Figure: Ground state population vs. laser detuning, under given magnetic field
This package implements rate equation model in python. Rate equation model is commonly used to simulate the evolution of atomic populations in different ground states, under given external radiation (e.g. lasers) and magnetic fields.
Rate equation model assumes the time atoms spend in excited states is negligible. That is, once excited, they immediately decay back to ground states. Therefore, all coherence terms are discarded, leaving a set of equations describing the population transfer from one ground state to others. This assumption is equivalent to assuming the timescale of interest is much larger than the decay rate of studied energy levels, while the laser intensity is way below saturation intensity.
A very good reference for this approach can be found at: F. Atoneche and A. Kastberg, Simplified Approach for Quantitative Calculations of Optical Pumping, Eur. J. Phys. 38, 045703 (2017).
This package
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Takes hyperfine structure and transition strength as input, normalizes transition strength properly and produces the rate equation matrix
$G$ . -
Supports configurations that include multiple radiation fields with different frequencies and polarizations.
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Provides flexible ways of defining detuning terms (Zeeman shift and Doppler shift).
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Each part is individually tested against published results to ensure correctness.
- This package is designed to work with hyperfine states
$I, J, F, m_F$ as the eigenstates of the unperturbed Hamiltonian. However, under strong magnetic field, hyperfine states are no longer eigenstates and the system is better described by$I, J, m_J, m_I$ (Paschen-Back effect). The only way to correctly deal with this is to diagonalize the Hamiltonian under all magnetic field configurations and use the acquired eigenstates to perform calculation. This package is not well geared to achieve this.
In the example.ipynb IPython notebook, I reproduced all relevant figures in Atoneche (2017).