Electron superposition in an $m$-level system

I understand second quantization, and how absorption and spontaneous/stimulated emission works for an electron in $m$-level system. In other words, I know how a photon with the right frequency can take an electron from the $n^{th}$ energy level to the $(n+1)^{th}$ energy level (and vice versa).

Using the electric dipole interaction, and time-dependent perturbation theory, we can write the perturbing Hamiltonian as:

$$hat H_p = sum_{j, k, lambda} H_{jklambda} hat b_j^dagger hat b_k (hat a_lambda – hat a_lambda^dagger) $$

where, $H_{jklambda}$ is a constant containing the details of the electric dipole interaction, $hat a_lambda^dagger$, $hat a_lambda$ are the boson creation/annihilation operations, and $ hat b_j^dagger $ $hat b_j$ the fermion raising/lowering operators.

Using this expression, and the initial state of a photon and an electron, we can calculate the final state, absorption/emission energies, absorption/emission rates, etc.

My question is, using this formalism, how can I find the energy required by a photon to place the electron in a superposition of different energy levels?

Is superposition achieved through an absorption event? or is it through stimulated emission?

Is the reason why I can’t see how this works from the expression above because I am only using the first-order term in the perturbation expansion?