We are extending methods to describe spin-photon interfaces, transitioning from cavity QED to waveguide QED. This work focuses on complex four-level systems that incorporate polarization, magnetic fields, and nuclear spins, functioning effectively in both weak and strong coupling regimes. In cavity QED, the Hilbert space includes both the atom and the cavity, offering a highly accurate but computationally intensive approach. Conversely, waveguide QED simplifies the Hilbert space to just the atom, which, while less realistic, allows for more straightforward computations and practical implementations. This shift aims to balance complexity and computational feasibility, advancing our understanding and application of quantum systems.


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