Calculations/ODTCalculations.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a4246751",
   "metadata": {},
   "outputs": [],
   "source": [
    "from calculateDipoleTrapPotential import *"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c68468e4",
   "metadata": {},
   "source": [
    "## Plot ideal trap potential resulting for given parameters only"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "38c770ac",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Karthik\\anaconda3\\lib\\site-packages\\scipy\\optimize\\minpack.py:833: OptimizeWarning: Covariance of the parameters could not be estimated\n",
      "  warnings.warn('Covariance of the parameters could not be estimated',\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAoAAAAHwCAYAAAA2B95/AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAACYpElEQVR4nOzdd3hUVfrA8e+Z9N57gFBC7yDYAUVRxN4bKpZd27Ju+bmuu7quW9x1Xfu6a+8de0NUULEgSO8JKZAQ0kN6nfP74yZjQibJJMzMzcy8n+eZZ5Jb39xMJu+ce857lNYaIYQQQgjhOyxmByCEEEIIIdxLEkAhhBBCCB8jCaAQQgghhI+RBFAIIYQQwsdIAiiEEEII4WMkARRCCCGE8DEekQAqpU5RSu1SSmUrpX5ndjxCCCGEEJ5MDfY6gEopP2A3cBJQAKwFLtZabzc1MCGEEEIID+UJLYCzgGytdY7Wuhl4FTjT5JiEEEIIITyWv9kBOCAN2Nfp+wJgducNlFLXAdcBhISEzBgyZIjLg2pshQP11m7LE0MVof6K+lZNSX331tXkMAvBflDboilr6L4+NcxCoB/UNGvKG7uvTwu3EGCBg02ayqbu64dEWPBTUNWkqbKzfliEBaWgolFT3dx9fUak8ZmgrEFT29J1vQKGta8vrdfUtXZd76eM8wMU12saDlkfYDHiBzhQZ6Wxreu5Ay2Q2r5+f62V5kMub7Cfcf0ACmqttB6yPsRfkRSqANhXY6XtkB8vLECREGKsz6+2cuhPHxGoiAs21hfVWVGAUgqLAouCEH8I9TfWN7YZP69f+zoAq9WKxeIJn6lcS66DQa6DobfrENRUQWBzJbXhw9HKu69Vx3XQQKsV2qzQpjVWbbz3gPF/oa4FdPtyDWgN6RGue1/2t0C6k96XC2uttPT3fdlfkRDay/tygCKu/X07r7r7/9zIQEVssMKqYW9N9/XRQYroIEWbNs5/qJggRVSQosVqxH+ouGBFRKCiuQ3213VfnxCiCAtQ/c4JkkMh2N89r/ndu3eXaa0TDl3uCQmgsrOsy2tEa/048DjAzJkz9bp161weVENzG++u+JJZs2Z1CSY5MpiwIH9qm1o5cLCh236p0SGEBvpzsKGF4urGbuuHxoYSHOBHZV0zxTXd1w+PDyPI34+y2iZKqpsA0J0iGJ0UQYCfhZLqRkpqmrrtPy4lEj+LYn9VA+W1zV321xqmDIkGYF9FPeV1zV32tSiYnG6szy2ro7LeWL9+/XqmT59OgMXCpPQoALJLajjY0GI7LkCQv59t/Y6iamqbWrusDw30Y2KasX5r4UHqmlq7XNuIYH8mpBrr1++tpLGl6ztVTGgg41IiAViTU059SxutbZqWNistbVbSokOYmRELwPPf5dHY0kZLm6a1TdPU2sbk9ChOmZhCc6uV615YR11TK3VNbdQ1t3KwoYXFR2Xwq5NGU1bbxMy/fIYVsALRoQEMiQnlmPhGfnfxfJpa29h1oIbRSREEB/h1+x14u1WrVjF37lyzwzCdXAdDr9fh+bOgrgyuX+3OkFyuobmNPaW1ZJXUkFVcy8/njmT999+wgyH845OdgPGPreMf8Ld/mE9ceBBPrc7l7Q0FhAX6ExroR2igPyGBftxzziT8/Sx8ubuUHUXV+FsUAX4W/P0UQf5+nDcjHYDNBVWUVDfh76fwsygsShHob+GI9ve9rGLjfVkp48OtAoID/Gzvm3llddQ3t6EUWJRCKQjytzAsLgyAveX1NLV2fd8NDvBjSGyobf+Wtq5JUGiQP2nRIQDklNby/ZofmDXrCNv68KAAkqOCAdhTWsuh3dIigwNIjDTWZ5fUdrvWUSEBJEQEYbVqcsvruq2PCQ0kNiyQ1jYr+RX13dbHhQUSHRpIc6uVgko768ODiAoJoLGljf1V3f+nJ0QEEREcQENzG0V2/ucntecEdU2tXf7n79mylpNOmNdte1dQSuXbW+4JCWAB0LlJLx3Yb1IsNiGBfiSHWRiREG53fXiQP6MSI3rcPyokgKiQgB7Xx4QFEhMW2OP6+PAg4sODelyfGBls+6OxJzU6hNT2P0p7hsSG2v6o7RkeH8ZwjDeF6hw/pg+N6bK+t58dsL3h9KQjEezJoec71OwRcb2uX3xURo/rAv0tPHvVrG7LO96YwoP8efHq2ZTXNVF0sJF9FfXsq2zAXxl/3DuLajjz0W+wKOM6TUqLYtbwOOaPTyQxouffiRA+xdoGBetg8gVmR3JYOlrr/CyKb7LLuOv9bWSV1No+2PpbFAsnpQAwa3gMv10whpSoYJKjgokPDyI6NICYUOO9/upjh3P1scN7PNec0QnMGd2tIcem4wN6TzKTen9fzogP63X90Lie/yc4sv+IhHD2hlt6/P8wsof/px1GJfa83mJRve7v72fpdX2gf8//z8FIdHtbHxLY+/qwIP8u6/da7LVtuZcnJIBrgUyl1HCgELgIuMTckIQvUsr4gw0O8OPYzPhu61etWgVARlwYj106nR1F1WwvqmF1djnvbNxPRvxsEiOCySquYXdxLXPGJBAe5Al/gkK4QMkOaK6BIbP73naQqW1q5ctdpXy1u5Qvd5dy5+njOXVSClEhAaRFh3DqxBTGJkeQmRTOsLgwAvwsrMqCGcNimTEs1uzwhQA8IAHUWrcqpW4ClgN+wNNa620mhyVEj6JCAzh1Ugqntn/q11qTV15PSvttjnc2FvLoyj0E+lk4NjOe82ekc+K4JALd1B9EiEFh3xrjeUj31vbBqqaxhd+9tYXPthfT1GolItif4zLjiWu/GzMxLYpn7Nw9EGIwGvQJIIDW+iPgI7PjEGIglFIM73Rr5Jb5ozk+M4EV24t5f/N+vthZwtDYUFb9Zi6WQXBbQAi32PcDhCVCTIbZkfSqpLqRHQdqmDPaaLEvqmrggplDWDQ5hRnDYvD3kw9uwjN5RAIohDfx97Mwe0Qcs0fE8btTx/J1dhlFVY1YLAqtNfev2M0ZU1P77EcphEfbt8Zo/VOD80PPvop6Hv4ii7fWFxIW5M8Pt59IkL8fb91wjNmhCeEUkgAKYSJ/PwvzxiTavs8vr+eJr3N5ZGU2Fx4xhFvmj+51MI8QHqm2BCpzYeYSsyPppqy2iQc+281ra/ehlOKyI4dx5dEZBPn73oh+4d0kARRiEMmID+Ob353Aw19k8cJ3+by7cT83n5DJtccNl1tNwnvs+8F4HoQDQPLL63l9bQEXHjGEG+eNIiWq52oJQngy+Y8ixCATGxbInadP4LNfzeGYUfE8/10eDYfUPBTCo+1bA36BkDLF7EgAo/7cU6tzAZgxLIZvfncCfzlrkiR/wqtJC6AQg1RGfBhPLJ5JaU0TEcEBNLda+WhLEWdOTbWVpBHCI+37AVKmQoC53Ru01rz8w17u/mA7YYH+XHjEEMKD/EmI6LnGqhDeQloAhRjkOv4ZvbOhkF++tpHrX1xPdWOLyVEJMUCtzbB/g+nlXxqa2/jFqxu5/e2tzBwWy0dLj5O6nMKnyKtdCA9x/sx0qhtbuOfjnZz16Dc8d9WsXmdrEWJQKt4KbU2QNsO0EKxWzaVPfs+GfVX8dsEYrp8zUkowCZ8jLYBCeAilFNccN4KXrplNeW0zZ//nGzYXVJkdlhD9s3+98WxiAmixKC6ZPYwnLp/JjfNGSfInfJIkgEJ4mNkj4lh2/dEkRATjb5E/YeFhCtdDaDxED3X7qTfuq2LF9mIAzpuRzvzxSW6PQYjBQm4BC+GBRiWG8+HNx9paLgoq60mPkdvBwgMU/ghp091eAHpdXgVXPP0DyVHBzBuTIGWVhM+TvwAhPFRH8vfSmnzm//tL1uSUmxyREH1oqoHSXW6//btt/0GuenYtSZHBvHTNkZL8CYEkgEJ4vAUTkkmLDuHa59exu7jG7HCE6Nn+jYB2awKYU1rL4qd+ICLInxeumU1ylMysIwRIAiiEx4sPD+K5JbMICvDjyqd/oLi60eyQhLCv8EfjOXW62075zoZCAF64ZjZp0VLYWYgOkgAK4QXSY0J55sojONjQwpJn19LaZjU7JCG6278eYjIgLM5tp7zlpNF
      "text/plain": [
       "<Figure size 648x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Power = 1.07*u.W\n",
    "Polarizability = 184.4 # in a.u, most precise measured value of Dy polarizability\n",
    "Wavelength = 1.064*u.um\n",
    "w_x, w_z = 30*u.um, 30*u.um # Beam Waists in the x and y directions\n",
    "\n",
    "#Power = 11*u.W\n",
    "#Polarizability = 184.4 # in a.u, most precise measured value of Dy polarizability\n",
    "#w_x, w_z = 67*u.um, 67*u.um # Beam Waists in the x and y directions\n",
    "\n",
    "options = {\n",
    "    'axis': 2, # axis referenced to the beam along which you want the dipole trap potential\n",
    "    'extent': 1e2, # range of spatial coordinates in one direction to calculate trap potential over\n",
    "    'crossed': False,\n",
    "    'delta': 70, # angle between arms in degrees\n",
    "    'modulation': False,\n",
    "    'aspect_ratio': 4, # required aspect ratio of modulated arm\n",
    "    'gravity': True,\n",
    "    'tilt_gravity': False,\n",
    "    'theta': 0.75, # gravity tilt angle in degrees\n",
    "    'tilt_axis': [1, 0, 0], # lab space coordinates are rotated about x-axis in reference frame of beam\n",
    "    'astigmatism': False,\n",
    "    'disp_foci': 2.5*u.mm, #0.9 * z_R(w_0 = np.asarray([30]), lamb = 1.064)[0]*u.um, # difference in position of the foci along the propagation direction (Astigmatism)\n",
    "    'extract_trap_frequencies': False\n",
    "}\n",
    "\n",
    "ComputedPotentials = [] \n",
    "Params = []  \n",
    "\n",
    "Positions, IdealTrappingPotential, TrappingPotential, TrapDepthsInKelvin, CalculatedTrapFrequencies, ExtractedTrapFrequencies = computeTrapPotential(w_x, w_z, Power, Polarizability, options)\n",
    "ComputedPotentials.append(IdealTrappingPotential)\n",
    "ComputedPotentials.append(TrappingPotential)\n",
    "Params.append([TrapDepthsInKelvin, CalculatedTrapFrequencies, ExtractedTrapFrequencies])\n",
    "\n",
    "cpots = np.asarray(ComputedPotentials)\n",
    "plotPotential(Positions, cpots, options, Params)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc9809de",
   "metadata": {},
   "source": [
    "## Plot harmonic fit for trap potential resulting for given parameters only"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0f3e80f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "v, dv, popt, pcov = extractTrapFrequency(Positions, TrappingPotential, options['axis'])\n",
    "plotHarmonicFit(Positions, TrappingPotential, TrapDepthsInKelvin, options['axis'], popt, pcov)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37b40607",
   "metadata": {},
   "source": [
    "## Plot trap potential resulting for given parameters (with one parameter being a list of values and the potential being computed for each of these values) only"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8504f99f",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Karthik\\anaconda3\\lib\\site-packages\\scipy\\optimize\\minpack.py:833: OptimizeWarning: Covariance of the parameters could not be estimated\n",
      "  warnings.warn('Covariance of the parameters could not be estimated',\n"
     ]
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 648x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Potentials = [] \n",
    "Params = []  \n",
    "Power = [10, 30, 40]*u.W # Single Beam Power\n",
    "for p in Power: \n",
    "    Positions, IdealTrappingPotential, TrappingPotential, TrapDepthsInKelvin, CalculatedTrapFrequencies, ExtractedTrapFrequencies = computeTrapPotential(w_x, w_z, p, Polarizability, options)\n",
    "    Potentials.append(IdealTrappingPotential)\n",
    "    Potentials.append(TrappingPotential)\n",
    "    Params.append([TrapDepthsInKelvin, CalculatedTrapFrequencies, ExtractedTrapFrequencies])\n",
    "\n",
    "cpots = np.asarray(Potentials)\n",
    "plotPotential(Positions, cpots, options, Params)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "951010c6",
   "metadata": {},
   "source": [
    "## Plot transverse intensity profile and trap potential resulting for given parameters only"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f3e4afd9",
   "metadata": {},
   "outputs": [],
   "source": [
    "options = {\n",
    "    'extent': 60, # range of spatial coordinates in one direction to calculate trap potential over\n",
    "    'modulation': True,\n",
    "    'modulation_function': 'arccos',\n",
    "    'modulation_amplitude': 2.16\n",
    "}\n",
    "\n",
    "positions, waists, I, U, p = computeIntensityProfileAndPotentials(Power, [w_x, w_z], Polarizability, Wavelength, options)\n",
    "plotIntensityProfileAndPotentials(positions, waists, I, U)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db0df307",
   "metadata": {},
   "source": [
    "## Plot gaussian fit for trap potential resulting from modulation for given parameters only"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7afa7d82",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_Positions = positions[0].value\n",
    "z_Positions = positions[1].value\n",
    "x_Potential = U[:, np.where(z_Positions==0)[0][0]].value\n",
    "z_Potential = U[np.where(x_Positions==0)[0][0], :].value\n",
    "poptx, pcovx = p[0], p[1]\n",
    "poptz, pcovz = p[2], p[3]\n",
    "plotGaussianFit(x_Positions, x_Potential, poptx, pcovx)\n",
    "plotGaussianFit(z_Positions, z_Potential, poptz, pcovz)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e5b8123",
   "metadata": {},
   "source": [
    "## Calculate relevant parameters for evaporative cooling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "95ab43bd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Particle Density = 4.63E+13 1 / cm3\n",
      "Elastic Collision Rate = 2813.75 1 / s\n",
      "PSD = 9.00E-05 \n",
      "v_x = 2588.17 Hz\n",
      "v_y = 20.66 Hz\n",
      "v_z = 2588.17 Hz\n",
      "a_s = 111.31 \n"
     ]
    }
   ],
   "source": [
    "Power = 40*u.W\n",
    "Polarizability = 184.4 # in a.u, most precise measured value of Dy polarizability\n",
    "Wavelength = 1.064*u.um\n",
    "w_x, w_z = 30*u.um, 30*u.um # Beam Waists in the x and y directions\n",
    "\n",
    "AtomNumber = 1.00 * 1e7\n",
    "BField = 2.5 * u.G\n",
    "\n",
    "modulation_depth = 0.0\n",
    "Temperature = convert_modulation_depth_to_temperature(modulation_depth)[0] * u.uK\n",
    "n = particleDensity(w_x, w_z, Power, Polarizability, N = AtomNumber, T = Temperature, m = 164*u.u).decompose().to(u.cm**(-3))\n",
    "Gamma_elastic = calculateElasticCollisionRate(w_x, w_z, Power, Polarizability, N = AtomNumber, T = Temperature, B = BField)\n",
    "PSD = calculatePSD(w_x, w_z, Power, Polarizability, N = AtomNumber, T = Temperature).decompose()\n",
    "\n",
    "print('Particle Density = %.2E ' % (n.value) + str(n.unit))\n",
    "print('Elastic Collision Rate = %.2f ' % (Gamma_elastic.value) + str(Gamma_elastic.unit))\n",
    "print('PSD = %.2E ' % (PSD.value))\n",
    "\n",
    "v_x = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'x')\n",
    "v_y = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'y')\n",
    "v_z = calculateTrapFrequency(w_x, w_z, Power, Polarizability, dir = 'z')\n",
    "\n",
    "print('v_x = %.2f ' %(v_x.value) + str(v_x.unit))\n",
    "print('v_y = %.2f ' %(v_y.value) + str(v_y.unit))\n",
    "print('v_z = %.2f ' %(v_z.value) + str(v_z.unit))\n",
    "\n",
    "print('a_s = %.2f ' %(scatteringLength(BField)[0] / ac.a0))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff252fbe",
   "metadata": {},
   "source": [
    "## Plot alphas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "dd7fc03d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotAlphas()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c09cb260",
   "metadata": {},
   "source": [
    "## Plot Temperatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5c79840e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotTemperatures(w_x, w_z, plot_against_mod_depth = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "063879ee",
   "metadata": {},
   "source": [
    "##  Calculate and Plot calculated trap frequencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "0ddff726",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "AtomNumber = 1.00 * 1e7\n",
    "BField = 1.4 * u.G\n",
    "modulation_depth = np.arange(0, 1.0, 0.08)\n",
    "\n",
    "w_xs = w_x * convert_modulation_depth_to_alpha(modulation_depth)[0]\n",
    "\n",
    "v_x = np.zeros(len(modulation_depth))\n",
    "v_y = np.zeros(len(modulation_depth))\n",
    "v_z = np.zeros(len(modulation_depth))\n",
    "\n",
    "for i in range(len(modulation_depth)):\n",
    "    v_x[i] = calculateTrapFrequency(w_xs[i], w_z, Power, Polarizability, dir = 'x').value\n",
    "    v_y[i] = calculateTrapFrequency(w_xs[i], w_z, Power, Polarizability, dir = 'y').value\n",
    "    v_z[i] = calculateTrapFrequency(w_xs[i], w_z, Power, Polarizability, dir = 'z').value\n",
    "\n",
    "plotTrapFrequencies(v_x, v_y, v_z, modulation_depth, new_aspect_ratio, plot_against_mod_depth = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76ff8301",
   "metadata": {},
   "source": [
    "## Plot measured trap frequencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7a85ec41",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "modulation_depth_radial = [0, 0.5, 0.3, 0.7, 0.9, 0.8, 1.0, 0.6, 0.4, 0.2, 0.1]\n",
    "fx = [3.135, 0.28, 0.690, 0.152, 0.102, 0.127, 0.099, 0.205, 0.404, 1.441, 2.813]\n",
    "dfx = [0.016, 0.006, 0.005, 0.006, 0.003, 0.002, 0.002,0.002, 0.003, 0.006, 0.024]\n",
    "fz = [2.746, 1.278, 1.719, 1.058, 0.923, 0.994, 0.911, 1.157, 1.446, 2.191, 2.643]\n",
    "dfz = [0.014, 0.007, 0.009, 0.007, 0.005, 0.004, 0.004, 0.005, 0.007, 0.009, 0.033]\n",
    "\n",
    "modulation_depth_axial = [1, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1]\n",
    "fy = [3.08, 3.13, 3.27, 3.46, 3.61, 3.82, 3.51, 3.15, 3.11, 3.02]\n",
    "dfy = [0.03, 0.04, 0.04, 0.05, 0.07, 0.06, 0.11, 0.07, 0.1, 1.31]\n",
    "\n",
    "plotMeasuredTrapFrequencies(fx, dfx, fy, dfy, fz, dfz,  modulation_depth_radial, modulation_depth_axial, w_x, w_z, plot_against_mod_depth = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a4843d2",
   "metadata": {},
   "source": [
    "## Plot ratio of measured to calculated trap frequencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "58cf3f64",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "modulation_depth = [0.5, 0.3, 0.7, 0.9, 0.8, 1.0, 0.6, 0.4, 0.2, 0.1]\n",
    "w_xs = w_x * convert_modulation_depth_to_alpha(modulation_depth)[0]\n",
    "\n",
    "v_x = np.zeros(len(modulation_depth))\n",
    "v_y = np.zeros(len(modulation_depth))\n",
    "v_z = np.zeros(len(modulation_depth))\n",
    "\n",
    "for i in range(len(modulation_depth)):\n",
    "    v_x[i] = calculateTrapFrequency(w_xs[i], w_z, Power, Polarizability, dir = 'x').value / 1e3\n",
    "    v_y[i] = calculateTrapFrequency(w_xs[i], w_z, Power, Polarizability, dir = 'y').value\n",
    "    v_z[i] = calculateTrapFrequency(w_xs[i], w_z, Power, Polarizability, dir = 'z').value / 1e3\n",
    "\n",
    "fx = [0.28, 0.690, 0.152, 0.102, 0.127, 0.099, 0.205, 0.404, 1.441, 2.813]\n",
    "dfx = [0.006, 0.005, 0.006, 0.003, 0.002, 0.002,0.002, 0.003, 0.006, 0.024]\n",
    "fy = [3.08, 3.13, 3.27, 3.46, 3.61, 3.82, 3.51, 3.15, 3.11, 3.02]\n",
    "dfy = [0.03, 0.04, 0.04, 0.05, 0.07, 0.06, 0.11, 0.07, 0.1, 1.31]\n",
    "fz = [1.278, 1.719, 1.058, 0.923, 0.994, 0.911, 1.157, 1.446, 2.191, 2.643]\n",
    "dfz = [0.007, 0.009, 0.007, 0.005, 0.004, 0.004, 0.005, 0.007, 0.009, 0.033]\n",
    "\n",
    "plotRatioOfTrapFrequencies(fx, fy, fz, dfx, dfy, dfz, v_x, v_y, v_z, modulation_depth, w_x, w_z, plot_against_mod_depth = True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44e92099",
   "metadata": {},
   "source": [
    "## Plot Feshbach Resonances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d15205ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 648x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotScatteringLengths(B_range = [0, 3.6])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a2e113f",
   "metadata": {},
   "source": [
    "##  Calculate and Plot Collision Rates and PSD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "86e9ba21",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "AtomNumber = 1.00 * 1e7\n",
    "BField = 1.4 * u.G\n",
    "modulation_depth = np.arange(0, 1.0, 0.08)\n",
    "\n",
    "w_xs = w_x * convert_modulation_depth_to_alpha(modulation_depth)[0]\n",
    "new_aspect_ratio  = w_xs / w_z\n",
    "Temperatures = convert_modulation_depth_to_temperature(modulation_depth)[0] * u.uK\n",
    "\n",
    "# n = np.zeros(len(modulation_depth))\n",
    "Gamma_elastic = np.zeros(len(modulation_depth))\n",
    "PSD = np.zeros(len(modulation_depth))\n",
    "\n",
    "for i in range(len(modulation_depth)):\n",
    "    # n[i] = particleDensity(w_xs[i], w_z, Power, Polarizability, N = AtomNumber, T = Temperatures[i], m = 164*u.u).decompose().to(u.cm**(-3))\n",
    "    Gamma_elastic[i] = calculateElasticCollisionRate(w_xs[i], w_z, Power, Polarizability, N = AtomNumber, T = Temperatures[i], B = BField).value\n",
    "    PSD[i] = calculatePSD(w_xs[i], w_z, Power, Polarizability, N = AtomNumber, T = Temperatures[i]).decompose().value\n",
    "\n",
    "\n",
    "plotCollisionRatesAndPSD(Gamma_elastic, PSD, modulation_depth, new_aspect_ratio, plot_against_mod_depth = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74d353c9",
   "metadata": {},
   "source": [
    "## Plot Collision Rates and PSD from only measured trap frequencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "6c81d9da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fin_mod_depth = [0.5, 0.3, 0.7, 0.9, 0.8, 1.0, 0.6, 0.4, 0.2, 0.1]\n",
    "v_x = [0.28, 0.690, 0.152, 0.102, 0.127, 0.099, 0.205, 0.404, 1.441, 2.813] * u.kHz\n",
    "dv_x = [0.006, 0.005, 0.006, 0.003, 0.002, 0.002,0.002, 0.003, 0.006, 0.024] * u.kHz\n",
    "v_z = [1.278, 1.719, 1.058, 0.923, 0.994, 0.911, 1.157, 1.446, 2.191, 2.643] * u.kHz\n",
    "dv_z = [0.007, 0.009, 0.007, 0.005, 0.004, 0.004, 0.005, 0.007, 0.009, 0.033] * u.kHz\n",
    "sorted_modulation_depth, sorted_v_x = zip(*sorted(zip(fin_mod_depth, v_x)))\n",
    "sorted_modulation_depth, sorted_dv_x = zip(*sorted(zip(fin_mod_depth, dv_x)))\n",
    "sorted_modulation_depth, sorted_v_z = zip(*sorted(zip(fin_mod_depth, v_z)))\n",
    "sorted_modulation_depth, sorted_dv_z = zip(*sorted(zip(fin_mod_depth, dv_z)))\n",
    "\n",
    "fin_mod_depth = [1, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1] \n",
    "v_y = [3.08, 3.13, 3.27, 3.46, 3.61, 3.82, 3.51, 3.15, 3.11, 3.02] * u.Hz\n",
    "dv_y = [0.03, 0.04, 0.04, 0.05, 0.07, 0.06, 0.11, 0.07, 0.1, 1.31] * u.Hz\n",
    "sorted_modulation_depth, sorted_v_y = zip(*sorted(zip(fin_mod_depth, v_y)))\n",
    "sorted_modulation_depth, sorted_dv_y = zip(*sorted(zip(fin_mod_depth, dv_y)))\n",
    "\n",
    "fin_mod_depth = [1.0, 0.8, 0.6, 0.4, 0.2, 0.9, 0.7, 0.5, 0.3, 0.1]\n",
    "T_x = [22.1, 27.9, 31.7, 42.2, 145.8, 27.9, 33.8, 42.4, 61.9, 136.1] * u.uK\n",
    "dT_x = [1.7, 2.6, 2.4, 3.7, 1.1, 2.2, 3.2, 1.7, 2.2, 1.2] * u.uK\n",
    "T_y = [13.13, 14.75, 18.44, 26.31, 52.55, 13.54, 16.11, 21.15, 35.81, 85.8] * u.uK\n",
    "dT_y = [0.05, 0.05, 0.07, 0.16, 0.28, 0.04, 0.07, 0.10, 0.21, 0.8] * u.uK\n",
    "\n",
    "sorted_modulation_depth, sorted_T_x = zip(*sorted(zip(fin_mod_depth, T_x)))\n",
    "sorted_modulation_depth, sorted_dT_x = zip(*sorted(zip(fin_mod_depth, dT_x)))\n",
    "sorted_modulation_depth, sorted_T_y = zip(*sorted(zip(fin_mod_depth, T_y)))\n",
    "sorted_modulation_depth, sorted_dT_y = zip(*sorted(zip(fin_mod_depth, dT_y)))\n",
    "\n",
    "modulation_depth = sorted_modulation_depth\n",
    "\n",
    "pd, dpd, T, dT, new_aspect_ratio = calculateParticleDensityFromMeasurements(sorted_v_x, sorted_dv_x, sorted_v_y, sorted_dv_y, sorted_v_z, sorted_dv_z, w_x, w_z, sorted_T_x, sorted_T_y, sorted_dT_x, sorted_dT_y, sorted_modulation_depth, AtomNumber, m = 164*u.u)\n",
    "\n",
    "Gamma_elastic = [(pd[i] * scatteringCrossSection(BField) * meanThermalVelocity(T[i]) / (2 * np.sqrt(2))).decompose()  for i in range(len(pd))]\n",
    "Gamma_elastic_values = [(Gamma_elastic[i]).value  for i in range(len(Gamma_elastic))]\n",
    "dGamma_elastic = [(Gamma_elastic[i] * ((dpd[i]/pd[i]) + (dT[i]/(2*T[i])))).decompose() for i in range(len(Gamma_elastic))]\n",
    "dGamma_elastic_values = [(dGamma_elastic[i]).value for i in range(len(dGamma_elastic))]\n",
    "\n",
    "PSD = [((pd[i] * thermaldeBroglieWavelength(T[i])**3).decompose()).value for i in range(len(pd))]\n",
    "dPSD = [((PSD[i] * ((dpd[i]/pd[i]) - (1.5 * dT[i]/T[i]))).decompose()).value for i in range(len(Gamma_elastic))]\n",
    "\n",
    "fig, ax1 = plt.subplots(figsize=(8, 6))\n",
    "ax2 = ax1.twinx()\n",
    "ax1.errorbar(modulation_depth, Gamma_elastic_values, yerr = dGamma_elastic_values, fmt = 'ob', markersize=5, capsize=5)\n",
    "ax2.errorbar(modulation_depth, PSD, yerr = dPSD, fmt = '-^r', markersize=5, capsize=5)\n",
    "ax2.yaxis.set_major_formatter(mtick.FormatStrFormatter('%.1e'))\n",
    "ax1.set_xlabel('Modulation depth', fontsize= 12, fontweight='bold')\n",
    "ax1.set_ylabel('Elastic Collision Rate (' + str(Gamma_elastic[0].unit) + ')', fontsize= 12, fontweight='bold')\n",
    "ax1.tick_params(axis=\"y\", labelcolor='b')\n",
    "ax2.set_ylabel('Phase Space Density', fontsize= 12, fontweight='bold')\n",
    "ax2.tick_params(axis=\"y\", labelcolor='r')\n",
    "plt.tight_layout()\n",
    "plt.grid(visible=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9329ee37",
   "metadata": {},
   "source": [
    "## Investigate deviation in alpha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "7b8191f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Power = 40*u.W\n",
    "Polarizability = 184.4 # in a.u, most precise measured value of Dy polarizability\n",
    "Wavelength = 1.064*u.um\n",
    "w_x, w_z = 27.5*u.um, 33.8*u.um\n",
    "\n",
    "options = {\n",
    "    'axis': 0, # axis referenced to the beam along which you want the dipole trap potential\n",
    "    'extent': 3e2, # range of spatial coordinates in one direction to calculate trap potential over\n",
    "    'crossed': False,\n",
    "    'delta': 70, # angle between arms in degrees\n",
    "    'modulation': False,\n",
    "    'aspect_ratio': 5, # required aspect ratio of modulated arm\n",
    "    'gravity': False,\n",
    "    'tilt_gravity': False,\n",
    "    'theta': 0.75, # gravity tilt angle in degrees\n",
    "    'tilt_axis': [1, 0, 0], # lab space coordinates are rotated about x-axis in reference frame of beam\n",
    "    'astigmatism': True,\n",
    "    'disp_foci': 2.5*u.mm, #0.9 * z_R(w_0 = np.asarray([30]), lamb = 1.064)[0]*u.um, # difference in position of the foci along the propagation direction (Astigmatism)\n",
    "    'extract_trap_frequencies': False\n",
    "}\n",
    "\n",
    "modulation_depth = np.arange(0, 1.1, 0.1)\n",
    "Alphas, fin_mod_dep, meas_alpha_x, meas_alpha_z, dalpha_x, dalpha_z = convert_modulation_depth_to_alpha(modulation_depth) \n",
    "meas_alpha_deviation = [(g - h) for g, h in zip(meas_alpha_x, meas_alpha_z)]\n",
    "sorted_fin_mod_dep, sorted_meas_alpha_deviation = zip(*sorted(zip(fin_mod_dep, meas_alpha_deviation)))\n",
    "avg_alpha = [(g + h) / 2 for g, h in zip(meas_alpha_x, meas_alpha_z)]\n",
    "sorted_fin_mod_dep, new_aspect_ratio = zip(*sorted(zip(fin_mod_dep, (w_x * avg_alpha) / w_z)))\n",
    "\n",
    "current_ar = w_x/w_z\n",
    "aspect_ratio = np.arange(current_ar, 10*current_ar, 0.8)\n",
    "w_x = w_x * (aspect_ratio / current_ar)\n",
    "\n",
    "v_x = np.zeros(len(w_x))\n",
    "#v_y = np.zeros(len(w_x))\n",
    "v_z = np.zeros(len(w_x))\n",
    "\n",
    "for i in range(len(w_x)):\n",
    "    \n",
    "    options['axis'] = 0\n",
    "    ExtractedTrapFrequencies = computeTrapPotential(w_x[i], w_z, Power, Polarizability, options)[5]\n",
    "    tmp = ExtractedTrapFrequencies[0][0]\n",
    "    v_x[i] = tmp if not np.isinf(tmp) else np.nan\n",
    "    \n",
    "    # options['axis'] = 1\n",
    "    # ExtractedTrapFrequencies = computeTrapPotential(w_x[i], w_z, Power, Polarizability, options)[5]\n",
    "    # tmp = ExtractedTrapFrequencies[1][0]\n",
    "    # v_y[i] = tmp if not np.isinf(tmp) else np.nan\n",
    "    \n",
    "    options['axis'] = 2\n",
    "    ExtractedTrapFrequencies = computeTrapPotential(w_x[i], w_z, Power, Polarizability, options)[5]\n",
    "    tmp = ExtractedTrapFrequencies[0][0]\n",
    "    v_z[i] = tmp if not np.isinf(tmp) else np.nan\n",
    "\n",
    "    #v_x[i] = calculateTrapFrequency(w_x[i], w_z, Power, Polarizability, dir = 'x').value\n",
    "    #v_y[i] = calculateTrapFrequency(w_x[i], w_z, Power, Polarizability, dir = 'y').value\n",
    "    #v_z[i] = calculateTrapFrequency(w_x[i], w_z, Power, Polarizability, dir = 'z').value\n",
    "\n",
    "alpha_x = [(v_x[0]/v)**(2/3) for v in v_x]\n",
    "alpha_z = [(v_z[0]/v)**2 for v in v_z]\n",
    "\n",
    "calc_alpha_deviation = [(g - h) for g, h in zip(alpha_x, alpha_z)]\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(aspect_ratio, alpha_x, '-o', label = 'From horz TF')\n",
    "plt.plot(aspect_ratio, alpha_z, '-^', label = 'From vert TF')\n",
    "plt.xlabel('Aspect Ratio', fontsize= 12, fontweight='bold')\n",
    "plt.ylabel('$\\\\alpha$', fontsize= 12, fontweight='bold')\n",
    "plt.tight_layout()\n",
    "plt.grid(visible=1)\n",
    "plt.legend(prop={'size': 12, 'weight': 'bold'})\n",
    "plt.show()\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(aspect_ratio, calc_alpha_deviation, '--ob', label = 'Extracted')\n",
    "plt.plot(new_aspect_ratio, sorted_meas_alpha_deviation, '-or', label = 'Measured')\n",
    "plt.xlabel('Aspect Ratio', fontsize= 12, fontweight='bold')\n",
    "plt.ylabel('$\\\\Delta \\\\alpha$', fontsize= 12, fontweight='bold')\n",
    "plt.ylim([-0.5, 1])\n",
    "plt.tight_layout()\n",
    "plt.grid(visible=1)\n",
    "plt.legend(prop={'size': 12, 'weight': 'bold'})\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29a1cf87",
   "metadata": {},
   "source": [
    "## Quick calculation of PSD and elastic collision rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3950f1b5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Particle Density = 1.87E+12 1 / cm3\n",
      "Elastic Collision Rate = 37.24 1 / s\n",
      "PSD = 2.50E-05 \n"
     ]
    }
   ],
   "source": [
    "Power = 9.5*u.W\n",
    "Polarizability = 184.4 # in a.u, most precise measured value of Dy polarizability\n",
    "Wavelength = 1.064*u.um\n",
    "w_x, w_z = 50*u.um, 45*u.um # Beam Waists in the x and y directions\n",
    "\n",
    "NCount = 11000\n",
    "AtomNumber = calculateAtomNumber(NCount, pixel_size = 3.45 * u.um, magnification = 0.5, eta = 0.5)\n",
    "\n",
    "BField = 3.75 * u.G\n",
    "modulation_depth = 0.00\n",
    "\n",
    "w_x = w_x * convert_modulation_depth_to_alpha(modulation_depth)[0]\n",
    "new_aspect_ratio  = w_x / w_z\n",
    "Temperature = 33 * u.uK\n",
    "\n",
    "n = particleDensity(w_x, w_z, Power, Polarizability, N = AtomNumber, T = Temperature, m = 164*u.u).decompose().to(u.cm**(-3))\n",
    "Gamma_elastic = calculateElasticCollisionRate(w_x, w_z, Power, Polarizability, N = AtomNumber, T = Temperature, B = BField)\n",
    "PSD = calculatePSD(w_x, w_z, Power, Polarizability, N = AtomNumber, T = Temperature).decompose()\n",
    "\n",
    "print('Particle Density = %.2E ' % (n.value) + str(n.unit))\n",
    "print('Elastic Collision Rate = %.2f ' % (Gamma_elastic.value) + str(Gamma_elastic.unit))\n",
    "print('PSD = %.2E ' % (PSD.value))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d975586b",
   "metadata": {},
   "source": [
    "## Plot measured PSDs and collision rates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "b11b6aae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Gamma_elastic = [96.01, 82.53, 102.95, 143.5, 110.92, 471.77, 908.46]\n",
    "PSD = [8.95e-05, 4.19e-04, 2.94e-04, 2.17e-04, 8.98e-04, 5.52e-04, 6.10e-04]\n",
    "\n",
    "fig, ax1 = plt.subplots(figsize=(8, 6))\n",
    "ax2 = ax1.twinx()\n",
    "\n",
    "ax1.plot(Gamma_elastic, '-ob')\n",
    "ax2.plot(PSD, '-*r')\n",
    "ax2.yaxis.set_major_formatter(mtick.FormatStrFormatter('%.1e'))\n",
    "\n",
    "ax1.set_xlabel('Optimization Steps', fontsize= 12, fontweight='bold')\n",
    "ax1.set_ylabel('Elastic Collision Rate', fontsize= 12, fontweight='bold')\n",
    "ax1.tick_params(axis=\"y\", labelcolor='b')\n",
    "ax2.set_ylabel('Phase Space Density', fontsize= 12, fontweight='bold')\n",
    "ax2.tick_params(axis=\"y\", labelcolor='r')\n",
    "plt.tight_layout()\n",
    "plt.grid(visible=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da1a3346",
   "metadata": {},
   "source": [
    "## Plot ideal crossed beam trap potential resulting for given parameters only"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "f17a4d01",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Powers = [35, 11] * u.W\n",
    "Polarizability = 184.4 # in a.u, most precise measured value of Dy polarizability\n",
    "Wavelength = 1.064*u.um\n",
    "w_x = [27, 67]*u.um # Beam Waists in the x direction\n",
    "w_z = [32, 67]*u.um # Beam Waists in the y direction\n",
    "\n",
    "options = {\n",
    "    'axis': 1, # axis referenced to the beam along which you want the dipole trap potential\n",
    "    'extent': 1e3, # range of spatial coordinates in one direction to calculate trap potential over\n",
    "    'crossed': True,\n",
    "    'delta': 70, # angle between arms in degrees\n",
    "    'modulation': False,\n",
    "    'aspect_ratio': 5, # required aspect ratio of modulated arm\n",
    "    'gravity': False,\n",
    "    'tilt_gravity': False,\n",
    "    'theta': 0.75, # gravity tilt angle in degrees\n",
    "    'tilt_axis': [1, 0, 0], # lab space coordinates are rotated about x-axis in reference frame of beam\n",
    "    'astigmatism': False,\n",
    "    'disp_foci': 2.5*u.mm, #0.9 * z_R(w_0 = np.asarray([30]), lamb = 1.064)[0]*u.um, # difference in position of the foci along the propagation direction (Astigmatism)\n",
    "    'extract_trap_frequencies': False\n",
    "}\n",
    "\n",
    "Positions, TrapPotential = computeTrapPotential(w_x, w_z, Powers, Polarizability, options)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(Positions[options['axis']], TrapPotential[options['axis']], label = 'Crossed beam potential')\n",
    "#plt.xlim([-500, 500])\n",
    "#plt.ylim([-1800, -200])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a28b820",
   "metadata": {},
   "source": [
    "## Calculate trap frequencies in a crossed beam trap for given parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "09149423",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v_x = 442.04 Hz\n",
      "v_y = 459.15 Hz\n",
      "v_z = 637.34 Hz\n"
     ]
    }
   ],
   "source": [
    "Powers = [1, 11] * u.W\n",
    "w_x = [30, 50]*u.um # Beam Waists in the x direction\n",
    "w_z = [30, 50]*u.um # Beam Waists in the y direction\n",
    "\n",
    "options = {\n",
    "    'axis': 1, # axis referenced to the beam along which you want the dipole trap potential\n",
    "    'extent': 1e3, # range of spatial coordinates in one direction to calculate trap potential over\n",
    "    'crossed': True,\n",
    "    'delta': 70, # angle between arms in degrees\n",
    "    'modulation': False,\n",
    "    'aspect_ratio': 5, # required aspect ratio of modulated arm\n",
    "    'gravity': False,\n",
    "    'tilt_gravity': False,\n",
    "    'theta': 0.75, # gravity tilt angle in degrees\n",
    "    'tilt_axis': [1, 0, 0], # lab space coordinates are rotated about x-axis in reference frame of beam\n",
    "    'astigmatism': False,\n",
    "    'disp_foci': 2.5*u.mm, #0.9 * z_R(w_0 = np.asarray([30]), lamb = 1.064)[0]*u.um, # difference in position of the foci along the propagation direction (Astigmatism)\n",
    "    'extract_trap_frequencies': False\n",
    "}\n",
    "\n",
    "v_x = calculateCrossedBeamTrapFrequency(options['delta'], [w_x, w_z], Powers, dir = 'x')\n",
    "v_y = calculateCrossedBeamTrapFrequency(options['delta'], [w_x, w_z], Powers, dir = 'y')\n",
    "v_z = calculateCrossedBeamTrapFrequency(options['delta'], [w_x, w_z], Powers, dir = 'z')\n",
    "\n",
    "print('v_x = %.2f ' %(v_x.value) + str(v_x.unit))\n",
    "print('v_y = %.2f ' %(v_y.value) + str(v_y.unit))\n",
    "print('v_z = %.2f ' %(v_z.value) + str(v_z.unit))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "712ec2c7",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
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