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Library to calculate Stark and Zeeman maps for Rydberg helium, in either the n,L,S,m_L or n,L,S,J,m_J basis, using the Numerov method.

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Helium Stark Zeeman

Calculate Stark and Zeeman maps for Rydberg helium, in either the n, L, S, M_L or n, L, S, J, M_J basis, using the Numerov method.

M. L. Zimmerman et al., Phys. Rev. A, 20, 2251 (1979) http://dx.doi.org/10.1103/PhysRevA.20.2251

Install

Install using setuptools,

git clone https://github.com/aa-morgan/helium-stark-zeeman
cd helium-stark-zeeman
python setup.py install

Basic usage

Import libraries,

from hsz import HamiltonianMatrix
import numpy as np
from scipy.constants import h

Instantiate HamiltonianMatrix object,

ham = Hamiltonian(n_min=20, n_max=22, S=1, basis_type='ML')

Calculate Stark map,

Efield = np.linspace(0.0, 1000.0, 101) # V /m
sm = ham.stark_map(Efield,
                   Bfield=0.1, # Telsa
                   field_angle=0.0, # Degrees

Plot Stark map,

plt.plot(Efield, sm / (h*10**9), '-')
plt.xlabel('electric field (V cm$^{-1}$)')
plt.ylabel('energy / $h$ (GHz)')

Parameters

Class: HamiltonianMatrix

Parameter Description Data type Required Default
n_min Minimum value of the principle quantum number n, to allow in the basis. Int Yes N/A
n_max Maximum value of the principle quantum number n, to allow in the basis. Int Yes N/A
L_max Maximum value of the orbital angular momentum quantum number to allow in the basis. None means no restriction. Int [or None] No None
S Value of the total spin orbital angular momentum. [Singlet: S=0, Triplet: S=1]. None means both. Int [or None] No None
M Single value of the azimuthal quantum number to use in the basis. None means no restriction. Int [or None] No None
M_max Maximum value of the azimuthal quantum number to allow in the basis. None means no restriction. Int [or None] No None
basis_type Whether to use the n, L, S, M_L, or n, L, S, J, M_J basis. Specify using 'ML', or 'MJ', respectively. String No 'ML'

Method: stark_map

Parameter Description Data type Required Default
Efield Electric field values in V/cm numpy.array Yes N/A
Bfield Magnetic field values in T Float No 0.0
field_angle Angle between electric and magnetic fields Float No 0.0
cache_matrices Cache Stark and Zeeman matrices Boolean No True
load_matrices Load Stark and Zeeman matrices from .npz files Boolean No False
save_matrices Save Stark and Zeeman matrices to .npz files Boolean No False
matrices_dir Directory to save Stark and Zeeman matrices String No './'
eig_vec Return eigenvectors Boolean No False
tqdm_disable Disable tqdm output Boolean No False

Method: zeeman_map

Parameter Description Data type Required Default
Bfield Magnetic field values in T numpy.array Yes N/A
Efield Electric field values in V/cm Float No 0.0
field_angle Angle between electric and magnetic fields Float No 0.0
cache_matrices Cache Stark and Zeeman matrices Boolean No True
load_matrices Load Stark and Zeeman matrices from .npz files Boolean No False
save_matrices Save Stark and Zeeman matrices to .npz files Boolean No False
matrices_dir Directory to save Stark and Zeeman matrices String No './'
eig_vec Return eigenvectors Boolean No False
tqdm_disable Disable tqdm output Boolean No False

Version information

Library Version
Python 3.6.1 64bit [GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]
IPython 5.3.0
OS Darwin 17.4.0 x86_64 i386 64bit
attr 17.4.0
matplotlib 2.0.2
numba 0.35.0
numpy 1.14.3
scipy 1.00.0
sympy 1.0
tqdm 4.15.0
version_information 1.0.3

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Library to calculate Stark and Zeeman maps for Rydberg helium, in either the n,L,S,m_L or n,L,S,J,m_J basis, using the Numerov method.

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