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Physical Review Letters

Strong-Field Atomic Phase Matching

Carlos A Trallero-Herrero, J. L. Cohen, Thomas C. Weinacht

Published Feb 16, 2006• 85 citations
Publisher

Abstract

We interpret a learning-control experiment with the goal of optimizing multiphoton population transfer in atomic sodium in the strong-field limit. Despite multiple experimental constraints, a learning algorithm discovers optimal pulses that can be understood in terms of a simple dynamic picture of the atom-field interaction. We show that the shaped pulses counteract the dynamic Stark-induced stimulated emission that would otherwise impede the efficient use of a pi pulse to invert a multiphoton transition.

DOI
10.1103/physrevlett.96.063603

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We interpret a learning-control experiment with the goal of optimizing multiphoton population transfer in atomic sodium in the strong-field limit. Despite multiple experimental constraints, a learning algorithm discovers optimal pulses that can be understood in terms of a simple dynamic picture of the atom-field interaction. We show that the shaped pulses counteract the dynamic Stark-induced stimulated emission that would otherwise impede the efficient use of a pi pulse to invert a multiphoton transition.
We compare the results of two strong field coherent control experiments: one which optimizes multi-photon population transfer in atomic sodium (from the 3s to the 4s state, measured by spontaneous emission from the 3p-3s transition) with one that optimizes stimulated emission on the 3p-3s transition in an ensemble of sodium atoms. Both experiments make use of intense, shaped ultrafast laser pulses discovered by a Genetic Algorithm inside a learning control loop. Optimization leads to improvements in the spontaneous and stimulated emission yields of about 444 and 104{10}^{4}104, respectively, over an unshaped pulse. We interpret these results by modeling both the single atom dynamics as well as the stimulated emission buildup through numerical integration of Schr\"odinger's and Maxwell's equations. Our interpretation leads to the conclusion that modest yields for controlling single quantum systems can lead to dramatic effects whenever an ensemble of such systems acts collectively following controlled impulsive excitation.
We show that coherent control of multiphoton transitions is possible in the strong field limit, even in the presence of large dynamic Stark shifts. By tailoring the phase of an ultrafast laser pulse, one can compensate for the dynamic Stark shift during the atom-field interaction to achieve efficient population transfer in two-photon absorption. Numerical simulations for atomic sodium reveal efficient population transfer from the $\ensuremath{\mid}3s⟩$ ground state to the $\ensuremath{\mid}4s⟩$ excited state using an appropriately shaped ultrafast laser pulse. The theory and simulations provide insight into coherent control of more complicated multiphoton processes.
We demonstrate a population inversion in a three-level system via three-photon absorption from a single shaped ultrafast laser pulse. The optimal pulse shape for the inversion is discovered using closed-loop learning control and interpreted via pulse shape parameter scans and numerical integration of the Schrödinger equation. The population inversion is measured using a combination of spontaneous and stimulated emissions. Our results illustrate the importance of dynamic Stark shifts in coherent multi-photon excitation.
We trace out the transition from weak- to strong-field coherent control, focusing on multiphoton population transfer in atomic sodium. We show how dynamic Stark shifts and ground-state depletion mark the departure from perturbative to strong-field excitation, and how a time-domain picture yields insight into the dynamics when a static resonance, frequency-domain approach breaks down. Experimental measurements are interpreted with the help of calculations that numerically integrate the Schr\"odinger equation.
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 Schr\"odinger 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 $3s\ensuremath{\rightarrow}4s$ two-photon transition of atomic sodium. By solving the time-dependent Schr\"odinger 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.
We have considered an analytical control of two-photon absorption process of atoms in the strong-field interaction regime. The experiment was performed on gaseous cesium atoms strongly interacting with a shaped laser-pulse from a femtosecond laser amplifier and a programmable pulse-shaper. When this shaped laser-pulse transfers the atomic population from the 6s ground state to the 8s excited state, we have found that both positively- and negatively-chirped laser pulses, compared with a Gaussian pulse, enhance this excitation in the strong-field regime of laser-atom interaction. This unusual phenomena is explained because the temporal shape of the laser intensity compensates the effect of dynamic Stark shift for the two-photon resonant condition to be optimally maintained. We provide analytic calculations using the strong-field phase matching, which show good agreement with the experiment.