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