Anharmonicity Analysis

Overview

This package is developed from a subset of the PaulTrapAnalysis package, with a focus on analyzing the anharmonicities in trapping potentials. The recommended workflow is to perform DC/BEM simulations in COMSOL, then export the data into a .csv, and load the data using this package and perform the analysis.

Installation

git clone https://github.com/HaeffnerLab/anharmonicity-analysis.git  
cd <path>/anharmonicity-analysis  # cd into the cloned directory
pip install -e .  # install with edit capabilities

COMSOL simulations

Simulation setup

Refer to bem-comsol package authored by Xiaotian Feng, specifically the Build an model in COMSOL section.

Parametric sweep

If you are simulating multiple electrodes in COMSOL, you can use the parametric sweeping method to apply voltage exciations individually to each electrode. In the following example, 5 electrodes are used, and an Electric Potential boundary condition is applied to each electrode ei with voltage created as a variable named Vei. Then, a parametric sweep is set up as shown in the following figure. The parameter value is created using one-hot encodings, indicating separate 1V excitations for each electrode. The 1V value is chosen here as a convention, and this is needed for the package to identify the field created by each electrode.

Exporting results

The result can be directly exported into a .csv file, with Parameter layout in the Columns format, as shown in the figure below. An example output file can be found in example/output.csv. Note that in this output file, the first 8 rows should be skipped if pd.read_csv is used to load the file. In addition, the parameteric sweep configuration is embedded in the header of the spreadsheet. Here, Vr=1, for example, is used as a flag in the code when loading data to correlate that data column to the electrode named r, and this is why a variable and electrode naming convention should be used for convenience.

Data analysis

This package mainly contains four files located in ./anharm_analysis. The main structure follows:

• Electrode.py: Contains the Electrode object that loads and stores the data for each individual electrode.
• Trap.py: Contains the Trap object that collects several electrodes and perform all higher-level analysis including spherical harmonics expansion and frequency shift estimation.
• Grid.py: Contains different data structures to store the spatial coordinates of the simulation and fitting data.
• utils.py: Contains all utility functions used in the code. Several functions can be useful separately outside of this code framework for specific analysis as well.

An example of using the package can be found in ./example/example.ipynb.