Strong-field control by reverse engineering

Based on the idea of reverse engineering, we design an optimal laser pulse to control strong-field multiphoton atomic transitions. Starting from the time-dependent Schrodinger equation of the full system, we adiabatically eliminate the nonessential states and apply the rotating-wave approximation to arrive at an effective two-state representation that involves dynamic Stark shifts and multiphoton coupling. Solving this equation inversely for the field, we obtain an analytical laser pulse shape that is expected to induce the full system's evolution according to user-defined quantum pathways. In our procedure, the amplitude and phase of the laser pulse are engineered such that the dynamically shifted electronic states are resonantly coupled during the action of the pulse at each moment of time. As a result, the driven system evolves from an arbitrary initial population distribution to any desired final quantum state superposition at a predefined rate. The proposed scheme is demonstrated using the example of the 3s -> 4s two-photon transition of atomic sodium. By solving the time-dependent Schrodinger equation of the single-active electron with two different methods, either propagating time-dependent coefficients of many field-free states or directly propagating the three-dimensional electronic wave packet on a grid, we demonstrate the robustness as well as the limitations of the presented reverse engineering scheme.

Automated summary

This study designs an optimal laser pulse for controlling strong-field multiphoton atomic transitions through reverse engineering, eliminating nonessential states and applying the rotating-wave approximation. By engineering the amplitude and phase of the laser pulse, resonant coupling of dynamically shifted electronic states is achieved, allowing the system to evolve along user-defined quantum pathways.