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Journal of Physics B Atomic Molecular and Optical Physics

Spatio-temporal coherent control of atomic systems: weak to strong field transition and breaking of symmetry in 2D maps

Haim Suchowski, Adi Natan, Barry D. Bruner, Yaron R. Silberberg

Published Mar 26, 2008• 21 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/41/7/074008

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•Aug 1, 2010•1 citation
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.
Simple analytical approaches for implementing strong field coherent control schemes are often elusive due to the complexity of the interaction between the intense excitation field and the system of interest. Here, we demonstrate control over multiphoton excitation in a three-level resonant system using simple, analytically derived ultrafast pulse shapes. We utilize a two-dimensional spatiotemporal control technique, in which temporal focusing produces a spatially dependent quadratic spectral phase, while a second, arbitrary phase parameter is scanned using a pulse shaper. In the current work, we demonstrate weak-to-strong field excitation of 85Rb^{85}\mathrm{Rb}85Rb, with a $\ensuremath{\pi}$ phase step and the quadratic phase as the chosen control parameters. The intricate dependence of the multilevel dynamics on these parameters is exhibited by mapping the data onto a two-dimensional control landscape. Further insight is gained by simulating the complete landscape using a dressed-state, time-domain model, in which the influence of individual shaping parameters can be extracted using both exact and asymptotic time-domain representations of the dressed-state energies.
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.
We present and experimentally demonstrate for the first time the observation and femtosecond coherent control over the temporal evolution of a transient population that is excited via nonresonant two-photon absorption. Based on symmetry properties of the two-photon absorption process, the exciting femtosecond pulses are phase-shaped to photoinduce different evolutions of the transient excited population for a given final excited population. As a study case, we focus here on the attractive case of two-photon dark pulses that, although inducing zero final population (hence, the terminology of "dark pulses"), they induce a transient excited population during the pulse irradiation that can significantly deviate from zero. This nonzero transient population can be viewed as the bright side of such dark pulses. The symmetry-based coherent control is demonstrated first with dark pulses that we shape to induce transient excited population that at all times is kept below different target levels. Then, it is further demonstrated with pairs of dark pulses where one is rationally shaped to induce temporal evolution of the transient excited population that is the inverse of the evolution induced by the other. The work is conducted in the weak-field regime with the sodium atom as the model system. The approach developed here is general, conceptually simple, and very effective.
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.
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.
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.