{ "cells": [ { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "# NV Center in Diamond\n", "In this tutorial we will go over the main steps of running CCE calculations for the NV center in diamond with the **PyCCE** module. Those include:\n", "\n", "* Generating the spin bath using the `pycce.BathCell` instance.\n", "* Setting up properties of the `pycce.Simulator` instance.\n", "* Running the calculations with the `Simulator.compute` function.\n", "\n", "We will compute the Hahn-echo coherence function (with decoupling $\\pi$-pulse applied) using the following available methods: \n", "\n", "* Conventional CCE.\n", "* Generalized CCE (gCCE).\n", "* gCCE with Monte-Carlo bath sampling.\n", "\n", "Finally, we will run a simulation on how different bath polarization will impact Hahn-echo signal." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "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", "from mpl_toolkits import mplot3d\n", "\n", "seed = 8805\n", "np.random.seed(seed)\n", "np.set_printoptions(suppress=True, precision=5)" ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "## Generate nuclear spin bath\n", "Building a supercell of nuclear spins from the `ase.Atoms` object." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Build BathCell\n", "\n", "To generate cell it from `ase.atoms` object, use classmethod `BathCell.from_ase`." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "from ase.build import bulk\n", "\n", "# Generate unitcell from ase\n", "diamond = bulk('C', 'diamond', cubic=True)\n", "diamond = pc.read_ase(diamond)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following attributes are created with this initiallization:\n", "\n", "* `.cell` is ndarray containing information of lattice vectors. Each **column** is a lattice vector in cartesian coordinates.\n", "* `.atoms` is a dictionary with keys corresponding to the atom name, and each item is a list of the coordinates in cell coordinates." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Cell\n", " [[3.57 0. 0. ]\n", " [0. 3.57 0. ]\n", " [0. 0. 3.57]]\n", "\n", "Atoms\n", " defaultdict(, {'C': [array([0., 0., 0.]), array([0.25, 0.25, 0.25]), array([0. , 0.5, 0.5]), array([0.25, 0.75, 0.75]), array([0.5, 0. , 0.5]), array([0.75, 0.25, 0.75]), array([0.5, 0.5, 0. ]), array([0.75, 0.75, 0.25])]})\n" ] } ], "source": [ "print('Cell\\n', diamond.cell)\n", "print('\\nAtoms\\n', diamond.atoms)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Populate BathCell with isotopes\n", "\n", "The **PyCCE** package uses EasySpin database of the concentrations of all common stable isotopes with non-zero spin, however the user can proide custom concentrations.\n", "\n", "\n", "Use function `BathCell.add_isotopes` to add one (or several) isotopes of the element. Each isotope is initiallized with ``tuple`` containing name of the isotope and its concentration.\n", "\n", "Name of the isotope includes the number and element symbol, provided in the `atoms` object. As an output, the `BathCell.add_isotopes` method returns view on dictionary `BathCell.isotopes` which can be modified directly. Structure of the dictionary-like object:\n", "\n", "```\n", "{element_1: {isotope_1: concentration, isotope_2: concentration},\n", " element_2: {isotope_3: concentration ...}}\n", "```\n" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "defaultdict(dict, {'C': {'13C': 0.011}})" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Add types of isotopes\n", "diamond.add_isotopes(('13C', 0.011))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Isotopes may also be directly added to `BathCell.isotopes`. For example, below we are adding an isotope without the nuclear spin:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "diamond.isotopes['C']['14C'] = 0.001" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Set z-direction of the bath (optional)\n", "\n", "In the `Simulator` object everything is set in $S_z$ basis. When the quantization axis of the defect does not allign with the (0, 0, 1) direction of the crystal axis, the user needs to define the axis.\n", "\n", "If one wants to specify the complete rotation of cartesian axes, one can provide a rotation matrix to rotate the cartesian reference frame with respect to the cell coordinates by calling the `BathCell.rotate` method." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "# set z direction of the defect\n", "diamond.zdir = [1, 1, 1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Generate spin bath\n", "\n", "To generate the spin bath, use the `BathCell.gen_supercell` method. First argument is the linear size of the supercell (minimum distance between any two faces of the supercell is equal to or larger than this parameter). Additional keyword arguments are `remove` and `add`.\n", "\n", "`remove` takes a ``tuple`` or ``list of tuples`` as an argument. First element of each tuple is the name of the **atom** at that location, second element - coordinates in unit cell coordinates. If such atoms are found in the supercell, they are removed from it.\n", "\n", "`add` takes a ``tuple`` or ``list of tuples`` as an argument. First element of each tuple is the name of the **isotope** at that location, second element - coordinates in unit cell coordinates. Each of the specified isotopes will be added in the final supercell at specified locations." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/onizhuk/midway/codes_development/pyCCE/pycce/bath/array.py:222: UserWarning: Spin type for 14C was not provided and was not found in common isotopes.\n", " obj[n] = array[n]\n" ] } ], "source": [ "# Add the defect. remove and add atoms at the positions (in cell coordinates) \n", "atoms = diamond.gen_supercell(200, remove=[('C', [0., 0, 0]),\n", " ('C', [0.5, 0.5, 0.5])],\n", " add=('14N', [0.5, 0.5, 0.5]),\n", " seed=seed)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note, that because the `14C` isotope doesn't have a spin, **PyCCE** does not find it in common isotopes, and raises a warning. We have to provide `SpinType` for it separately, or define the properties as follows:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "atoms['14C'].gyro = 0\n", "atoms['14C'].spin = 0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## BathArray Structure\n", "The bath spins are stored in the `BathArray` object - a subclass of `np.ndarray` with fixed datastructure:\n", "\n", "* `N` field `dtype('= 1).\n", "\n", "All of the fields are accesible as attributes of `BathArray`.\n", "Additionally, the subarrays of the specific spins are accessible with their name as indicated above.\n", "\n", "Upon generation of the array from the cell, the `Q` and `A` fields are empty. The Hyperfine couplings will be automatically computed by the `Simulator` object, however the quadrupole couplings must be set by the user.\n", "\n", "The additional attributes allow one to access `SpinType` properties:\n", "\n", "+ `name` returns the spin name or array of spin names;\n", "+ `spin` returns the value of the spin or array of ones;\n", "+ `gyro` returns gyromagnetic ratios of the spins;\n", "+ `q` returns quadrupole constants of the spins;\n", "+ `h` returns a dictionary with user-defined additions to the Hamiltonian. \n", "+ `detuning` returns detunings of the spins (See definition below).\n", "\n", "For example, below we print out the attributes of the first two spins in the `BathArray`." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Names\n", " ['13C' '13C']\n", "\n", "Coordinates\n", " [[-13.97678 -1.48178 -92.75132]\n", " [ 27.89939 42.17939 -45.86038]]\n", "\n", "Hyperfine tensors\n", " [[[0. 0. 0.]\n", " [0. 0. 0.]\n", " [0. 0. 0.]]\n", "\n", " [[0. 0. 0.]\n", " [0. 0. 0.]\n", " [0. 0. 0.]]]\n", "\n", "Quadrupole tensors\n", " [[[0. 0. 0.]\n", " [0. 0. 0.]\n", " [0. 0. 0.]]\n", "\n", " [[0. 0. 0.]\n", " [0. 0. 0.]\n", " [0. 0. 0.]]]\n" ] } ], "source": [ "print('Names\\n', atoms[:2].N)\n", "print('\\nCoordinates\\n', atoms[:2].xyz)\n", "print('\\nHyperfine tensors\\n', atoms[:2].A)\n", "print('\\nQuadrupole tensors\\n',atoms[:2].Q)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The properties of spin types (gyromagnetic ratio, quadrupole moment, etc) are stored in the `BathArray.types` attribute, which is an instance of `SpinDict` containing `SpinType` classes. For most known isotopes `SpinType` can be found in the `pycce.common_isotopes` dictionary, and is set by default (including electron spin-1/2, which is denoted by setting `N = e`). The user can add additional `SpinType` objects, by calling `BathArray.add_type` method or setting elements of `SpinDict` directly. For details of the first approach see documentation of `SpinDict.add_type` method.\n", "\n", "The direct setting of types is rather simple. The user can set elements of `SpinDict` with ``tuple``, containing:\n", "\n", "* **(spin, gyromagnetic ratio, quadrupole moment *(optional)*, detuning *(optional)*, )** \n", "\n", " **OR**\n", " \n", "* **(isotope, spin, gyromagnetic ratio, quadrupole moment *(optional)*, detuning *(optional)*, )** \n", "\n", "where:\n", "\n", "- **isotope** (*str*) is the name of the given spin (same one as in `N` field of `BathArray`) to define new `SpinType` object.\n", " The key of `SpinDict` **has** to be the correct name of the spin (\"isotope\" field in the tuple).\n", "- **spin** (*float*) is the total spin of the given bath spin.\n", "- **gyromagnetic ratio** (*float*) is the gyromagnetic ratio of the given bath spin.\n", "- **quadrupole moment** (*float*) is the quadrupole moment of the given bath spin. Relevant only when electric field gradient are used\n", " to generate quadrupole couplings for spins, stored in the ``BathArray``, with ``BathArray.from_efg`` method.\n", "- **detuning** (float) is an additional energy splitting for model spins, included as an extra $+\\omega \\hat S_z$ term in the Hamiltonian,\n", " where $\\omega$ is the detuning.\n", "\n", "Units of gyromagnetic ratio are rad / ms / G, quadrupole moments are given in barn, detunings are given in kHz." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SpinDict(13C: (0.5, 6.7283), 14N: (1.0, 1.9338, 0.0204), 14C: (0.0, 0.0000), ...)\n" ] } ], "source": [ "# Several ways to set SpinDict elements\n", "atoms.types['14C'] = 0, 0, 0\n", "atoms.types['Y'] = ('Y', 0, 0, 0)\n", "atoms.types['A'] = pc.SpinType('A', 0, 0, 0)\n", "\n", "print(atoms.types)" ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "## Simulator class\n", "\n", "The parameters of the CCE simulator engine.\n", "\n", "Main parameters to consider:\n", "\n", "* `spin` — Either instance of the `CenterArray` or float - total spin of the central spin (assuming one central spin).\n", "\n", "* `bath` — spin bath in any specified format. Can be either:\n", "\n", " - Instance of `BathArray` class;\n", " - `ndarray` with ``dtype([('N', np.str_, 16), ('xyz', np.float64, (3,))])`` containing names\n", " of bath spins (same ones as stored in self.ntype) and positions of the spins in angstroms;\n", " - The name of the `.xyz` text file containing 4 columns: name of the bath spin and xyz coordinates in A.\n", "\n", "* `r_bath` — cutoff radius around the central spin for the bath.\n", "\n", "* `order` — maximum size of the cluster.\n", "\n", "* `r_dipole` — cutoff radius for the pairwise distance to consider two nuclear spins to be connected.\n", "\n", "* `magnetic_field` — applied magnetic field. Can also be provided during the simulation run.\n", "\n", "* `pulses` — number of pulses in Carr-Purcell-Meiboom-Gill (CPMG) sequence or the pulse sequence itself.\n", "\n", "For the full description see the documentation of the `Simulator` object." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we setup a \"mock\" instance of `Simulator` to visualize the smaller part of the bath around the central spin." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "# Setting the runner engine\n", "mock = pc.Simulator(spin=1, position=[0,0,0],\n", " bath=atoms, r_bath=20,\n", " r_dipole=6, order=3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "During the initiallization, depending on the provided keyword arguments several methods may be called:\n", "\n", "* `Simulator.read_bath` is called if keyword `bath` is provided. It may take several additional arguments:\n", "\n", " * `r_bath` - cutoff distance from the qubit for the bath.\n", " * `skiprows` - if `bath` is provided as `.xyz` file, this argument tells how many rows to skip when reading the file.\n", " * `external_bath` - `BathArray` instance, which contains bath spins with pre defined hyperfines to be used.\n", " * `hyperfine` - defines the way to compute hyperfine couplings. If it is not given and `bath` doesn't contain any predefined hyperfines\n", " (`bath['A'].any() == False`) the point dipole approximation is used.\n", " Otherwise it can be an instance of ``pc.Cube`` object, or callable with signature ``func(coord, gyro, central_gyro)``,\n", " where `coord` is an array of the bath spin coordinate, gyro is the gyromagnetic ratio of bath spin,\n", " central_gyro is the gyromagnetic ratio of the central bath spin.\n", " * `types` - instance of `SpinDict` or input to create one.\n", " * `error_range` - maximum allowed distance between positions in `bath` and `external_bath` for two spins to be considered the same.\n", " * `ext_r_bath` - cutoff distance from the qubit for the `external_bath`. \n", " Useful if `external_bath` has very assymetric shape and user wants to keep the precision level of the hyperfine at different distances consistent.\n", " * `imap` - instance of the `pc.InteractionMap` class, which contain tensor of bath spin interactions.\n", " If not provided, interactions between bath spins are assumed to be the same as one of point dipoles.\n", " \n", " Generates `BathArray` object with hyperfine tensors to be used in the calculation.\n", "\n", "* `Simulator.generate_clusters` is called if `order` and `r_dipole` are provided.\n", " It produces `dict` object, which contains the indexes of the bath spins in the clusters.\n", " \n", " We implemented the following procedure to determine the clusters:\n", " \n", " Each bath spin $i$ forms a cluster of one. \n", " Bath spins $i$ and $j$ form cluster of two if there is an edge between them (distance $d_{ij} \\le$ `r_dipole`).\n", " Bath spins $i$, $j$, and $k$ form a cluster of three if enough edges connect them (e.g., there are two edges $ij$ and $jk$) and so on.\n", " In general, we assume that spins $\\{i..n\\}$ form clusters if they form a connected graph.\n", " Only clusters up to the size indicated by the `order` parameter (equal to CCE order) are included.\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use `matplotlib` to visualize the spatial distribution of the spin bath. The grey lines show connected pairs of nuclear spins, red dashed lines show clusters of three. You can try to increase `r_dipole`, `r_bath` parameters, or increase `order` and visuallize." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# add 3D axis\n", "fig = plt.figure(figsize=(6,6))\n", "ax = fig.add_subplot(projection='3d')\n", "\n", "# We want to visualize the smaller bath\n", "data = mock.bath\n", "\n", "# First plot the positions of the bath \n", "colors = np.abs(data.A[:,2,2]/data.A[:,2,2].max())\n", "ax.scatter3D(data.x, data.y, data.z, c=colors, cmap='viridis');\n", "# Plot all pairs of nuclear spins, which are contained\n", "# in the calc.clusters dictionary under they key 2\n", "for c in mock.clusters[2]:\n", " ax.plot3D(data.x[c], data.y[c], data.z[c], color='grey')\n", "# Plot all triplets of nuclear spins, which are contained\n", "# in the calc.clusters dictionary under they key 3\n", "for c in mock.clusters[3]:\n", " ax.plot3D(data.x[c], data.y[c], data.z[c], color='red', ls='--', lw=0.5)\n", "\n", "ax.set(xlabel='x (A)', ylabel='y (A)', zlabel='z (A)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we setup `Simulator` object for the actual simulation. " ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "# Parameters of CCE calculations engine\n", "\n", "# Order of CCE aproximation\n", "order = 2\n", "# Bath cutoff radius\n", "r_bath = 40 # in A\n", "# Cluster cutoff radius\n", "r_dipole = 8 # in A\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will use the ``CenterArray`` object to store the properties of the central spin,\n", "however for simple usecases one can provide the corresponding keywords to the `Simulator` object directly (see examples below)." ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "# position of central spin\n", "position = [0, 0, 0]\n", "# Qubit levels (in Sz basis)\n", "alpha = [0, 0, 1]; beta = [0, 1, 0]\n", "# ZFS Parametters of NV center in diamond\n", "D = 2.88 * 1e6 # in kHz\n", "E = 0 # in kHz\n", "nv = pc.CenterArray(spin=1, position=position, D=D, E=E, alpha=alpha, beta=beta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The code already knows the properties of the most common nuclear spins and of elecron spin (accessible under the name `'e'`), however the user can provide their own by calling `BathArray.add_type` method. The way to initiallize `SpinType` objects is the same as in `SpinDict` above." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [], "source": [ "# The code already knows most exsiting isotopes.\n", "# Bath spin types\n", "# name spin gyro quadrupole (for s>1/2)\n", "spin_types = [('14N', 1, 1.9338, 20.44),\n", " ('13C', 1 / 2, 6.72828),\n", " ('29Si', 1 / 2, -5.3188),]\n", "atoms.add_type(*spin_types)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setting the `Simulator` object\n", "All of the kwargs can be provided at the moment of creation. If all of the kwargs are provided, several methods of the `Simulator` class are called:\n", "\n", "* `Simulator.read_bath`;\n", "* `Simulator.generate_clusters`.\n", "\n", "The details are available in the `Simulator` methods description." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "# Setting the runner engine\n", "calc = pc.Simulator(spin=nv, bath=atoms,\n", " r_bath=r_bath, r_dipole=r_dipole, order=order)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Taking advantage of subclassing `np.ndarray` we can change *in situ* the quadrupole tensor of the Nitrogen nuclear spin." ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [], "source": [ "nspin = calc.bath\n", "# Set model quadrupole tensor at N atom\n", "quad = np.asarray([[-2.5, 0, 0],\n", " [0, -2.5, 0],\n", " [0, 0, 5.0]]) * 1e3 * 2 * np.pi\n", "\n", "nspin['Q'][nspin['N'] == '14N'] = quad" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note, that we need to apply the boolean mask **second** because of how structured arrays work." ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "### Compute coherence function with conventional CCE\n", "\n", "The general interface to compute any property with PyCCE is implemented through the `Simulator.compute` method. It takes two keyword arguments to determine which quantity to compute and how:\n", "\n", "* `method` can take 'cce' or 'gcce' values, and determines which method to use - conventional or generalized CCE.\n", "* `quantity` can take 'coherence' or 'noise' values, and determines which quantity to compute - coherence function\n", " or autocorrelation function of the noise.\n", "\n", "Each of the methods can be performed with Monte Carlo bath state sampling (if `nbstates` keyword is non zero) and with interlaced averaging (If `interlaced` keyword is set to `True`).\n", "\n", "In the first example we use the conventional CCE method without Monte Carlo bath state sampling. In the conventional CCE method the Hamiltonian is projected on the qubit levels, and the coherence is computed from the overlap of the bath evolution, entangled with two different qubit states.\n", "\n", "The conventional CCE requires one argument:\n", "\n", "* `timespace` — time points at which the coherence function is computed.\n", "\n", "Additionally, one can provide the following arguments now, instead of when initiallizing ``Simulator`` object:\n", "\n", "* `pulses` — number of pulses in CPMG sequence (0 - FID, 1 - HE etc., default 0) or explicit sequence of pulses as `Sequence` class instance.\n", "* `mangetic_field` — magnetic field along z-axis or vector of the magnetic field. Default (0, 0, 0)." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "# Time points\n", "time_space = np.linspace(0, 2, 201) # in ms\n", "# Number of pulses in CPMG seq (0 = FID, 1 = HE)\n", "n = 1\n", "# Mag. Field (Bx By Bz)\n", "b = np.array([0, 0, 500]) # in G\n", "\n", "l_conv = calc.compute(time_space, pulses=n, magnetic_field=b, \n", " method='cce', quantity='coherence', as_delay=False)" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "705 ms ± 9.74 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n" ] } ], "source": [ "%%timeit\n", "calc.compute(time_space, pulses=n, magnetic_field=b,\n", " method='cce', quantity='coherence', as_delay=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Generalized CCE (gCCE)\n", "\n", "In contrast to the conventional CCE method, in generalized CCE arpproach each cluster includes the central spin explicitly.\n", "\n", "`Simulator` can take `pulses` argument as an actual pulse sequence with an iterable of `Pulse` objects.\n", "\n", "For example:\n", "\n", "~~~\n", "p1 = pc.Pulse('x', np.pi)\n", "p2 = pc.Pulse('y', np.pi)\n", "seq = [p1, p2, p1, p2]\n", "~~~\n", "\n", "`seq` will define XY-4 pulse sequence.\n", "\n", "An integer number to define the number of pulses is also accepted as in the case of conventional CCE. If the integer is provided, the code assumes the CPMG sequence." ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "# Hahn-echo pulse sequence\n", "pulse_sequence = [pc.Pulse('x', np.pi)]\n", "\n", "# Calculate coherence function\n", "l_generatilze = calc.compute(time_space, magnetic_field=b,\n", " pulses=pulse_sequence,\n", " method='gcce', quantity='coherence')" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.92 s ± 24.6 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n" ] } ], "source": [ "%%timeit\n", "calc.compute(time_space, magnetic_field=b,\n", " pulses=pulse_sequence,\n", " method='gcce',\n", " quantity='coherence')" ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "### gCCE with random sampling of bath states\n", "\n", "Using this approach, one may carry out generalized CCE calculations for the set of random bath states. This functionality can be turned on by by setting the keyword argument `nbstates` to a number of bath states to sample over. Recommended number of bath states is above 100, but the convergence should be checked for each system. Note, that this computation is roughly `nbstates` times longer than an equivalent generalized CCE calculation, as it computes everything `nbstates` times.\n", "\n", "For details see `help(calc.compute)`." ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [], "source": [ "# Number of random bath states to sample over\n", "n_bath_states = 20\n", "\n", "# Calculate coherence function\n", "l_gcce = calc.compute(time_space, magnetic_field=b,\n", " pulses=pulse_sequence,\n", " nbstates=n_bath_states,\n", " method='gcce', quantity='coherence', seed=seed)" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "11.9 s ± 379 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n" ] } ], "source": [ "%%timeit\n", "n_bath_states = 5\n", "calc.compute(time_space, magnetic_field=b,\n", " pulses=pulse_sequence,\n", " nbstates=n_bath_states,\n", " method='gcce', quantity='coherence', seed=seed)" ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "Take a look at the results of three different methods, and check that they produce similar coherence decay. Note that the results obtained using gCCE with bath states sampling deviates from other ones (generalized and conventional CCE), as the chosen number of states (20) is not enough to converge." ] }, { "cell_type": "code", "execution_count": 57, "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(time_space, l_conv.real,\n", " label='conventional CCE')\n", "plt.plot(time_space, l_generatilze.real,\n", " label='generalized CCE', ls='--')\n", "plt.plot(time_space, l_gcce.real,\n", " label='gCCE with bath sampling', ls='', marker='.')\n", "plt.legend()\n", "plt.xlabel('Time (ms)')\n", "plt.ylabel('Coherence');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Convergence parameters\n", "Having confirmed that all methods produce the same results, we check the convergence of the conventional CCE with respect to `order`, `r_bath`, `r_dipole` parameters of the `Simulator` object.\n", "\n", "First, define all of the parameters." ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [], "source": [ "parameters = dict(\n", " order=2, # CCE order\n", " r_bath=40, # Size of the bath in A\n", " r_dipole=8, # Cutoff of pairwise clusters in A\n", " position=[0, 0, 0], # Position of central Spin\n", " alpha=[0, 0, 1],\n", " beta=[0, 1, 0],\n", " pulses = 1, # N pulses in CPMG sequence\n", " magnetic_field=[0,0,500]\n", ") # Qubit levels)\n", "\n", "time_space = np.linspace(0, 2, 201) # Time points in ms" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can define a little helper function to streamline the process. Note that resetting the parameters automatically recomputes the properties of the bath." ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [], "source": [ "def runner(variable, values):\n", " invalue = parameters[variable]\n", " calc = pc.Simulator(spin=1, bath=atoms, **parameters)\n", " ls = []\n", "\n", " for v in values:\n", " setattr(calc, variable, v)\n", " l = calc.compute(time_space, method='cce',\n", " quantity='coherence')\n", "\n", " ls.append(l.real)\n", "\n", " parameters[variable] = invalue\n", " ls = pd.DataFrame(ls, columns=time_space, index=values).T\n", " return ls" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can compute the coherence function at different values of the parameters:" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [], "source": [ "orders = runner('order', [1, 2, 3, 4])\n", "rbs = runner('r_bath', [20, 30, 40, 50, 60])\n", "rds = runner('r_dipole', [4, 6, 8, 10])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can visualize the convergence of the coherence function with respect to different parameters:" ] }, { "cell_type": "code", "execution_count": 53, "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, 3, figsize=(12, 3))\n", "orders.plot(ax=axes[0], title='order')\n", "rbs.plot(ax=axes[1], title='r_bath')\n", "rds.plot(ax=axes[2], title='r_dipole')\n", "for ax in axes:\n", " ax.set(xlabel='Time (ms)', ylabel='Coherence')\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bath polarization\n", "To study different bath polarization we will modify ``BathArray.state`` attribute, which contains spin states for each bath spin.\n", "For simplicity we will assume the gaussian profile of the polarization." ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [], "source": [ "def polarize(bath, gamma=5):\n", " # Polarizations of each bath spin\n", " if gamma > 0:\n", " polos = np.exp(-(bath.dist()/gamma)**2) * 0.5\n", " else:\n", " polos = np.zeros(bath.size)\n", " \n", " for a, pol in zip(bath, polos):\n", " \n", " # Skip 14N\n", " if a.N != '13C':\n", " continue\n", " # Generate density matrix\n", " dm = np.zeros((2, 2), dtype=np.complex128)\n", " dm[0,0] = 0.5 + pol\n", " dm[1,1] = 0.5 - pol\n", " a.state = dm\n", " \n", " return \n", "\n", "# Use already optimized parameters\n", "calc = pc.Simulator(spin=1, bath=atoms, **parameters)\n", "\n", "# Standard deviations of the polarization gaussian profile\n", "gammas = [0, 1, 2, 5, 10, 20, 30, 40, 60, 80]\n", "ls = []\n", "\n", "ts = np.linspace(0, 5, 501)\n", "for gamma in gammas:\n", " polarize(calc.bath, gamma=gamma)\n", " l = calc.compute(ts)\n", " ls.append(l.real)\n", "\n", "df = pd.DataFrame(ls, columns=ts, index=gammas).T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With increased polarization in the bath the Hahn-echo signal decays significantly slower." ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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