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Physical Review A

Understanding strong-field coherent control: Measuring single-atom versus collective dynamics

Carlos A Trallero-Herrero, Michael Spanner, Thomas C. Weinacht

Published Nov 17, 2006• 11 citations
Publisher

Abstract

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 $4$ and ${10}^{4}$, 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.

DOI
10.1103/physreva.74.051403

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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 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 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 demonstrate ultrafast coherent control of multiphoton absorption in a dynamically shifted energy level structure. In a three-level system that models optical interactions with sodium atoms, we control the quantum interference of sequential 2 + 1 photons and direct three-photon transitions. Dynamic change in energy levels predicts an enormous enhancement of |7p>-state excitation in the strong-field regime by a negatively chirped pulse. In addition, the |4s>-state excitation is enhanced symmetrically by nonzero linear chirp rates given as a function of laser peak intensity and laser detuning. Experiments performed by ultrafast shaped-pulse excitation of ground-state atomic sodium verifies the various strong-field contributions to |3s>-|7p> and |3s>-|4s> transitions. The result suggests that for systems of molecular level understanding adiabatic control approach with analytically shaped pulses becomes a more direct control than feedback-loop black-box approaches.
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.
In this thesis, we present work on coherent control of multilevelquantum systems in the strong field limit using shaped ultrafastlaser pulses. In recent years there have been numerous multiphotonabsorption experiments in two,three, and four-level atomic/molecularsystems and many are performed in the limit of weak fields whereperturbation theory is valid. Here, we describe a series ofexperiments aimed at exploring and understanding multiphotontransitions when the exciting field is strong and perturbationtheory breaks down. Our approach to strong field control utilizesboth parameterized scans of various pulse shapes and closed-looplearning control to identify a pulse shape that is optimal forpopulating a target quantum state. With this we will highlight thedifference between sequential population transfer and adiabaticrapid passage in multilevel systems with multiphoton couplingbetween levels. Additionally, we examine strong field control of afour-level atomic interferometer and show how interference in atarget state changes from resonant pathways in the frequency domainto time-domain interference via a singe path.Further, we use shaped femtosecond pulses to demonstrate aphenomenon in which a three-level atom becomes a modulator of anultrafast pulse. The results are based on a pump-probe scheme thatis very similar to Electromagnetically Induced Transparency (EIT).Important dynamics associated with a time-dependent coupling fieldare examined. Lastly, we extend previous work on two-photon drivensuperfluorescence from a shaped ultrafast drive laser and show howstimulated emission near threshold can turn modest coherent controlyields into essentially perfect discrimination between systems wherea control factor of about 104 is achieved between atomic andmolecular species.
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.