notebooks/NVNeg_full_H_Zeeman_ESR_spectrum.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f9d968c4-0f4b-4a95-9e0c-b805cf3242b0",
   "metadata": {},
   "source": [
    "# External Static B and ESR spectra\n",
    "\n",
    "The electron-spin resonance spectrum in the context of ODMR contrasts is\n",
    "modeled for a single $\\text{NV}^-$ center and four NV centers along each orientation in a \n",
    "homogenous static magnetic field. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "70961cd3",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "50e44d4b",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import qutip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6e37e73a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import nvmodels\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b0481c2a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "14a6e97a-1246-4d7d-9c5f-6d5e05f9ac40",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# matplotlib widget requires jupyter-lab and ipympl\n",
    "# turns matplotlib figures interactive and zoomable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "10de2daf",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# %matplotlib widget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "edaee58d",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "nv = nvmodels.NVNegativeGroundState()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "083fb2cb",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.   0.   0.01]\n"
     ]
    }
   ],
   "source": [
    "polar = 0\n",
    "azimuthal = 0\n",
    "_x = np.sin(polar)*np.cos(azimuthal)\n",
    "_y = np.sin(polar)*np.sin(azimuthal)\n",
    "_z = np.cos(polar)\n",
    "B_mag = 100e-4  # 100 Gauss in the z direction\n",
    "static_B_field = B_mag*np.array([_x, _y, _z])\n",
    "print(static_B_field)\n",
    "\n",
    "h = nv.zero_field_hamiltonian()\n",
    "h += nv.nitrogen_hyperfine_hamiltonian()\n",
    "h += nv.nitrogen_electric_quadrupole_hamiltonian()\n",
    "h += nv.static_mag_field_hamiltonian(static_B_field, include_nucleus = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b2b49bf2",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[3, 3], [3, 3]], shape = (9, 9), type = oper, isherm = True $ \\\\ \\left(\\begin{matrix}1.233\\times10^{+09} & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 1.240\\times10^{+09} & 0.0 & -2.700\\times10^{+06} & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.237\\times10^{+09} & 0.0 & -2.700\\times10^{+06} & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & -2.700\\times10^{+06} & 0.0 & -1.915\\times10^{+09} & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & -2.700\\times10^{+06} & 0.0 & -1.910\\times10^{+09} & 0.0 & -2.700\\times10^{+06} & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -1.915\\times10^{+09} & 0.0 & -2.700\\times10^{+06} & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & -2.700\\times10^{+06} & 0.0 & 6.768\\times10^{+08} & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -2.700\\times10^{+06} & 0.0 & 6.797\\times10^{+08} & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 6.726\\times10^{+08}\\\\\\end{matrix}\\right)$"
      ],
      "text/plain": [
       "Quantum object: dims = [[3, 3], [3, 3]], shape = (9, 9), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 1.23314270e+09  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
       "   0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
       "   0.00000000e+00]\n",
       " [ 0.00000000e+00  1.24032346e+09  0.00000000e+00 -2.70000000e+06\n",
       "   0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
       "   0.00000000e+00]\n",
       " [ 0.00000000e+00  0.00000000e+00  1.23748422e+09  0.00000000e+00\n",
       "  -2.70000000e+06  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
       "   0.00000000e+00]\n",
       " [ 0.00000000e+00 -2.70000000e+06  0.00000000e+00 -1.91503410e+09\n",
       "   0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
       "   0.00000000e+00]\n",
       " [ 0.00000000e+00  0.00000000e+00 -2.70000000e+06  0.00000000e+00\n",
       "  -1.90999333e+09  0.00000000e+00 -2.70000000e+06  0.00000000e+00\n",
       "   0.00000000e+00]\n",
       " [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
       "   0.00000000e+00 -1.91497257e+09  0.00000000e+00 -2.70000000e+06\n",
       "   0.00000000e+00]\n",
       " [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
       "  -2.70000000e+06  0.00000000e+00  6.76789109e+08  0.00000000e+00\n",
       "   0.00000000e+00]\n",
       " [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
       "   0.00000000e+00 -2.70000000e+06  0.00000000e+00  6.79689873e+08\n",
       "   0.00000000e+00]\n",
       " [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
       "   0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
       "   6.72570637e+08]]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "05b4d3cc",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'State index')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eigenvalues, eigenstates = h.eigenstates()\n",
    "eigenvalues = eigenvalues - np.min(eigenvalues)\n",
    "state_probs_text = [nvmodels.utilities.two_qutrit_state_to_text(s, decimals=5) for s in eigenstates]\n",
    "\n",
    "fig, ax = nvmodels.plotting.plot_eigenspectrum_mpl(eigenvalues, state_probs_text)\n",
    "ax.set_ylabel('Energy (Hz)')\n",
    "ax.set_xlabel('State index')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "36a5a476-a83a-4199-afab-dfd0a119bb60",
   "metadata": {
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "state_probs_text = [nvmodels.utilities.two_qutrit_state_to_text(s, decimals=5) for s in eigenstates]\n",
    "nvmodels.plotting.plot_eigenspectrum_plotly(eigenvalues, state_probs_text, ylabel = \"Energy (Hz)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "1db649a0",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "rf_freq = np.arange(2.0e9, 3.5e9, 1e6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "12101713",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "energy_transitions = nv.electron_spin_resonances(h)\n",
    "contrast = 1 + np.array([nvmodels.utilities.lorentzian(rf_freq, e, -0.01, 10e6) for e in energy_transitions]).sum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b0fb764b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f86203afb80>]"
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     "execution_count": 15,
     "metadata": {},
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fix,ax = plt.subplots()\n",
    "\n",
    "plt.plot(rf_freq, contrast)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "13c134c9",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# hyperfine splitting\n",
    "\n",
    "rf_freq = np.arange(2.586e9, 2.594e9, .05e6)\n",
    "contrast = 1 + np.array([nvmodels.utilities.lorentzian(rf_freq, e, -.1, .1e6) for e in energy_transitions]).sum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "ea05888a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8623072b90>]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fix,ax = plt.subplots()\n",
    "plt.plot(rf_freq, contrast)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e333d846-05f0-466f-9889-e95e79c9e1c0",
   "metadata": {
    "tags": []
   },
   "source": [
    "## All 4 orientations\n",
    "\n",
    "For ensembles of NV centers, we will have NV centers oriented in four different ways, according to the crystal structure of diamond. \n",
    "We want to add the other three NV center orientations but use the same B field that is was applied to our NV center above.\n",
    "We need to find the rotation to the other three NV center axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "49b054f0-fd98-4fed-b1dc-7494aff87bfc",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "z = np.array([0,0,1])\n",
    "nv111 = np.array([1,1,1])/np.linalg.norm(np.array([1,1,1]))\n",
    "nv1b1b1 = np.array([1,-1,-1])/np.linalg.norm(np.array([1,-1,-1]))\n",
    "nvb11b1 = np.array([-1, 1, -1])/np.linalg.norm(np.array([-1,1,-1]))\n",
    "nvb1b11 = np.array([-1, -1, 1])/np.linalg.norm(np.array([-1,-1,1]))\n",
    "\n",
    "nv_orientations = [nv111, nv1b1b1, nvb11b1, nvb1b11]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "2c519a07-4dcb-45c8-8658-fa98b46678e7",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "B_nv111_axis_in_lab_frame = 100e-4*np.array([1,1,1])/np.linalg.norm(np.array([1,1,1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "82e389c6-f572-4fe0-894e-4fce082837bc",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.78867513, -0.21132487, -0.57735027],\n",
       "       [-0.21132487,  0.78867513, -0.57735027],\n",
       "       [ 0.57735027,  0.57735027,  0.57735027]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Demonstrate our rotation matrices\n",
    "nvmodels.utilities.rotation_matrix_from_vectors(nv111,z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "b6f79dcc-ebe6-4f37-ba99-379d21e0eb7c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.57735027, -0.57735027,  0.57735027])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nvmodels.utilities.lab_to_nv_orientation(z, nv111)# a z-vector in the lab frame represened in the nv111 frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "98a87362-685b-45d7-9f9c-c07eeb5aec33",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-5.55111512e-17, -5.55111512e-17,  1.00000000e+00])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nvmodels.utilities.lab_to_nv_orientation(nv111, nv111)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "055714ca-c234-4786-b371-a3129f5b0dfb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4.33680869e-19, -4.33680869e-19,  1.00000000e-02])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nvmodels.utilities.lab_to_nv_orientation(B_nv111_axis_in_lab_frame, nv111) # rotate to nv111 axis -- B should be entirely along Z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "6d984ce8-851a-4243-8013-f9fda144db11",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.00666667,  0.00666667, -0.00333333])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nvmodels.utilities.lab_to_nv_orientation(B_nv111_axis_in_lab_frame, nvb1b11) #  rotate to nvb1b11 axis"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "128893ad-f2c4-45ba-a07e-fa6a4a2415ef",
   "metadata": {},
   "source": [
    "### B field aligned along 111\n",
    "\n",
    "Using the B field aligned along 111, what should our ODMR spectrum look like?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "621ffbdb-1f04-4389-b906-cec42e9c770c",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "energy_transitions = []\n",
    "contrasts = []\n",
    "rf_freq = np.arange(2.0e9, 3.5e9, 1e6)\n",
    "lorentz_width = 10e6\n",
    "contrast_amp = -0.01\n",
    "\n",
    "for nv_orient in nv_orientations:\n",
    "    h = nv.zero_field_hamiltonian()\n",
    "    h += nv.nitrogen_hyperfine_hamiltonian()\n",
    "    h += nv.nitrogen_electric_quadrupole_hamiltonian()\n",
    "\n",
    "    B = nvmodels.utilities.lab_to_nv_orientation(B_nv111_axis_in_lab_frame, nv_orient)\n",
    "\n",
    "    h += nv.static_mag_field_hamiltonian(B, include_nucleus = True)\n",
    "    energy_transitions += nv.electron_spin_resonances(h)\n",
    "    contrasts.append(np.array([nvmodels.utilities.lorentzian(rf_freq, e, contrast_amp, lorentz_width) for e in energy_transitions]).sum(axis=0))\n",
    "    \n",
    "full_spectrum = 1 + np.array(contrasts).sum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "be6d9ef4-3632-44c1-867a-f095d4a24bd5",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8623116320>]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fix,ax = plt.subplots()\n",
    "plt.plot(rf_freq, full_spectrum)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f8bb623-d45b-4080-b350-37cd5ebc93f1",
   "metadata": {},
   "source": [
    "### Arbitrary B field direction.\n",
    "\n",
    "Through trial and error, found a B field that ensures we see all splittings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "0066de3f-0012-402c-8bfc-9543e51290aa",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "energy_transitions = []\n",
    "contrasts = []\n",
    "# high res\n",
    "rf_freq = np.arange(2.6e9, 3.15e9, .025e6)\n",
    "lorentz_width = .5e6\n",
    "contrast_amp = -0.01\n",
    "\n",
    "# low res\n",
    "# rf_freq = np.arange(2.0e9, 3.5e9, 1e6)\n",
    "# lorentz_width = 10e6\n",
    "# contrast_amp = -0.01\n",
    "\n",
    "v = np.array([.2,-.5,1]) #choose the direction of the B field\n",
    "\n",
    "B_in_lab_frame = 100e-4*v/np.linalg.norm(v)\n",
    "\n",
    "for nv_orient in nv_orientations:\n",
    "    h = nv.zero_field_hamiltonian()\n",
    "    h += nv.nitrogen_hyperfine_hamiltonian()\n",
    "    h += nv.nitrogen_electric_quadrupole_hamiltonian()\n",
    "\n",
    "    B = nvmodels.utilities.lab_to_nv_orientation(B_in_lab_frame, nv_orient)\n",
    "\n",
    "    h += nv.static_mag_field_hamiltonian(B, include_nucleus = True)\n",
    "    energy_transitions += nv.electron_spin_resonances(h)\n",
    "    contrasts.append(np.array([nvmodels.utilities.lorentzian(rf_freq, e, contrast_amp, lorentz_width) for e in energy_transitions]).sum(axis=0))\n",
    "    \n",
    "full_spectrum = 1 + np.array(contrasts).sum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "76abe4e9-ad5a-48a6-ad11-ae375f8c137a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8622f81a20>]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fix,ax = plt.subplots(figsize=(10,4))\n",
    "plt.plot(rf_freq, full_spectrum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "96b102aa-de19-464c-9fbd-c3b5a37dccb9",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}