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Physical Review A

Influence of propagation on the coherent accumulation of excitation induced by an ultrashort pulse train

Antônio Augusto Soares, Luı́s E. E. de Araujo

Published Jul 29, 2009• 10 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.80.013832

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•Feb 3, 2009•1 citation
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 investigate the excitation of an atomic degenerate-$\ensuremath{\Lambda}$ system by a train of ultrashort pulses. An iterative analytic solution to the optical Bloch equations is found describing the temporal evolution of the density matrix elements. We show that electromagnetically induced transparency of the excitation pulses develops through the coherent accumulation of excitation (population and coherence) between the degenerate lower states. The influence of the pulse train parameters (area, repetition period, and phase between successive pulses) on establishing the transparency is investigated.
In this paper, I numerically investigate the propagation of ultrashort pulses through an extended collection of multilevel systems under the condition of electromagnetically induced transparency. The transparency of a weak probe pulse is induced by a much stronger coupling pulse. In the limit of a weak probe excitation and a large number of excited states, I show that the free-induction decay signal that would naturally follow the excitation pulse is strongly suppressed, and the envelope of the probe pulse suffers a distortion in its temporal profile as the pulse propagates into the medium. This distortion is characterized by a stronger absorption of the leading edge of the pulse than that of its trailing edge. The temporal phase of the pulse, however, remains constant throughout propagation.
We investigate coherent accumulation processes in three-level atoms excited by a train of ultrashort pulses in the case where the atomic relaxation times are greater than the laser repetition period. In this situation the resonances of the laser field with the atomic system are determined by the laser frequency comb rather than by the spectrum of a single pulse. Using the density matrix formalism, we develop a perturbative theory that is valid for arbitrary pulse shapes. The excitation of a Doppler-broadened atomic vapor by hyperbolic-secant pulses and $0\ensuremath{\pi}$ pulses is analyzed. It is shown that pulse shape has a great influence on the accumulation process and can change the spectral periodicity of the pattern impressed on the Doppler profile of the medium due to the two-photon absorption process. The effect of interpulse phases is also investigated, and we show that the atomic populations can vary by more than one order of magnitude with small variations of the laser repetition rate, while being insensitive to variations of the laser offset. Finally, the theory is adapted for the temporal-coherent-control technique, and its results are compared with previously reported experimental data.
This paper analyzes the result of a temporal coherent control experiment using trains of ultrashort laser pulses in the situation where the laser repetition period is smaller than the relaxation times of the system. We focus on the accumulative effects present in sequential two-photon absorption. It is shown that stimulated emission due to the accumulation of population in the excited state give an important contribution to the coherently controlled process. Excellent agreement is obtained in the comparison between experiments in rubidium vapor and theory, where resonant pulse propagation is also taken into account.
This thesis deals with the study of propagation effects experienced by weak light pulses as they propagate in atomic media driven by strong pulses. We explore both the ultra-short and long pulse regime and investigate the phenomena that arise at these different time scales. In the short pulse regime, a strongly driven two level atomic system presents transient light shifts, and non-adiabatic transitions occur between these adiabatic levels. We have studied a method to probe these light shifts in real time by propagating a weak probe through the medium. The light shifts enrich the spectrum of the probe and the probe gets shaped as a result. In this way a strongly driven two-level system can act as an active pulse shaper, and can introduce oscillations in the temporal profile of an ultra-short pulse at a time scale shorter than the pulse duration. We also show that by driving the system with two time delayed non-resonant strong fields, the non-adiabatic effects can be rendered phase dependent. This gives very sensitive phase control of the excited state population and can be used to formulate new techniques in interferometry. In the long pulse regime we present a new method of slowing light that can be realized in a double two-level system interacting with two orthogonally polarized light pulses that propagate along different axis. Spatio-temporal dependence of the total polarization induces a grating in the ground Zeeman coherence. The stronger of the two fields (the control field) is diffracted from this grating into the direction of the weak probe field compensating for the absorption of this latter field. A transparency window is thus created in the absorption spectrum of the probe leading to the slowing down of light. The transparency window exhibits characteristics similar to the one obtained by EIT (electromagnetic induced transparency) method. However, the important difference between our method and the traditional EIT method, is that ours doesn't rely on realizing dark state in the system. This may open the possibility of slowing down light in more complex atomic media. Moreover, when the linear absorptive response of the medium is cancelled in this manner, the nonlinear response becomes more important. In the situation where fields propagate in the same direction and have same frequency, two regimes have been investigated. For small optical depths, the effective susceptibility behaves as chi_lin exp[2 i phi] (with phi the phase difference between two fields). This renders phase control of the medium response, and the medium can be changed from an absorber to an amplifier, with normal or anomalous dispersion, by adjusting the relative phase phi.  In the regime of large optical thickness, phase saturation takes place and the effective susceptibility turns into chi_lin*, changing an absorber into an amplifier without effecting the dispersive response (chi_lin is linear susceptibility).