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Journal of the Optical Society of America B

Coherence induced by a train of ultrashort pulses in a Λ-type system

Marco Polo Moreno de Souza, S. S. Vianna

Published Apr 14, 2011• 16 citations
Publisher

Abstract

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.

DOI
10.1364/josab.28.001124

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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.
Here, I discuss the interaction of two matched ultrashort pulses with a \ensuremath{\Lambda}-like system in which the upper intermediate state is replaced by a manifold of discrete states. Many of these states are simultaneously accessed by the broad bandwidth of the two excitation pulses. The equations of motion for the probability amplitudes of the levels involved in the excitation process are solved analytically in the quasi-impulsive regime. In this regime, the excitation pulses are made shorter than the characteristic time of the excited manifold; population is then transferred to the manifold without Rabi cycling. Under the appropriate conditions, this ``multi-\ensuremath{\Lambda}'' system can exhibit coherence effects such as coherent population trapping and electromagnetically induced transparency of one of the excitation pulses.
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.
Near-degenerate lower levels in a $\ensuremath{\Lambda}$ system have an additional coherence term due to interaction with the vacuum of the radiation field. We report the effects of this spontaneously generated coherence on the formation of a trapped state in the presence of two coherent fields of arbitrary intensity. We show that such coherence preserves both electromagnetically induced transparency and coherent population trapping (CPT) phenomena. However, it changes the time scales associated with the formation of the CPT state, and brings about quantitative changes in the line profiles. We present a clear analytical explanation for our numerical results. We also report the dependence of line shapes on the relative phase between the two applied fields.