The nonperturbative regime

Notice that, in the limit of a strong laser field, where atomic effects are small, the solution has a universal and simple form, whose main properties may therefore be sought in observed spectra. As will be shown below, several features of experimental data for atoms in strong fields can be explained from this very simple starting point. 

There is no clear evidence that any one of these models is sufficient or complete. Examples exist of situations in which one or other of these pictures applies, and which model is appropriate depends on (a) the atom (b) the intensity of the laser pulse and (c) its duration. 

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We now turn our attention to the nonperturbative regime. Due to advances in laser technology over the past decade, many experiments are now possible where the laser field is stronger than the nuclear attraction. The time-dependent field cannot be treated perturbatively, and even solving the time-dependent Schrodinger equation in three dimensions for the evolution of two interacting electrons is barely feasible with present-day computer technology. ... 

First we discuss the scaling aspects. We expect, in the nonperturbative regime... 

In contrast to weak-held (perturbative) quantum control schemes where the population of the initial state is approximately constant during the interaction with the external light held, the strong-held (nonperturbative) regime is characterized by efficient population transfer. Adiabatic strong-held techniques such as rapid... 

In this chapter, we discuss some new developments in TDDFT beyond the linear response regime for accurate and efficient nonperturbative treatment of multiphoton dynamics and very-high-order nonlinear optical processes of atomic and molecular systems in intense and superintense laser fields. In Section 2, we briefly describe the time-dependent optimized effective potential (OEP) method and its simplified version, i.e., the time-dependent Krieger-Li-Iafrate (KLI) approximation, along with self-interaction correction (SIC). In Section 3, we present the TDDFT approaches and the time-dependent generalized pseudospectral (TDGPS) methods for the accurate treatment of multiphoton processes in diatomic and triatomic molecules. In Section 4, we describe the Floquet formulation of TDDFT. This is followed by a conclusion in Section 5. Atomic units will be used throughout this chapter. 

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