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I came across following types of three-level systems like V-system, Λ-system and 2-photon absorption enter image description here

It seems that their Hamiltonians can be written intuitively by checking out the coupled levels and the gap between levels both in general and in the dressed picture (rotating frame approximation). Do V and Λ systems have the same Hamiltonian due to the symmetry in the level structure ? By following the analogy, I designed the Hamiltonian for 2-photon absorption process to be same as the other 2 cases but it is not so :- What are the coupled levels in the 2-photon absorption process and how can the Hamiltonian for this process be written ? How do I extend the design to N-level system -lets say for N-photon absorption in N-level system ?

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