{ "cells": [ { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "# Multiple central spins\n", "\n", "Instead of one central spin, the PyCCE can be used to consider the dynamics of *N* central spins.\n", "\n", "Then the central spin Hamiltonian and spin-bath Hamiltonian are written as:\n", "\n", "\\begin{equation}\n", "\\hat H_S = \\sum_i \\mathbf{S_i D_i S_i} + \\mathbf{S_i \\gamma_{S_i} B} + \\sum_{i < j} \\mathbf{S_i K_{ij} S_j}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Where $\\mathbf{K_{ij}}$ are interaction tensors between central spins $i$ and $j$.\n", "\n", "The central spin-bath couplings can be defined as:\n", "\n", "\\begin{equation}\n", "\\hat H_{SB} = \\sum_{i,l} \\mathbf{S_{i} A_{il} I_{l}}\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "!pip install pycce\n", "!pip install ase\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "\n", "import sys\n", "import pycce as pc\n", "import ase\n", "\n", "seed = 8805\n", "np.random.seed(seed)\n", "np.set_printoptions(suppress=True, precision=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Two NV Centers in Diamond\n", "First example is two NV centers in diamond. We begin by considering two non-interacting electron spins in the nuclear spin bath.\n", "\n", "We generate the nuclear $^{13}$C spin bath using a well-defined procedure." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from ase.build import bulk\n", "\n", "# Generate unitcell from ase\n", "diamond = pc.read_ase(bulk('C', 'diamond', cubic=True))\n", "diamond.zdir = [1,1,1]\n", "\n", "bath = diamond.gen_supercell(200, seed=seed, remove=('C', [0,0,0]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Generating the `CenterArray` object\n", "\n", "The properties of the NVs are stored in the `CenterArray`.\n", "\n", "`CenterArray` object contains the properties of all central spins in the system. In this example, we prepare the array consisting of two electron spin-1, with the same ZFS and gyromagnetic ratio." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CenterArray\n", "(s: [1. 1.],\n", "xyz:\n", "[[ 0. 0. 0.]\n", " [ 0. 0. 1000.]],\n", "zfs:\n", "[[[-800000. 0. 0.]\n", " [ 0. -800000. 0.]\n", " [ 0. 0. 1600000.]]\n", "\n", " [[-800000. 0. 0.]\n", " [ 0. -800000. 0.]\n", " [ 0. 0. 1600000.]]],\n", "gyro:\n", "[[[-17608.5971 -0. -0. ]\n", " [ -0. -17608.5971 -0. ]\n", " [ -0. -0. -17608.5971]]\n", "\n", " [[-17608.5971 -0. -0. ]\n", " [ -0. -17608.5971 -0. ]\n", " [ -0. -0. -17608.5971]]])\n" ] } ], "source": [ "D = 2.4e6 # in kHz\n", "gyro = pc.ci['e'].gyro # gyromagnetic ratio of electron in rad/G/ms\n", "\n", "# Generate an array of two central spins, \n", "# each with the same D and gyromagnetic ratio value,\n", "# separated by 100 nm.\n", "nvs = pc.CenterArray(spin=[1, 1], D=[D, D], \n", " position=[[0, 0, 0], [0, 0, 1000]],\n", " gyro=[gyro, gyro], alpha=0, beta=2) \n", "\n", "print(nvs) # Print properties of the central spin array" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can access the properties of the central spins (and modify them) as items in `CenterArray`." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Center\n", "(s: 1.0,\n", "xyz:\n", "[0. 0. 0.],\n", "zfs:\n", "[[-800000. 0. 0.]\n", " [ 0. -800000. 0.]\n", " [ 0. 0. 1600000.]],\n", "gyro:\n", "-17608.59705) \n", "\n", "CenterArray\n", "(s: [1. 1.],\n", "xyz:\n", "[[ 0. 0. 0.]\n", " [ 0. 0. 1000.]],\n", "zfs:\n", "[[[-800000. 0. 0.]\n", " [ 0. -800000. 0.]\n", " [ 0. 0. 1600000.]]\n", "\n", " [[-800000. 0. 0.]\n", " [ 0. -800000. 0.]\n", " [ 0. 0. 1600000.]]],\n", "gyro:\n", "[[[ 989.9394 629.7526 554.6254]\n", " [ 641.9013 943.0174 56.2197]\n", " [ 568.4803 978.1593 265.0863]]\n", "\n", " [[-17608.5971 -0. -0. ]\n", " [ -0. -17608.5971 -0. ]\n", " [ -0. -0. -17608.5971]]])\n" ] } ], "source": [ "print(nvs[0], '\\n')\n", "nvs[0].gyro = np.random.random((3,3)) * 1000\n", "print(nvs)\n", "nvs[0].gyro = np.eye(3) * pc.ELECTRON_GYRO" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For illustrative purposes, we will use identical nuclear spin environment for two NVs. For that we create a copy of the `BathArray`, shift it by 1000 angstroms, and concatenate two arrays.\n", "\n", "The `CenterArray` instance is provided as a `spin` keyword to the `Simulator` object. It can be later accesed as `Simulator.center` attribute." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Simulator for center array of size 2.\n", "magnetic field:\n", "array([ 0., 0., 500.])\n", "\n", "Parameters of cluster expansion:\n", "r_bath: [40, 40]\n", "r_dipole: 6\n", "order: 2\n", "\n", "Bath consists of 1046 spins.\n", "\n", "Clusters include:\n", "1046 clusters of order 1.\n", "836 clusters of order 2.\n", "\n" ] } ], "source": [ "bath2 = bath.copy()\n", "bath2.z += 1000\n", "\n", "calc = pc.Simulator(spin=nvs, bath=np.concatenate([bath, bath2]),\n", " r_bath=[40, 40], r_dipole=6, order=2, magnetic_field=500)\n", "print(calc)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When the number of central spins is greater than one, hyperfine couplings in the ``BathArray`` have an additional dimension, corresponding to the two sets of the hyperfine couplings." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(1046, 2, 3, 3)\n", "[[[ 2.3048 1.1078 -0.6608]\n", " [ 1.1078 -1.0451 -0.1988]\n", " [-0.6608 -0.1988 -1.2597]]\n", "\n", " [[-0. 0. 0. ]\n", " [ 0. -0. 0. ]\n", " [ 0. 0. 0. ]]]\n" ] } ], "source": [ "print(calc.bath.A.shape)\n", "print(calc.bath[0].A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Decoherence of entangled state\n", "Let's do some calculations! Note that `gcce` method in this case includes a lot (9-fold) larger Hilbert space, so it will take a bit longer.\n", "\n", "Here we compute the coherence function, defined as a decay of the offdiagonal element of the density matrix:\n", "\n", "\\begin{equation}\n", "L=\\langle 0 | \\hat \\rho | 1 \\rangle\n", "\\end{equation}\n", "\n", "Where $| 0 \\rangle$ and $| 1 \\rangle$ are defined as eigenstates of the central spin Hamiltonian introduced above." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/onizhuk/midway/codes_development/pyCCE/pycce/h/functions.py:298: NumbaPerformanceWarning: \u001b[1m\u001b[1m\u001b[1m\u001b[1m'@' is faster on contiguous arrays, called on (array(complex128, 2d, A), array(complex128, 2d, A))\u001b[0m\u001b[0m\u001b[0m\u001b[0m\n", " hself = vec_tensor_vec(svec, tensor, svec)\n", "/home/onizhuk/midway/codes_development/pyCCE/pycce/h/functions.py:298: NumbaPerformanceWarning: \u001b[1m\u001b[1m\u001b[1m'@' is faster on contiguous arrays, called on (array(complex128, 2d, A), array(complex128, 2d, A))\u001b[0m\u001b[0m\u001b[0m\n", " hself = vec_tensor_vec(svec, tensor, svec)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 1.72 s, sys: 20.3 ms, total: 1.74 s\n", "Wall time: 629 ms\n", "CPU times: user 2min 22s, sys: 1.99 s, total: 2min 24s\n", "Wall time: 24.4 s\n" ] } ], "source": [ "ts = np.linspace(0, 2)\n", "calc.alpha = 0 # 00 state\n", "calc.beta = 1 # -10 state\n", "cce = {}\n", "gcce = {}\n", "\n", "cce['01'] = calc.compute(ts, pulses=1)\n", "gcce['01'] = calc.compute(ts, method='gcce', pulses=1)\n", "\n", "calc.beta = 1 # 0-1 state\n", "cce['02'] = calc.compute(ts, pulses=1)\n", "gcce['02'] = calc.compute(ts, method='gcce', pulses=1)\n", "\n", "calc.beta = 3 # -1 -1 state\n", "%time cce['03'] = calc.compute(ts, pulses=1)\n", "%time gcce['03'] = calc.compute(ts, method='gcce', pulses=1)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, in the case of decoupled NV centers the coherence of the bell state decays as a product of separated NVs decoherence." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(ts, cce['01'].real, label='01 CCE')\n", "plt.plot(ts, gcce['01'].real, ls='--', label='01 gCCE')\n", "\n", "plt.plot(ts, cce['02'].real, markevery=(2, 4), ls='', marker='o', label='02 CCE')\n", "plt.plot(ts, gcce['02'].real, ls='', marker='o', markevery=4, label='02 gCCE')\n", "\n", "plt.plot(ts, cce['03'].real, label='03 CCE')\n", "plt.plot(ts, gcce['03'].real, ls='--', label='03 gCCE')\n", "\n", "plt.plot(ts, gcce['02'].real * gcce['01'].real, ls='', marker='o', markevery=2, label='01*02')\n", "plt.ylabel('Coherence')\n", "plt.xlabel('Time (ms)')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Entanglement between two NVs\n", "\n", "We can use the PyCCE to predict how the entanglement evolves between two dipolarly coupled electron spins, initially prepared in the product state:\n", "\n", "\\begin{equation}\n", "| \\Psi \\rangle = \\frac{1}{2} (| 0 \\rangle + | -1 \\rangle) \\otimes (| 0 \\rangle + | -1 \\rangle)\n", "\\end{equation}\n", "\n", "We add interaction between two NVs by calling `nvs.point_dipole` method, that generates interaction tensors from point dipole approximation. We can also directly set interaction tensors by calling `nvs.add_interaction` method or modifiying `nvs.imap` attribute.\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Initial amplitudes in Sz x Sz basis: [0. 0. 0. 0. 0.5 0.5 0. 0.5 0.5]\n", "Interaction tensor:\n", "[[ 416.3281 -0. -0. ]\n", " [ -0. 416.3281 -0. ]\n", " [ -0. -0. -832.6562]]\n" ] } ], "source": [ "nvs = pc.CenterArray(spin=[1, 1], D=[D, D],\n", " position=[[0, 0, 0], [0, 0, 50]],\n", " gyro=[gyro, gyro], alpha=0, beta=2)\n", "\n", "nvs.point_dipole() # Add interactions\n", "\n", "zero = np.array([0, 1, 0])\n", "one = np.array([0, 0, 1])\n", "nvs[0].alpha = zero # Set qubit levels\n", "nvs[0].beta = one\n", "nvs[1].alpha = one\n", "nvs[1].beta = zero\n", "\n", "# Generate product state\n", "state = pc.normalize(np.kron(zero + one, zero + one))\n", "nvs.state = state\n", "print(\"Initial amplitudes in Sz x Sz basis:\", np.abs(nvs.state)) # Initial state\n", "print(\"Interaction tensor:\")\n", "print(nvs.imap[0, 1]) # in kHz" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will use negativity (https://en.wikipedia.org/wiki/Negativity_(quantum_mechanics)) as a metric of entanglement, defined as:\n", "\n", "$ \\mathcal{N}(\\rho) \\equiv \\frac{||\\rho^{\\Gamma_A}||_1-1}{2}$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# 0 1 2 3 4 5 6 7 8\n", "states = ['11', '10', '1-1', '01', '00', '0-1', '-11', '-10', '-1-1']\n", "\n", "def pltdm(t, dm, ax):\n", " \"\"\"\n", " Function to plot nonzero elements of the density matrix.\n", " \"\"\"\n", " for i, j in np.argwhere(np.triu(dm[0])):\n", " label=r'$\\langle$' + f'{states[i]}'+r'$|\\rho|$'+ f'{states[j]}'+ r'$\\rangle$'\n", " ax.plot(t, np.abs(dm[:, i, j]), label=label)\n", "\n", "\n", "def partial_transpose(dm0, dim, which):\n", " \"\"\"\n", " Get partial transpose of the density matrix.\n", " \"\"\"\n", " ish = dm0.shape\n", " n = len(dim)\n", " indexes = np.arange(len(dim)*2)\n", " indexes[which] = n + which\n", " indexes[n + which] = which\n", " return dm0.reshape(*dim, *dim).transpose(*indexes).reshape(ish)\n", "\n", "def negativities(dms):\n", " \"\"\"\n", " Compute negativity for an array of density matrices.\n", " \"\"\"\n", " negs = []\n", " for dm in dms:\n", " pt = partial_transpose(dm, [3,3], 0)\n", " tr_norm = np.linalg.norm(pt, ord='nuc')\n", " negs.append((tr_norm - 1) / 2)\n", " return np.array(negs)\n", "\n", "def rz(dm):\n", " \"\"\"\n", " Set density matrix elements equal to zero at zero timepoint to zero.\n", " Removes numerical instabilities when we divide by a near-zero value.\n", " \"\"\"\n", " dm[np.broadcast_to((dm[0] == 0), dm.shape)] = 0\n", " return dm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, compute the entanglement without dynamical decoupling pulses applied." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "tfid = np.linspace(0, 0.01, 151)\n", "\n", "c = pc.Simulator(nvs, bath=bath, r_bath=40, r_dipole=6,\n", " order=2, pulses=0, magnetic_field=500)\n", "dmfid = rz(c.compute(tfid, method='gcce', fulldm=True))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n", "\n", "pltdm(tfid, dmfid, axes[0])\n", "axes[1].plot(tfid, negativities(dmfid))\n", "\n", "axes[0].legend()\n", "axes[0].set(ylabel='DM element', xlabel='Time (ms)')\n", "axes[1].set(ylabel='Negativity', xlabel='Time (ms)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compare that to the case, when $\\pi$ pulse is applied to each of the electron spins.\n", "\n", "To create such pulse sequence, we specify the `which` keyword argument of the `Pulse` class with indexes of both NVs in the `CenterArray`." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "# Pulse, flipping simultaneously the two NVs\n", "p = pc.Pulse('x', np.pi, which=[0, 1])\n", "the = np.linspace(0, 0.3, 151)\n", "\n", "c = pc.Simulator(nvs, bath=bath, r_bath=40, r_dipole=6,\n", " order=2, pulses=[p], magnetic_field=500)\n", "\n", "dm_short = rz(c.compute(tfid, method='gcce', fulldm=True))\n", "dm = rz(c.compute(the, method='gcce', fulldm=True))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, we find a significantly prolonged entanglement between two electron spins." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(2, 2, figsize=(12, 8))\n", "\n", "pltdm(tfid, dm_short, axes[0, 0])\n", "axes[0, 1].plot(tfid, negativities(dm_short))\n", "\n", "pltdm(the, dm, axes[1, 0])\n", "axes[1, 1].plot(the, negativities(dm))\n", "\n", "axes[0, 0].legend()\n", "\n", "for row in axes:\n", " row[0].set(ylabel='DM element', xlabel='Time (ms)', ylim=(-0.01, 0.26))\n", " row[1].set(ylabel='Negativity', xlabel='Time (ms)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Si:Bi donor\n", "\n", "We use the PyCCE framework to reproduce paper: PHYSICAL REVIEW B 91, 245416 (2015) by S. J. Balian et al. Here, $^{209}$Bi nuclear spin 9/2 and electron spin 1/2 interact very strongly (~1.5 GHz hyperfine), with many avoided crossings arising and leading to clock transitions. The qubit states is chosen as a two energy levels of the hybrid electron and nuclear spins system.\n", "\n", "\n", "\n", "First, we prepare a `CenterArray`, containing the properties of two central spins." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "aiso = 1.4754e6\n", "im = np.eye(3) * aiso # Isotropic interaction tensor \n", "ebi = pc.CenterArray(spin=[1/2, 9/2],\n", " gyro=[pc.ci['e'].gyro, pc.ci['209Bi'].gyro],\n", " imap=im, alpha=6, beta=13)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For visualization purposes, plot a diagram of the energies of the hybrid system as a function of magnetic field.\n", "Here the chosen qubit levels are highlighted with black points." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ens = []\n", "ms = np.linspace(0, 4000, 51) # applied magnetic field\n", "for mf in ms:\n", " ebi.generate_states([0,0, mf])\n", " ens.append(ebi.energies)\n", "\n", "ens = np.asarray(ens)\n", "\n", "lowerdf = pd.DataFrame(ens[:, :10]/1e6, index=ms/1e4,\n", " columns=np.arange(10))\n", "higherdf = pd.DataFrame(ens[:, :10:-1]/1e6, index=ms/1e4,\n", " columns=np.arange(11, ens.shape[1])[::-1])\n", "\n", "fig, ax = plt.subplots(figsize=(3, 4))\n", "\n", "lowerdf.plot(ax=ax, cmap='viridis', legend=False, lw=1)\n", "higherdf.plot(ax=ax, cmap='viridis', legend=False, lw=1)\n", "lowerdf[6].plot(ax=ax, color='black', ls=':', lw=2)\n", "higherdf[13].plot(ax=ax, color='black', ls=':', lw=2)\n", "ax.set(xlabel='B (T)', ylabel='E (GHz)', xlim=(0, 0.4));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we define the calculations of hyperfine couplings for the electron spin." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "# PHYSICAL REVIEW B 68, 115322 (2003)\n", "# https://link.springer.com/content/pdf/10.1007%2FBF02725533.pdf for Bi\n", "n_parameter = np.sqrt(0.029/0.069)\n", "# https://journals.aps.org/pr/pdf/10.1103/PhysRev.114.1219\n", "a_parameter = 25.09\n", "\n", "def factor(x, y, z, n=n_parameter, a=a_parameter, b=14.43):\n", " top = np.exp(-np.sqrt(x ** 2 / (n * b) **2 + (y ** 2 + z ** 2) / (n * a) ** 2))\n", " bottom = np.sqrt(np.pi * (n * a) ** 2 * (n * b) )\n", "\n", " return top / bottom\n", "\n", "def contact_si(r, gamma_n, gamma_e=pc.ELECTRON_GYRO, \n", " a_lattice=5.43, nu=186, n=n_parameter,\n", " a=a_parameter, b=14.43):\n", "\n", " k0 = 0.85 * 2 * np.pi / a_lattice\n", " pre = 8 / 9 * gamma_n * gamma_e * pc.HBAR_MU0_O4PI * nu\n", " xpart = factor(r[0], r[1], r[2], n=n, a=a, b=b) * np.cos(k0 * r[0])\n", " ypart = factor(r[1], r[2], r[0], n=n, a=a, b=b) * np.cos(k0 * r[1])\n", " zpart = factor(r[2], r[0], r[1], n=n, a=a, b=b) * np.cos(k0 * r[2])\n", " return pre * (xpart + ypart + zpart) ** 2\n", "\n", "\n", "def func(bath):\n", " na = np.newaxis\n", " aiso = contact_si(bath.xyz.T, bath.gyro) # Contact term\n", " # Generate dipolar terms\n", " bath.from_center(ebi) \n", " # Add contact term for electron spni\n", " bath.A[:, 0] += np.eye(3)[na, :, :] * aiso[:, na, na]\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And prepare the spin bath using `ase` interface." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "si = pc.read_ase(bulk('Si', cubic=True))\n", "atoms = si.gen_supercell(200, remove=('Si', [0., 0, 0]), seed=seed)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Away from avoided crossings\n", "Chosen energy levels 6 <-> 14 give raise to the clock transition (CT) at ~800 G. First compute the coherence avay from CT at 3200 G. It will take some time, as the bath is large." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "nts = np.linspace(0, 2, 101)\n", "sicalc = pc.Simulator(ebi, bath=atoms, r_bath=80, r_dipole=6,\n", " order=2, magnetic_field=3200, pulses=1,\n", " hyperfine=func)\n", "orders = [1, 2, 3]\n", "\n", "ls = []\n", "for v in orders:\n", " sicalc.order = v\n", " ls.append(sicalc.compute(nts).real)\n", "\n", "dfoff = pd.DataFrame(ls, columns=nts, index=orders).T" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "dfoff.plot()\n", "plt.xlabel('Time (ms)')\n", "plt.ylabel('Coherence');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Near avoided crossings\n", "\n", "Now compare that to the coherence near the CT ( -4G from CT). Note, that number of clusters considered here is already rather large, so the calculations will take a minute or two." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "ts = np.linspace(0, 100, 101)\n", "\n", "sicalc.magnetic_field = 791\n", "orders = [1, 2, 3, 4]\n", "\n", "ls = []\n", "for v in orders:\n", " sicalc.order = v\n", " ls.append(sicalc.compute(ts).real)\n", "\n", "dfat = pd.DataFrame(ls, columns=ts, index=orders).T" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "dfat.plot()\n", "plt.xlabel('Time (ms)')\n", "plt.ylabel('Coherence');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Exactly at CT one needs even higher `order`, larger `r_bath` and `r_dipole`, and random bath state sampling to get accurate results. It is left as an exersize to the reader to try and converge the coherence at clock transition." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.9" }, "pycharm": { "stem_cell": { "cell_type": "raw", "metadata": { "collapsed": false }, "source": [] } } }, "nbformat": 4, "nbformat_minor": 4 }