Adiabatic time evolution of atoms and molecules in intense radiation fields

Abstract

We derive the condition for a time dependent quantum system to exhibit an exact or higher order adiabatic time evolution. To this end, the concept of adiabaticity is first analyzed in terms of the transformation properties of the time-dependent Schrödinger equation under a general unitary transformation Û(t). The system will follow an adiabatic time evolution, if the transformed Hamiltonian, K̂(t)=Û°ĤÛ−iℏÛ°Û, is divisible into an effective Hamiltonian ĥ(t), defining adiabatic quasistationary states, and an interaction term Ω̂(t), whose effect on the adiabatic states exactly cancels the nonadiabatic couplings arising from the adiabatic states’ parametric dependence on the time. This decoupling condition, which ensures adiabaticity in the system’s dynamics, can be expressed in a state independent manner, and governs the choice of the unitary operator Û(t), as well as the construction of the effective Hamiltonian ĥ(t). Using a restricted class of unitary transformations, the formalism is applied to the time evolution of an atomic or molecular system in interaction with a spatially uniform electromagnetic field, and gives an adiabatic approximation of higher order to the solutions of the semiclassical Schrödinger equation for this system. The adiabatic approximation so obtained exhibits two properties that make it suitable for the studies of intense field molecular dynamics: It is valid for any temporal profile of the field, and improves further as the field intensity increases, as reflected in the weakening of the associated residual nonadiabatic couplings with increasing field strength.