Polarization gradients in a dipole trap.ipynb

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   "source": [
    "# Polarization gradients in a dipole trap"
   ]
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   "source": [
    "Starting From Mikhail Lukin's paper, \"Cohernece and Raman Sideband Cooling of a Single Atom in an Optical Tweezer\""
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    "Lukin reports that the maximum field gradient is at the center, as expected, and is well approximated by\n",
    "\n",
    "$$\n",
    "\\frac{2.6 \\alpha \\sin\\{\\alpha\\}}{\\lambda}\n",
    "$$"
   ]
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   "source": [
    "For a focused gaussian beam, where $\\alpha$ is the NA of the lens. On further inspection, it is unclear whether $\\alpha$ is the NA or the angle. :("
   ]
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   "source": [
    "### Comparison for NAs in our experiment"
   ]
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   "source": [
    "We've previously worked with NA 0.55 with the ASE lens, but I want to get a sense of how much worse this effect is for the Sill lens."
   ]
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  {
   "cell_type": "code",
   "execution_count": 1,
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   "source": [
    "import numpy as np"
   ]
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   "source": [
    "def getMaxGradientFromApprox(NA, wavelength=850e-9):\n",
    "    return 2.6 * NA * np.sin(NA)/wavelength"
   ]
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      "879344.396907\n",
      "1101916.09269\n",
      "1379383.75385\n"
     ]
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   ],
   "source": [
    "print(getMaxGradientFromApprox(0.55))\n",
    "print(getMaxGradientFromApprox(0.62))\n",
    "print(getMaxGradientFromApprox(0.7))"
   ]
  },
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   "source": [
    "a"
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