.grid(color='y')\n",
    "ax2.set_ylim(0,2200)\n",
    "ax2.yaxis.set_label_coords(1.035, 0.9)\n",
    "ax2.annotate(\"{:.1f}\".format(depths[index850]*10**-3/h),\n",
    "             xy=(lightWavelengths[index850], depths[index850]*10**-3/h+50), color='y')\n",
    "ax2.annotate(\"{:.1f}\".format(depths[index820]*10**-3/h),\n",
    "             xy=(lightWavelengths[index820], depths[index820]*10**-3/h+50), color='y')\n",
    "ax2.legend(loc=1)\n",
    "# third\n",
    "ax3 = ax1.twinx()\n",
    "plt.plot(lightWavelengths, trapFrequencies*10**-3, 'c', marker='o', markevery=[index850, index820], label='Lattice Trap Frequency')\n",
    "plt.plot(lightWavelengths, totalTrapFrequencies*10**-3, 'c', linestyle='--', marker='o', markevery=[index850, index820], label='Lattice+Tweezer Trap Frequency')\n",
    "ax3.set_ylabel('Trap Frequency', color='c')\n",
    "for tl in ax3.get_yticklabels():\n",
    "    tl.set_color('c')\n",
    "ax3.set_yticks(np.arange(0,130,25))\n",
    "ax3.grid(color='c')\n",
    "ax3.set_ylim(0,130)\n",
    "ax3.yaxis.set_label_coords(1.035, 0.1)\n",
    "ax3.annotate(\"{:.1f}\".format(trapFrequencies[index850]*10**-3),\n",
    "             xy=(lightWavelengths[index850], trapFrequencies[index850]*10**-3+5), color='c')\n",
    "ax3.annotate(\"{:.1f}\".format(trapFrequencies[index820]*10**-3),\n",
    "             xy=(lightWavelengths[index820], trapFrequencies[index820]*10**-3+5), color='c')\n",
    "ax3.annotate(\"{:.1f}\".format(totalTrapFrequencies[index850]*10**-3),\n",
    "             xy=(lightWavelengths[index850], totalTrapFrequencies[index850]*10**-3+5), color='c')\n",
    "ax3.annotate(\"{:.1f}\".format(totalTrapFrequencies[index820]*10**-3),\n",
    "             xy=(lightWavelengths[index820], totalTrapFrequencies[index820]*10**-3+5), color='c')\n",
    "\n",
    "ax3.set_xlim(810*10**-9, 860*10**-9)\n",
    "ax3.legend(loc=4)\n",
    "plt.title('Trap Parameters at different light wavelengths');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-04-26T13:47:00.296338",
     "start_time": "2017-04-26T19:46:50.055Z"
    },
    "heading_collapsed": "false",
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\wdwor\\Miniconda3\\lib\\site-packages\\ipykernel\\ipkernel.py:283: DeprecationWarning:\n",
      "\n",
      "`should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.\n",
      "\n"
     ]
    },
    {
     "ename": "NameError",
     "evalue": "name 'h' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-20-4bc4a5630bb7>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m     19\u001b[0m                                                           \u001b[0mlatticeWaist\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlightWavelengths\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mwavelengthInc\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     20\u001b[0m                                                           latticeWavelengths[wavelengthInc], positions, 0)\n\u001b[1;32m---> 21\u001b[1;33m     \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpositions\u001b[0m \u001b[1;33m*\u001b[0m \u001b[1;36m10\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m6\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m-\u001b[0m\u001b[0mdepthProfile\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mwavelengthInc\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m/\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mh\u001b[0m \u001b[1;33m*\u001b[0m \u001b[1;36m10\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m6\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mstr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlightWavelengths\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mwavelengthInc\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m10\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m9\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;34m' nm'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     22\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mxlabel\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34mr'Position $(\\mu m)$'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     23\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mylabel\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'Depth (MHz)'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'h' is not defined"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 2500x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# (in meters) This is different from the wavelength because of the bowtie configuration.\n",
    "powerEstimate = 1.4 * 0.8 * 0.8 * 0.9\n",
    "# \n",
    "tweezerWavelength = 850*10**-9\n",
    "tweezerIntensity = 3.185 * 10**11 * 0.00715\n",
    "tweezerWaist = 707*10**-9\n",
    "latticeWaist = 170*10**-6\n",
    "tweezerPower = tweezerIntensity * tweezerWaist**2 * np.pi/2\n",
    "positions = np.linspace(-2*10**-6, 2*10**-6, 1000)\n",
    "lightWavelengths = np.linspace(810 * 10**-9, 860 * 10**-9, 6)\n",
    "latticeWavelengths = np.sqrt(2) * lightWavelengths\n",
    "depthProfile = np.zeros([len(lightWavelengths), len(positions)])\n",
    "phases = np.linspace(0, np.pi/2, 4)\n",
    "\n",
    "plt.figure(1)\n",
    "plt.title('Trap profile with different wavelengths of lattice light')\n",
    "for wavelengthInc in range(len(lightWavelengths)):\n",
    "    depthProfile[wavelengthInc] = tweezerPlusLatticeDepth(tweezerPower, tweezerWaist, tweezerWavelength, powerEstimate,\n",
    "                                                          latticeWaist, lightWavelengths[wavelengthInc], \n",
    "                                                          latticeWavelengths[wavelengthInc], positions, 0)\n",
    "    plt.plot(positions * 10**6, -depthProfile[wavelengthInc] / (h * 10**6), label=str(lightWavelengths[wavelengthInc]*10**9) + ' nm')\n",
    "plt.xlabel(r'Position $(\\mu m)$')\n",
    "plt.ylabel('Depth (MHz)')\n",
    "plt.legend()\n",
    "\n",
    "plt.figure(2)\n",
    "plt.title('Trap Profile for different phases with lattice light at ' + str(lightWavelengths[0]*10**9) + ' nm')\n",
    "for phaseInc in range(len(phases)):\n",
    "    depthProfile[phaseInc] = tweezerPlusLatticeDepth(tweezerPower, tweezerWaist, tweezerWavelength, powerEstimate,\n",
    "                                                          latticeWaist, lightWavelengths[0], latticeWavelengths[0], positions, phases[phaseInc])\n",
    "    plt.plot(positions * 10**6, -depthProfile[phaseInc] / (h * 10**6), label=str(phases[phaseInc]))\n",
    "plt.xlabel(r'Position $(\\mu m)$')\n",
    "plt.ylabel('Depth (MHz)')\n",
    "plt.legend()\n",
    "\n",
    "plt.figure(3)\n",
    "plt.title('Trap Profile for different phases with lattice light at ' + str(lightWavelengths[-2]*10**9) + ' nm')\n",
    "for phaseInc in range(len(phases)):\n",
    "    depthProfile[phaseInc] = tweezerPlusLatticeDepth(tweezerPower, tweezerWaist, tweezerWavelength, powerEstimate,\n",
    "                                                          latticeWaist, lightWavelengths[-2], latticeWavelengths[-2], positions, phases[phaseInc])\n",
    "    plt.plot(positions * 10**6, -depthProfile[phaseInc] / (h * 10**6), label=str(phases[phaseInc]))\n",
    "plt.xlabel(r'Position $(\\mu m)$')\n",
    "plt.ylabel('Depth (MHz)')\n",
    "plt.legend();\n",
    "\n",
    "plt.figure(4)\n",
    "plt.title('Trap Profile for different lattice powers with the lattice light at ' + str(lightWavelengths[0]*10**9) + ' nm')\n",
    "powers = np.linspace(0, powerEstimate, 4)\n",
    "for powerInc in range(len(powers)):\n",
    "    depthProfile[powerInc] = tweezerPlusLatticeDepth(tweezerPower, tweezerWaist, tweezerWavelength, powers[powerInc],\n",
    "                                                     latticeWaist, lightWavelengths[0], latticeWavelengths[0], positions, 0)\n",
    "    plt.plot(positions * 10**6, -depthProfile[powerInc] / (h * 10**6), label=str(powers[powerInc]))\n",
    "plt.xlabel(r'Position $(\\mu m)$')\n",
    "plt.ylabel('Depth (MHz)')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": "false",
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "source": [
    "### Calculating trap depth at different NAs and powers for simple tweezers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": "false"
   },
   "source": [
    "Wednesday, April 26th, 2017, for attempting to trap a bunch of atoms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-04-26T13:47:00.296839",
     "start_time": "2017-04-26T19:46:50.486Z"
    },
    "heading_collapsed": "false"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.1645710647779723e-06\n",
      "39.11168600923893 MHz\n"
     ]
    }
   ],
   "source": [
    "na = 0.25\n",
    "waist = 850e-9 / ((3.1415/2)*na)\n",
    "power = 30e-3\n",
    "\n",
    "print(waist)\n",
    "\n",
    "#intensity = 3.185e11 * 0.00715\n",
    "#waist = 707*10**-9\n",
    "#power = intensity * waist**2 * np.pi/2\n",
    "print(tweezerDepth(power, waist, 850*10**-9) / (6.626*10**-34 * 10**6), 'MHz')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": "false"
   },
   "source": [
    "### Calculating Scattering of tweezer light in very deep tweezer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:05:55.247654Z",
     "start_time": "2017-09-18T00:05:55.241638Z"
    },
    "heading_collapsed": "false"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1784.6767209525312"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scatterRate(200e-3, 0.6e-6, 850e-9) * 0.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# New lattice plan..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": "false"
   },
   "source": [
    "- Calculate intensity as a function of power / size parameters...\n",
    "- Lattice Spacing as function of angle...\n",
    "- Estimate lattice trap freq and depth...\n",
    "- as a function of angle...\n",
    "- think more fully about issues with depth being larger..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "2w_f = \\frac{4\\lambda}{\\pi} \\frac{f}{2w_0}\\\\\n",
    "w_f = \\frac{\\lambda f}{\\pi w_0}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c230 size: 5.985916001243852e-05\n",
      "c240 size: 3.3736085194042654e-05\n"
     ]
    }
   ],
   "source": [
    "w_0_c230 = 0.452 # mm\n",
    "w_0_c240 = 0.802\n",
    "def get_wf(w_0):\n",
    "    f_ = 0.1\n",
    "    return 850e-9*f_ / (np.pi * w_0)\n",
    "print('c230 size:', get_wf(w_0_c230*1e-3))\n",
    "print('c240 size:', get_wf(w_0_c240*1e-3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "trap freq: (Eq. c16 from \"Bose-Einstein condensates in optical lattice\" thesis by Henrik Andersen https://phys.au.dk/fileadmin/site_files/publikationer/phd/PhD_hka.pdf)\n",
    "$$\n",
    "\\omega_z \\approx \\sqrt{\\frac{2V_0}{m}}k=\\sqrt{\\frac{2V_0}{m}} \\frac{2\\pi \\sin\\{\\theta\\}}{\\lambda}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For perfect interference, $k = 2\\pi/\\lambda$. For two beams interfering at not perfect angles, I think this is $2\\pi\\sin\\{\\theta\\}/\\lambda$ where $\\theta$ is the *half-angle* between the beams (takes maximum value at $\\theta=\\pi/2$)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The lenses in the exp setup are ~10cm and 2.54 cm diameter. that means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1263237381579653 7.237817048767123\n"
     ]
    }
   ],
   "source": [
    "maxSingleLensAngle = np.arctan(2.54/2/10)\n",
    "print(maxSingleLensAngle, maxSingleLensAngle*180/np.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "maxSingleLensAngle = np.arctan(2.54/2/10)\n",
    "def trapFreq1DLattice_nu(V_0, angle=maxSingleLensAngle):\n",
    "    return np.sqrt(2*V_0/mc.Rb87_M) * np.sin(angle)/850e-9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0271798355946804 khz\n",
      "11.507084881819068 khz\n"
     ]
    }
   ],
   "source": [
    "print(trapFreq1DLattice_nu(1e-6*mc.k_B, maxSingleLensAngle/2)/1e3,\"khz\")\n",
    "print(trapFreq1DLattice_nu(1e-6*mc.k_B, np.pi/4)/1e3,\"khz\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0271798355946804 khz\n",
      "11.507084881819068 khz\n"
     ]
    }
   ],
   "source": [
    "print(trapFreq1DLattice_nu(1e-6*mc.k_B, maxSingleLensAngle/2)/1e3,\"khz\")\n",
    "print(trapFreq1DLattice_nu(1e-6*mc.k_B, np.pi/4)/1e3,\"khz\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "89.0786169627706"
      ]
     },
     "execution_count": 231,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "11.5 * np.sqrt(60)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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