MOLECULAR MULTIPHOTON TRANSITIONS - COMPUTATIONAL SPECTROSCOPY FOR PERTURBATIVE AND NONPERTURBATIVE REGIMENS

The total Schrodinger equation for an electromagnetic field interacting with a molecule is shown to lead to time independent or time dependent coupled differential equations. The time independent equations result from using a quantized representation, i.e., photon number states, of the electromagnetic field. The stationary states of such a quantized field-molecule system are called dressed states. Appropriate numerical methods are presented in order to treat radiative and non-radiative interactions simultaneously for any coupling strength, i.e. from the perturbative, Fermi-Golden rule limit, to the non-perturbative regime for both types of interactions. Both bound-bound, bound-continuum and continuum-continuum radiative and non-radiative transitions can be treated exactly in the present scheme. The relationship between the quantized time independent approach and the time dependent semiclassical field method is achieved through consideration of the coherent states of the quantized radiation field. In this limit, multiphoton transitions are more conveniently treated by coupled partial differential equations both in time and space. The time dependent approach is therefore more appropriate for very short laser pulses, especially for pulse time durations less than the molecular natural time-scales, in which case stationary states are ill-defined. Examples of both time-independent and time dependent calculations are presented. In the first case, coherent laser control of multiphoton transitions is illustrated by a time independent, all state, coupled equations method. Finally, high intensity direct photodissociation by subpicosecond pulses is presented as an example of laser pulse effects from a time dependent calculation in the non-perturbative regime, where laser-induced avoided crossings can be created by the pulse itself. The coupled equations methods are in principle exact and can be readily implemented for diatomics and triatomics with current computer technology.