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Physical Review A

Transition from weak- to strong-field coherent control

Carlos A Trallero-Herrero, Thomas C. Weinacht

Published Jun 1, 2007• 46 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.75.063401

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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.
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 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.
Coherent control of resonant and non-resonant two-photon absorption processes was examined using a spatio-temporal pulse-shaping technique. By utilizing a combination of temporal focusing and femtosecond pulse-shaping techniques, we spatially control multiphoton absorption processes in a completely deterministic manner. Distinctive symmetry properties emerge through two-dimensional mapping of spatio-temporal data. These symmetries break down in the transition to strong fields, revealing details of strong-field effects such as power broadenings and dynamic Stark shifts. We also present demonstrations of chirp-dependent population transfer in atomic rubidium, as well as the spatial separation of resonant and non-resonant excitation pathways in atomic caesium.
Weak-field coherent phase control of atomic non-resonant multiphoton excitation induced by shaped femtosecond pulses is studied theoretically in the single-cycle regime. The carrier-envelope phase (CEP) of the pulse, which in the multi-cycle regime does not play any control role, is shown here to be a new effective control parameter that its effect is highly sensitive to the spectral position of the ultrabroad spectrum. Rationally chosen position of the ultrabroadband spectrum coherently induces several groups of multiphoton transitions from the ground state to the excited state of the system: transitions involving only absorbed photons as well as Raman transitions involving both absorbed and emitted photons. The intra-group interference is controlled by the relative spectral phase of the different frequency components of the pulse, while the inter-group interference is controlled jointly by the CEP and the relative spectral phase. Specifically, non-resonant two- and three-photon excitation is studied in a simple model system within the perturbative frequency-domain framework. The developed intuition is then applied to weak-field multiphoton excitation of atomic cesium (Cs), where the simplified model is verified by non-perturbative numerical solution of the time-dependent Schrödinger equation. We expect this work to serve as a basis for a new line of femtosecond coherent control experiments.
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.
Coherent control of femtosecond two-photon absorption in the intermediate-field regime is analyzed in detail in the powerful frequency domain using an extended 4th-order perturbative description. The corresponding absorption is coherently induced by the weak-field non-resonant two-photon transitions as well as by four-photon transitions involving three absorbed photons and one emitted photons. The interferences between these two groups of transitions lead to a difference between the intermediate-field and weak-field absorption dynamics. The corresponding interference nature (constructive or destructive) strongly depends on the detuning direction of the pulse spectrum from half the two-photon transition frequency. The model system of the study is atomic sodium, for which both experimental and theoretical results are obtained. The detailed understanding obtained here serves as a basis for coherent control with rationally-shaped femtosecond pulses in a regime of sizable absorption yields.