This readme file was generated on 11-04-2025 by Jack Daniel Briscoe

PAPER TITLE: 
Light propagation through an atomic vapor with non-orthogonal electric field modes

DATASET TITLE: 
Light propagation through an atomic vapor with non-orthogonal electric field modes - Experiment

PRINCIPAL INVESTIGATOR:
Name: Jack Daniel Briscoe
ORCID: 0000-0002-8878-0528
Institution: Durham University
Address: Physics Department, Durham University, South Road, Durham, DH1 3LE, United Kingdom
Email: jack.d.briscoe@durham.ac.uk
Funded by: EPSRC (Grant No. EP/T518001/1 and Grant No. EP/R002061/1)

OTHER PAPER AUTHORS:
Name: Dr Danielle Pizzey
ORCID: 0000-0002-9025-8608
Institution: Durham University
Address: Physics Department, Durham University, South Road, Durham, DH1 3LE, United Kingdom

Name: Dr Robert Potvliege
ORCID: 0000-0003-4624-1064
Institution: Durham University
Address: Physics Department, Durham University, South Road, Durham, DH1 3LE, United Kingdom

Name: Dr Steven Wrathmall
ORCID: 0000-0003-1770-9721
Institution: Durham University
Address: Physics Department, Durham University, South Road, Durham, DH1 3LE, United Kingdom

Name: Dr Ifan Hughes
ORCID: 0000-0001-6322-6435
Institution: Durham University
Address: Physics Department, Durham University, South Road, Durham, DH1 3LE, United Kingdom



PAPER ABSTRACT:
Alkali-metal atomic vapors are the foundation of an ever-growing range of applications, driven 
by a comprehensive understanding of their interaction with light. In particular, many models 
have been developed which characterize this interaction for low intensity laser fields. An 
atomic medium subject to an external magnetic field of arbitrary direction exhibits two electric 
field modes that, in general, are non-orthogonal. Mode non-orthogonality is currently neglected 
by the models used in this context. We derive a new light propagation formalism which takes into 
account the non-zero overlap of the two modes. We verify the theory using weak-probe spectroscopy 
of the Rb D_{2} line, showing excellent agreement with experiment. The predictions of the new 
theory can be exploited, and optimized, to design better atomic photonic devices.



EXPERIMENT OVERVIEW:
Atomic spectroscopy of the Rb D2 line in an arbitrary magnetic field geometry. 
Arbitrary means the angle theta_{B} between the wavevector and the magnetic field can take any value.
Use Rb vapor cell of natural abundance; cell is length 2mm.
Use permanent top hat magnets placed in holders which rotate on a large platform to set theta_{B}.
Magnet separation controls the magnitude of the B field.
Cell heated using a resistive copper heater.
Light sourced from DFB laser and scanned across D2 transition (approx. 780 nm).
Light measured after traversing cell by photodetectors connected to oscilloscope.
Use linear incident light polarization, controlled before cell using Glan-Taylor polariser and a 
half-waveplate.
Weak-probe regime, so optical power through cell of order 100nW.
For a detailed experiment schematic, see paper.

Two regimes for atomic parameters: 
1) Regime I: low B field (for Rb) approx. 240 Gauss, theta_{B} = 80 degrees. Vary linear polarization 
incident on atoms to control atom-light coupling. Linear polarization angle characterized by angle 
theta_{E} with respect to x-axis.
2) Regime II: intermediate B field (for Rb) approx. 2500 Gauss, use fixed horizontal-linear polarization 
(theta_{E} approx. 0 Degrees) and fixed vertical-linear polarization (theta_{E} approx. 90 Degrees).
Vary theta_{B} in steps of 10 degrees between 100 Degrees and 130 Degrees to control atom-light 
coupling.
See paper for more details describing regimes.

Data calibrated using etalon and Rb atomic vapor cell reference (natural abundance, room temperature).

For more information, see this tutorial review:
D.Pizzey et al., “Laser spectroscopy of hot atomic vapours: from ’scope to theoretical fit,” New J.Phys.
24, 125001(2022).



EXPERIMENT AIM
For oblique theta_{B}, electric field modes are non-orthogonal which current models in this context do 
not properly account for. 
New theory for light propagation is derived which is fit to data taken in the experiment.
Data used to validate new theory (with excellent agreement to both fit and measured parameters in lab).



DATASETS
Two regimes, labelled Regime I and Regime II. Each dataset is a unique set of atom-light parameters.
We take multiple repeats, forming the dataset at those parameters.
For Regime I, there are 4 datasets representing 4 different incident linear polarization angles theta_{E}. 
There are 4 repeats for each angle.
There are therefore 16 spectra in total in Regime I.
For Regime II, there are 8 datasets.
There are 2 different incident linear polarization angles theta_{E}. At each polarization angle, there are 
4 datasets representing 4 different magnetic field angles theta_{B}. Each dataset contains 5 repeats.
There are therefore 40 spectra in total in Regime II.

IMPORTANT: Datasets are labelled tau_thetaBX_thetaEY_Z, where tau stands for transmission (laser then 
atoms then measure output), X is theta_{B} to the nearest degree, Y is theta_{E} to the nearest degree, 
and Z is the repeat number. The regime can be identified using X (80 for Regime I, Regime II otherwise).



SOFTWARE USED:
python/Jupyter notebook
ElecSus 4 (data fitting): THIS IS THE NEW LIGHT PROPAGATION FORMALISM. NOT YET PUBLICALLY AVAILABLE. 
ElecSus 3 (comparison to old light propagation formalism): https://github.com/durham-qlm/ElecSus

IMPORTANT: While ElecSus 4 is not available at the time of writing this README, the new theory described 
in the paper can be implemented into any user's ElecSus 3 code. We have other plans for ElecSus 4 which 
will become part of the total package that are still being developed.



FILE OVERVIEW:
The data availability folder consists of 2 jupyter notebooks, one data folder + this README. 

JUPYTER NOTEBOOKS: 
RegimeI_figure.ipynb
RegimeII_figure.ipynb

These notebooks will plot Figures 4 and 6 in the paper using data from the data folder (ElecSus 4 fit 
to data).
IMPORTANT: FITS REQUIRE ELECSUS4


 
DATA FOLDER:
Data folder contains two folders which separate the Regime I and Regime II datasets.
Within the Regime I/Regime II folders, data are labelled tau_thetaBX_thetaEY_Z, where tau stands 
for transmission (laser then atoms then measure output), X is theta_{B} to the nearest degree, Y 
is theta_{E} to the nearest degree, and Z is the repeat number (as described in the DATASETS section above).

Each data file is a .csv file with 2 columns:
Column 1 - Detuning data (in GHz)
Column 2 - Transmission data 


