Resources

• Logan’s thesis
• Spin–orbit-coupled Bose–Einstein condensates | Nature
• Synthetic magnetic fields for ultracold neutral atoms | Nature

These ones are for a more general audience, focussing more on the concepts. I think these are a good starting point.

• Spin–orbit coupling in quantum gases | Nature
• Artificial gauge fields with ultracold atoms | Physics Today | AIP Publishing

This one is a more detailed version of those reviews: 

• Synthetic gauge potentials for ultracold neutral atoms - IOPscience

There’s also this review from M. Aidelsburger that looks more at how these Hamiltonians (and geometric phase) are related to gauge theories. This is where I found the “effective Hamiltonian” approach: 

• Artificial gauge fields in materials and engineered systems - ScienceDirect

Lastly, theres the paper I used to verify the GPU-GPE code. While it isn’t directly focussing on SOC, I think it helped me learn how all the parameters change things, and connected the dots between BEC ground state structures and the artificial gauge fields influencing them:

• Phys. Rev. A 84, 063604 (2011) - Vortices in spin-orbit-coupled Bose-Einstein condensates (aps.org)

Questionnaire

1. Diagram and intuitive understanding, transistion and orientation
2. Hamiltonian and conclusions
3. Eigenvalues diagram and why there are two parabolas
4. Avoided crossing
5. How much splitting is there?
6. Strong and not strong coupling
7. How detuning makes one spin more favorabe
8. Meaning of dressed states.
9. SOC is a charged particle moving in em field