I would like to calculate the expected red- or blue- shifts in absorption that result from the Optical Stark effect in 2D TMDs as a function of excitation wavelength. The Optical Stark effect originates from exciton states that couple to and hybridize with Floquet states generated by a strong light field. The typical formulas cited in literature assume low light intensity and only give the energies (not the oscillator strengths).

Generally, one sets up a Hamiltonian (matrix) for the system which needs to be diagonalized to yield the eigenvalues (energies). That said, the derivations in literature are not always rigorous. Calculation of the oscillator strengths of the transitions between the hybridized states is often ignored. As is known from molecular exciton theory, the oscillator strength of a particular transition does not necessarily depended monotonically on the coupling strength.

Does anyone have experience with this specific calculation? Can anyone give guidance on, e.g., what the Franck-Condon overlap integrals will look like for the Floquet states?