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Journal of Physics B Atomic Molecular and Optical Physics

Autler–Townes doublet and electromagnetically induced transparency resonance probed by an ultrashort pulse train

Antônio Augusto Soares, Luı́s E. E. de Araujo

Published Apr 6, 2010• 9 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/43/8/085003

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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.
We report an experimental observation of Autler-Townes doublet splitting in electromagnetically induced transparency (EIT) resonance. The splitting is introduced by a coherent microwave field, which perturbs a three-level A-type EIT system through an auxiliary level. The doublet splitting of EIT resonance is demonstrated in two cases, where the microwave field shares a common lower level with coupled or probe transition, respectively. The dependence of doublet splitting on microwave field intensity and detuning is measured. This may provide a feasible way of manipulating the atomic states with both laser and microwave field.
In this paper we study the nonlinear behavior of an electromagnetically induced transparency (EIT) resonance subject to a coherent driving field. The EIT is associated with a $\ensuremath{\Lambda}$ three-level system where two hyperfine levels within an electronic ground state are coupled to a common excited state level by a coupling field and a probe field. In addition there is an radio-frequency (rf) field driving a hyperfine transition within the ground state. The paper contrasts two different situations. In one case the rf-driven transition shares a common level with the probed transition and in the second case it shares a common level with the coupled transition. In both cases the EIT resonance is split into a doublet and the characteristics of the EIT doublet are determined by the strength and frequency of the rf-driving field. The doublet splitting originates from the rf-field induced dynamic Stark effect and has close analogy with the Autler-Townes effect observed in three-level pump-probe spectroscopy study. The situation changes when the rf field is strong and the two cases are very different. One is analogous to two $\ensuremath{\Lambda}$ three-level systems with EIT resonance associated with each. The other corresponds to a doubly driven three-level system with rf-field-induced electromagnetically induced absorption resonance. The two situations are modeled using numerical solutions of the relevant equation of motion of density matrix. In addition a physical account of their behaviors is given in terms of a dressed state picture.
We present an analysis of coherent population trapping in a three-level Λ system when excited by an ultrashort pulse train near the one- and two-photon resonances. Numerical results using Bloch equations give the transient response of the system and clearly reveal a comb of electromagnetically induced transparency (EIT) lines. An analytical solution to describe the EIT lines is derived in the steady-state regime and in the weak field limit. Moreover, numerical results indicate that selective velocity spectroscopy makes possible the observation of the comb of EIT lines in Doppler broadening media.
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.
An unexpected interference effect between four-wave mixing excitation routes in rubidium vapor is observed using a combination of a cw diode laser and a 1-GHz femtosecond pulse train. The generated coherent blue light is analyzed by scanning the diode frequency and the repetition rate of the frequency comb. In both cases, the cw laser induces an Autler-Townes splitting, and a large separation is observed in the doublet structure due to the configuration of copropagating fields. Remarkably, by scanning the repetition rate, a narrow peak appears as a signature of the interfering pathways. A nonperturbative treatment of the Bloch equations achieves good agreement with the experimental data and demonstrates that the interfering effect appears only when both lasers are resonant with one- and two-photon transitions for the same atomic velocity group.