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arXiv:1306.3968

Resonant interaction between an ultrashort pulse train and a two-level system: frequency domain analysis

Marco P. Moreno, S. S. Vianna

Published Jun 17, 2013• 0 citations
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Abstract

We investigate the problem of two-level atoms driven by an ultrashort pulse train in the frequency domain. At low intensity regime, we obtain a perturbative analytical solution that allows us to discuss the role of the mode number of the frequency comb near or at resonance on the temporal evolution of the atomic coherence. At high intensities, the effect of the number of modes is analyzed in the steady-state regime through numerical calculations.

DOI
10.48550/arxiv.1306.3968

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We investigate the problem of two-level atoms driven by an ultrashort pulse train in the frequency domain. At low intensity regime, we obtain a perturbative analytical solution that allows us to discuss the role of the mode number of the frequency comb near or at resonance on the temporal evolution of the atomic coherence. At high intensities, the effect of the number of modes is analyzed in the steady-state regime through numerical calculations.
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Direct frequency-comb spectroscopy is a technique that employs a train of well-stabilized ultrashort pulses to study the spectral properties of atomic or molecular systems. In this way, it opens the possibility of incorporating various coherent-control techniques for such spectral investigations. Here we introduce a theory for the interaction of a multilevel atom with such pulse trains, which is general enough to take into account an arbitrarily shaped frequency comb. We illustrate its application by studying the interaction of 87Rb^{87}\text{R}\text{b}87Rb atoms with trains of pulses of various shapes, resonant with the $5S\text{\ensuremath{-}}5D$ two-photon transition of rubidium. More specifically, we treat the interaction with hyperbolic-secant pulses, chirped pulses, and 0-$\ensuremath{\pi}$ pulses, respectively. The theory is designed to work at an arbitrary perturbation order. For the results presented here, we mostly used a 12th-order perturbation series at the pulse's electric field. Due to the large number of levels involved, such modeling may be quite complex computationally, and an important point of the present work is then to introduce the required numerical approach to treat this problem efficiently.
We study the effects of propagation through an extended sample of two- and three-level atoms on the coherent accumulation of excitation by an ultrashort pulse train. In the two-level case, previous pulses in the train may prepare the medium such that a later pulse may experience amplification and absorption in different positions inside the sample. For a large number of pulses, the atomic medium may be saturated by the train, and some pulses propagate without experiencing either absorption or amplification. In general, absorption of the resonant pulse frequency during propagation compromises the accumulation efficiency. In the three-level case, the coherent accumulation of excitation leads to electromagnetically induced transparency of the pulse train, and the pulses exit the medium without any distortion in their temporal profile.
We study theoretically the interaction between an ultrashort pulse train and a three-level atom driven by a cw laser. We show that the pulse train can be employed to observe spectra of Autler–Townes doublet and electromagnetically induced transparency resonance that are time and frequency resolved. The observation of subnatural linewidth features associated with the electromagnetically induced transparency resonance is described. The temporal evolution of electromagnetically induced transparency of the pulse train is shown to exhibit new and different features compared to that of the related phenomenon of coherent population trapping. By matching the tooth separation of the frequency comb associated with the pulse train to that of the Autler–Townes doublet, quantum beats between the doublet components can be induced. We show that coherent accumulation of excitation plays a major role in the two studied phenomena.