Alignment of molecules by lasers: Derivation of the Hamiltonian within the (t, t′) formalism

Molecular alignment and molecular optics in moderately intense, far-off resonance laser fields have been the topic of intensive research during the past decade. Nonetheless, two qualitatively different forms of the interaction Hamiltonian that underlies these and related strong field manipulation methods have been consistently applied in theoretical and numerical studies. Using a generalization of the (t, t′) method, we derive the effective interaction Hamiltonian and prove that one form holds when the laser frequency is larger than the molecular rotational frequencies and the duration of the laser pulse is sufficiently large, while the other form holds only in the adiabatic limit when the laser frequency is smaller than the rotational ones and the field can be considered as a static field with slowly varying strength. Only the first form is applicable to the study of alignment of molecules by lasers.