For the molecular state prepared in the absorption/ stimulated emission step the condition ΔE± << ΔPVE has to be satisfied. For this limiting case we describe the time evolution in the basis of states with defined parity (‘+’ and ’-‘) and consider the parity violating energy difference as a perturbation. The wave function of the unperturbed level is given by:
Considering ΔPVE as a perturbation we get the following Hamiltom matrix
Including the perturbation we obtain for the time dependent wave function
Where we have applied the condition that ΔE± << ΔPVE. For the population level with "-" parity we get:
And the population of the level with "+" parity (the one not populated in the preparation step) is growing according to
The growth of this population with "+"-parity in probed in the multiphoton ionization step after a given delay time. The necessary interaction free evoluation time for the wave function depends in addition to ΔPVE strongly on the sensitivity to detect the population of this ("+") parity state.
Time evolution of the schematic wavefunctions during the preparation time (Δtprep) and free evolution time ((Δtevol >> Δtprep)