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Physical Review A

Coherent accumulation of excitation in the electromagnetically induced transparency of an ultrashort pulse train

Antônio Augusto Soares, Luı́s E. E. de Araujo

Published Oct 15, 2007• 27 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.76.043818

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We investigate the excitation of an atomic degenerate-\ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ 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.
We present an iterative analytic solution for the time dynamics of the 87Rb^{87}\text{R}\text{b}87Rb four-level atoms excited by a train of ultrashort pulses. It enables fast and accurate calculation of the system time evolution circumventing the use of time-consuming numerical procedures. The obtained solution is used to study the complex interaction of atoms with the pulse-train electric field, both in time and frequency domain. We investigate the influence of pulse-train physical parameters, such as the pulse peak power, the repetition frequency and the central laser wavelength on the accumulation of population and coherence in the system characterized by relaxation times larger than the pulse repetition period.
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 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 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 study the dynamics of three-level $\ensuremath{\Lambda}$-type atoms driven by a coherent train of short, nonoverlapping laser pulses. We derive analytical nonperturbative expressions for the density matrix by approximating the pulses by a $\ensuremath{\delta}$ function. We demonstrate that, depending on the train parameters, several scenarios of system dynamics can be realized. We show the possibility of driving Raman transitions between the two ground states of the $\ensuremath{\Lambda}$ system, avoiding populating excited states by using pulses with effective area equal to $2\ensuremath{\pi}$. The number of $2\ensuremath{\pi}$ pulses needed to transfer the entire population from one ground state to another depends on the ratio between the Rabi frequencies of two allowed transitions. In the case of equal Rabi frequencies, the system can be transferred from one ground state to another with a single $2\ensuremath{\pi}$ pulse. When the total pulse area differs from $2\ensuremath{\pi}$ and the two-photon resonance condition is fulfilled, the system evolves into a ``dark'' state and becomes transparent to subsequent pulses. The third possible scenario is the quasi-steady-state regime when neither the total single-pulse area is equal to $2\ensuremath{\pi}$ nor is the two-photon resonance condition fulfilled. In this regime the radiative-decay-induced drop in the population following a given pulse is fully restored by the subsequent pulse. We derive an analytical expression for the density matrix in the quasi-steady-state regime. We analyze the dependence of the postpulse excited-state population in the quasi-steady-state regime on the train parameters. We find the optimal values for the train parameters corresponding to the maximum of the excited-state population. The maximum of the excited-state population in the steady-state regime is reached at an effective single-pulse area equal to $\ensuremath{\pi}$ and is equal to 2/32/32/3 in the limiting case when its radiative lifetime is much shorter than the pulse repetition period.
We have theoretically studied the atomic populations, electromagnetically induced transparency (EIT), and dispersion in a three-level Λ-type system. The density matrix equations are set up with regard for the relaxation of populations of the ground states, and the optical Bloch equations are solved analytically in the weak probe field approximation. Decoherence effects in the ground and excited states on the EIT line shape and dispersive signals are studied, and it is found that the EIT line width increases and the peak height decreases, as the decoherence rates increase in the ground and excited states. On the other hand, we have observed that the dispersive signals are steeper and of high contrast for the lower decoherence rates in the ground and excited states. We have also analyzed the variations of atomic populations of the energy levels at the pump Rabi frequency, as well as the decoherence rate in the ground state.