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arXiv:0709.0486 · Physical Review A

Enhancement of intermediate-field two-photon absorption by rationally shaped femtosecond pulses

Lev Chuntonov, Leonid Rybak, Andrey Gandman, Zohar Amitay

Published Feb 19, 2008• 25 citations
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Abstract

We extend the powerful frequency-domain analysis of femtosecond two-photon absorption to the intermediate-field regime of considerable absorption yields, where additionally to the weak-field nonresonant two-photon transitions also four-photon transitions play a role. Consequently, we rationally find that the absorption is enhanced over the transform-limited pulse by any shaped pulse having a spectral phase that is antisymmetric around one-half of the transition frequency and a spectrum that is asymmetric around it (red or blue detuned according to the system). The enhancement increases as the field strength increases. The theoretical results for Na are verified experimentally.

DOI
10.1103/physreva.77.021403

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Physical Review Letters•Jul 23, 2014•6 citations
We extend the powerful frequency-domain analysis of femtosecond two-photon absorption to the intermediate-field regime of considerable absorption yields, where additionally to the weak-field nonresonant two-photon transitions also four-photon transitions play a role. Consequently, we rationally find that the absorption is enhanced over the transform-limited pulse by any shaped pulse having a spectral phase that is antisymmetric around one-half of the transition frequency and a spectrum that is asymmetric around it (red or blue detuned according to the system). The enhancement increases as the field strength increases. The theoretical results for Na are verified experimentally.
We study in detail the coherent interference mechanism leading to the intermediate-field two-photon absorption enhancement recently found for shaped femtosecond pulses with spectral phases that are antisymmetric around one-half of the transition frequency. We particularly investigate the tolerance of the phenomenon to the phase deviation from perfect antisymmetry. We theoretically and experimentally find that this tolerance increases as the field strength increases. For the present Na excitation, the enhancement occurs even when $~$30% of the phase pattern is not antisymmetric. Our findings are of particular importance for multichannel coherent control scenarios.
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.
We study in detail coherent phase control of femtosecond resonance-mediated (2+1)(2+1)(2+1) three-photon absorption and its dependence on the spectral bandwidth of the excitation pulse. The regime is the weak-field regime of third perturbative order. The corresponding interference mechanism involves a group of three-photon excitation pathways that are on resonance with the intermediate state and a group of three-photon excitation pathways that are near resonant with it. The model system of the study is atomic sodium (Na), for which experimental and numerical-theoretical results are obtained. Prominent among the results is our finding that with simple proper pulse shaping an increase in the excitation bandwidth leads to a corresponding increase in the enhancement of the three-photon absorption over the absorption induced by the (unshaped) transform-limited pulse. For example, here, a 40 nm bandwidth leads to an order-of-magnitude enhancement over the transform-limited absorption.
Femtosecond coherent phase control of resonance mediated (2+1)(2+1)(2+1) three-photon absorption is studied both theoretically and experimentally. The regime is perturbative of third order. The photoexcitation coherently combines elements of both nonresonant and resonance-mediated multiphoton transitions. By proper simple pulse shaping the three-photon absorption in Na is effectively controlled experimentally, enhanced up to $\ensuremath{\sim}300%$ of the absorption induced by the transform-limited pulse. It is achieved by phase manipulating intra- and intergroup interferences involving two groups of three-photon excitation pathways: (i) on resonance and (ii) near resonance with the intermediate resonance state accessed by nonresonant two-photon transition.
Coherent control of the atomic two-photon absorption with shaped single-cycle pulses is examined theoretically in the weak-field regime. The control over the stabilized carrier-envelope phase (CEP) of the pulses is determined as a key parameter allowing the full utilization of the ultrabroad pulse spectrum. This bandwidth is sufficient to provide besides the sequential two-photon pathways, additional Raman-type pathways coupling between the ground and the excited states. The interference between the different pathways is efficiently controlled via the control over the CEP. Simplified two-level model is analyzed in the frequency domain where the rational pulse shaping is applied. The developed intuition is applied to atomic Cs and verified by the exact numerical solution of time-dependent Schrodinger equation.
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.