Electrometry¶

The electrometry subpackage computes local electric fields from gate-bias voltages and screened disorder charges, and evaluates the resulting ODMR frequency shifts across a 2-D scan area.

`SpinDefectSim.electrometry.efield`¶

Low-level E-field building blocks.

`E_gate_bias`¶

from SpinDefectSim.electrometry.efield import E_gate_bias

def E_gate_bias(
    r_obs_xyz: tuple,
    E0=(0, 0, 0),
    grad=None,
) -> np.ndarray

Return the gate-bias electric field (uniform + optional linear gradient) at a single observation point.

Parameters:

Name	Type	Description
`r_obs_xyz`	`(x, y, z)`	Observation point (m)
`E0`	`array_like (3,)`	Uniform field components (Ex, Ey, Ez) in V/m
`grad`	`np.ndarray (2,2) \\| None`	In-plane gradient tensor [[∂Ex/∂x, ∂Ex/∂y], [∂Ey/∂x, ∂Ey/∂y]] in V/m²

Returns: np.ndarray shape (3,) in V/m

Example:

from SpinDefectSim.electrometry.efield import E_gate_bias
import numpy as np

E = E_gate_bias((0, 0, 0.34e-9), E0=(0, 0, 2e6))
# → array([0., 0., 2e6]) V/m

`E_disorder_point_charges`¶

from SpinDefectSim.electrometry.efield import E_disorder_point_charges

def E_disorder_point_charges(
    r_obs_xyz: tuple,
    charges_xyzq: np.ndarray,
    *,
    epsilon_eff: float,
    screening_model: Optional[str],
    lambda_screen: float,
    d_gate: float,
    n_images: int,
    r_min: float = 0.2e-9,
) -> np.ndarray

Compute the E-field at a single observation point due to a set of static point charges, using the selected screened Coulomb model.

Parameters:

Name	Type	Description
`r_obs_xyz`	`(x, y, z)`	Observation point (m)
`charges_xyzq`	`np.ndarray (M, 4)`	Charge positions and values [x, y, z, q] in SI units
`epsilon_eff`	`float`	Effective dielectric constant
`screening_model`	`str \\| None`	`None` (bare 1/r), `"yukawa"`, or `"dual_gate"`
`lambda_screen`	`float`	Yukawa screening length (m)
`d_gate`	`float`	Dual-gate separation (m)
`n_images`	`int`	Number of image-charge terms
`r_min`	`float`	Minimum distance regulariser (m)

Returns: np.ndarray shape (3,) in V/m

`apply_dielectric_transmission`¶

from SpinDefectSim.electrometry.efield import apply_dielectric_transmission

def apply_dielectric_transmission(
    E: np.ndarray,
    eps_layer: float,
    eps_host: float,
) -> np.ndarray

Scale an E-field by the quasi-static planar dielectric transmission factor:

\[\eta = \frac{2\,\varepsilon_\text{layer}}{\varepsilon_\text{layer} + \varepsilon_\text{host}}\]

Parameters:

Name	Type	Description
`E`	`np.ndarray`	Input E-field, any shape ending in `(..., 3)`
`eps_layer`	`float`	Dielectric constant of the layer
`eps_host`	`float`	Dielectric constant of the host

Returns: np.ndarray same shape as E

`ElectricFieldBuilder`¶

from SpinDefectSim.electrometry.efield import ElectricFieldBuilder

Combines gate-bias and disorder charge contributions into a single total() call. Inherits PhysicalParams.

Constructor¶

ElectricFieldBuilder(defaults: Optional[Defaults] = None)

`total`¶

def total(
    defect_xyz: tuple,
    *,
    E0_gate=(0, 0, 0),
    gate_grad=None,
    disorder_xyzq=None,
) -> tuple[np.ndarray, dict]

Compute the total E-field at defect_xyz.

Parameters:

Name	Type	Description
`defect_xyz`	`(x, y, z)`	Defect position (m)
`E0_gate`	`array_like (3,)`	Uniform gate field (V/m)
`gate_grad`	`np.ndarray \\| None`	Gate-field gradient tensor
`disorder_xyzq`	`np.ndarray (M, 4) \\| None`	Disorder charges

Returns: (E_tot, components) where E_tot is a (3,) array (V/m) and components is a dict with keys "gate" and "disorder".

`SpinDefectSim.electrometry.electrometry`¶

`ElectrometryExperiment`¶

from SpinDefectSim.electrometry.electrometry import ElectrometryExperiment

Computes ODMR observables at one point or across a 2-D scan grid from a known distribution of static charges and/or gate bias.

Inherits: PhysicalParams

Constructor¶

ElectrometryExperiment(
    charges_xyzq: np.ndarray,
    defaults: Optional[Defaults] = None,
    *,
    z_defect: Optional[float] = None,
    E0_gate=(0, 0, 0),
    gate_grad=None,
    epsilon_eff: Optional[float] = None,
    screening_model: Optional[str] = None,
    lambda_screen: Optional[float] = None,
    d_gate: Optional[float] = None,
    n_images: Optional[int] = None,
    bias_B_T=None,
)

Parameters:

Name	Type	Description
`charges_xyzq`	`np.ndarray (M, 4)`	Disorder charges [x, y, z, q] in SI units
`defaults`	`Defaults \\| None`	Global defaults
`z_defect`	`float \\| None`	Defect height above the charge plane (m); uses `defaults.z_defect` if `None`
`E0_gate`	`array_like (3,)`	Uniform gate-bias field (V/m)
`gate_grad`	`np.ndarray \\| None`	Gate-field gradient tensor (V/m²)
`epsilon_eff`	`float \\| None`	Effective dielectric (overrides `defaults.epsilon_eff`)
`screening_model`	`str \\| None`	`None`, `"yukawa"`, or `"dual_gate"`
`lambda_screen`	`float \\| None`	Yukawa length (m)
`d_gate`	`float \\| None`	Gate separation (m)
`n_images`	`int \\| None`	Image-charge sum length
`bias_B_T`	`array_like (3,) \\| None`	Bias B-field vector (T) to use when computing ODMR frequencies

`E_field`¶

def E_field(
    x_obs: float,
    y_obs: float,
    z_obs: Optional[float] = None,
) -> np.ndarray

Total E-field at a single observation point.

Parameters:

Name	Type	Description
`x_obs`	`float`	x position (m)
`y_obs`	`float`	y position (m)
`z_obs`	`float \\| None`	z position (m); if `None`, uses `self.z_defect`

Returns: np.ndarray shape (3,) in V/m

`transition_frequencies`¶

def transition_frequencies(
    x_obs: float,
    y_obs: float,
    z_obs: Optional[float] = None,
) -> np.ndarray

ODMR transition frequencies at a single point.

Returns: np.ndarray float64, shape (2S,), sorted ascending, in Hz

`E_field_map`¶

def E_field_map(
    x_obs: np.ndarray,
    y_obs: np.ndarray,
    z_obs: Optional[float] = None,
) -> np.ndarray

Compute the total E-field on a 2-D grid. x_obs and y_obs define 1-D coordinate arrays; the result is computed on their outer product mesh.

Parameters:

Name	Type	Description
`x_obs`	`np.ndarray`	1-D x coordinates (m)
`y_obs`	`np.ndarray`	1-D y coordinates (m)
`z_obs`	`float \\| None`	z height (m)

Returns: np.ndarray shape (Ny, Nx, 3) in V/m

`E_z_map`¶

def E_z_map(
    x_obs: np.ndarray,
    y_obs: np.ndarray,
    z_obs: Optional[float] = None,
) -> np.ndarray

Ez component on a 2-D grid.

Returns: np.ndarray shape (Ny, Nx) in V/m

`transition_frequency_map`¶

def transition_frequency_map(
    x_obs: np.ndarray,
    y_obs: np.ndarray,
    z_obs: Optional[float] = None,
) -> np.ndarray

ODMR transition frequencies on a 2-D scan grid.

Returns: np.ndarray shape (Ny, Nx, 2S) in Hz

Example:

import numpy as np
from SpinDefectSim.electrometry.electrometry import ElectrometryExperiment

# Single trapped electron charge
charges = np.array([[0., 0., 0., 1.6e-19]])

exp = ElectrometryExperiment(
    charges_xyzq=charges,
    z_defect=0.34e-9,
    screening_model="dual_gate",
    d_gate=15e-9,
)

x = np.linspace(-100e-9, 100e-9, 50)
y = np.linspace(-100e-9, 100e-9, 50)
freq_map = exp.transition_frequency_map(x, y)

# Frequency of the lower transition, in GHz
lower_freq_GHz = freq_map[:, :, 0] / 1e9

Electrometry¶

SpinDefectSim.electrometry.efield¶

E_gate_bias¶

E_disorder_point_charges¶

apply_dielectric_transmission¶

ElectricFieldBuilder¶

Constructor¶

total¶

SpinDefectSim.electrometry.electrometry¶

ElectrometryExperiment¶

Constructor¶

E_field¶

transition_frequencies¶

E_field_map¶

E_z_map¶

transition_frequency_map¶

`SpinDefectSim.electrometry.efield`¶

`E_gate_bias`¶

`E_disorder_point_charges`¶

`apply_dielectric_transmission`¶

`ElectricFieldBuilder`¶

`total`¶

`SpinDefectSim.electrometry.electrometry`¶

`ElectrometryExperiment`¶

`E_field`¶

`transition_frequencies`¶

`E_field_map`¶

`E_z_map`¶

`transition_frequency_map`¶