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Physical Review A

Interference in climbing a quantum ladder system with frequency-chirped laser pulses

Péter Balling, D. J. Maas, Lambertus D. Noordam

Published Nov 1, 1994• 99 citations
Publisher

Abstract

Excitation of a quantum ladder system by frequency-swept (-chirped) laser pulses has been investigated by studying an atomic model system, the 5s-5p-5d ladder of rubidium. The population transfer is significantly enhanced when the frequency is swept such that it follows the spacing of the ladder. At intermediate intensities we observe oscillations in the population transfer to the upper level (5d), which can be attributed to interference between two routes of excitation: sequential transfer and direct two-photon excitation via a virtual intermediate state. We determine simultaneously the population transfer to the upper level (5d) and the direct three-photon ionization, the latter corresponding to a three-step ladder with the final state being in the continuum: 5s-5p-5d-\ensuremath{\varepsilon}p/\ensuremath{\varepsilon}f. Experiments were performed, using 100 fs pulses at \ensuremath{\sim}780 nm from a self-mode-locked Ti:${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ oscillator amplified at 10 Hz.

DOI
10.1103/physreva.50.4276

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Excitation of a quantum ladder system by frequency-swept (-chirped) laser pulses has been investigated by studying an atomic model system, the 5s-5p-5d ladder of rubidium. The population transfer is significantly enhanced when the frequency is swept such that it follows the spacing of the ladder. At intermediate intensities we observe oscillations in the population transfer to the upper level (5d), which can be attributed to interference between two routes of excitation: sequential transfer and direct two-photon excitation via a virtual intermediate state. We determine simultaneously the population transfer to the upper level (5d) and the direct three-photon ionization, the latter corresponding to a three-step ladder with the final state being in the continuum: 5s-5p-5d-\ensuremath{\varepsilon}p/\ensuremath{\varepsilon}f. Experiments were performed, using 100 fs pulses at \ensuremath{\sim}780 nm from a self-mode-locked Ti:{\mathrm{Al}}_{2}$${\mathrm{O}}_{3} oscillator amplified at 10 Hz.
Enhanced population transfer from the lowest to the highest level in the three-state ladder 5s->5p->5d of the rubidium atom by frequency swept ultra short laser pulses is observed if the frequency sweep first makes the pulse resonant with the 5s->5p transition, and later with the 5p->5d transition. With this intuitive scheme it is possible to achieve complete population inversion via the intermediate level by two successive adiabatic passages. Complete inversion is also obtained by a {open_quote}counterintuitive{close_quote} direction of the frequency-sweep, in which case population of the intermediate level during the pulse is strongly reduced. The atomic system can be seen as a model system for multistep vibrational excitation in an anharmonic molecular potential.
Generally, high optical intensity is required for effective multiphoton excitation of quantum systems to highly excited states. In certain situations, however, lower-intensity, chirped pulses can provide more efficient transfer of population to the upper states by the process of adiabatic passage. We have studied the relative importance of these two mechanisms in the anharmonic $5s\ensuremath{-}5p\ensuremath{-}5d$ quantum ladder system of rubidium using frequency chirped laser pulses from an amplified Ti:sapphire laser (\ensuremath{\lambda}=780 and \ensuremath{\Delta}\ensuremath{\lambda}=10 nm). We measure simultaneously the three-photon ionization signal due to the Ti:sapphire and the population that remains in the 5d5d5d state with a postionizing 532-nm Nd:YAG pulse (where YAG denotes yttrium aluminum garnet). At low infrared fluences (80 \ensuremath{\mu}J/cm2{\mathrm{J}/\mathrm{c}\mathrm{m}}^{2}J/cm2), the transfer to the 5d5d5d state is significantly enhanced when the pulse frequency is swept from the red to the blue, such that it follows the frequency spacing of the rubidium ladder. Counterintuitively, population is also transferred efficiently for the blue-to-red chirp at high fluences (>5 mJ/cm2{\mathrm{m}\mathrm{J}/\mathrm{c}\mathrm{m}}^{2}mJ/cm2). We attribute both of these effects to adiabatic passage from the 5s5s5s state to the 5d5d5d state. Even at the highest fluences, more efficient transfer occurs for either direction of chirp than occurs at zero chirp, where the intensity is maximal. A comparison to theoretical predictions reveals striking agreement in both absolute magnitude and functional form. These results have important implications for the understanding of population transfer in complex ladder systems, such as molecular anharmonic vibrational ladders.
Enhanced population transfer from the lowest to the highest level in the three-state ladder 5s\ensuremath{\rightarrow}5p\ensuremath{\rightarrow}5d of the rubidium atom by frequency-swept ultrashort laser pulses is observed if the frequency sweep first makes the pulse resonant with the 5s\ensuremath{\rightarrow}5p transition, and later with the 5p\ensuremath{\rightarrow}5d transition. With this ``intuitive'' scheme it is possible to achive complete population inversion via the intermediate level by two successive adiabatic passages. Complete inversion is also obtained by a ``counterintuitive'' direction of the frequency sweep, in which case population of the intermediate level during the pulse is strongly reduced.
Two-photon excitation of a quantum ladder system by an ultrashort chirped pulse leads to interferences in the excited-state population, between direct and sequential paths. Experimental results have been obtained in atomic sodium vapor. The presence of several intermediate and final states leads to new phenomena. The interplay between the two sequential paths leads to strongly contrasted oscillations and a large enhancement of the transition probability for precise values of the chirp. A cubic spectral phase modifies significantly the behavior of the quantum interferences and can be used to enhance the two-photon absorption rate.
Two-photon excitation of a quantum ladder system by a chirped pulse leads to interferences in the excited-state population, due to the phase differences between direct and sequential paths. First, based on an analytical approach, we separate and discuss the features of the contributions arising from these two paths. Then interferences with two intermediate levels are observed experimentally in atomic sodium vapor. Interplay between the two sequential paths leads to strongly contrasted oscillations and a great enhancement of the transition probability for some values of the chirp.
The effects of coherent excitation of a two-level system with a linearly chirped pulse are studied theoretically and experimentally [in Rb (5s-5p)] in the low field regime. The coherent transients are measured directly on the excited state population on an ultrashort time scale. A sharp step corresponds to the passage through resonance. It is followed by oscillations resulting from interferences between off-resonant and resonant contributions. We finally show the equivalence between this experiment and Fresnel diffraction by a sharp edge.