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Modern Physics Letters B

Coherent population effect in a Λ-configuration atom driven by two trains of ultrashort pulses

Kang Jin, Yingjie Du

Published Apr 30, 2015• 0 citations
Publisher

Abstract

In this paper, we investigate the evolutional dynamics of a Λ-type atomic system of which two branches of transitions are driven by two trains of ultrashort pulse respectively. The accumulating of atomic populations and coherences due to excitations of successive pulses are demonstrated by the numerical simulations. The realization of the coherent population trapping (CPT) effect is verified. When the spontaneous generated coherence (SGC) is considered, the system will evolve to the dark state even when the initial state is not the dark state if the degree of the SGC is not maximal and the degree of the SGC will influence the time needed to reach the atomic steady state. With the maximal degree of SGC, whether the system will evolve into the dark state depends on the initial state. This fact means that the maximal SGC spoils the dark state geometry, which a Λ-type atom driven by light field satisfies. Additionally, we found that the involvement of the phase of the driving field can counteract the destruction stem from the maximal degree of the SGC on the dark state geometry, i.e. the system can be trapped in the dark state even when the initial state is not the dark state. Meanwhile, it is found that the phase can adjust the time needed by the system to reach the steady state in a quite wide range.

DOI
10.1142/s0217984915500487

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In this paper, we investigate the evolutional dynamics of a Λ-type atomic system of which two branches of transitions are driven by two trains of ultrashort pulse respectively. The accumulating of atomic populations and coherences due to excitations of successive pulses are demonstrated by the numerical simulations. The realization of the coherent population trapping (CPT) effect is verified. When the spontaneous generated coherence (SGC) is considered, the system will evolve to the dark state even when the initial state is not the dark state if the degree of the SGC is not maximal and the degree of the SGC will influence the time needed to reach the atomic steady state. With the maximal degree of SGC, whether the system will evolve into the dark state depends on the initial state. This fact means that the maximal SGC spoils the dark state geometry, which a Λ-type atom driven by light field satisfies. Additionally, we found that the involvement of the phase of the driving field can counteract the destruction stem from the maximal degree of the SGC on the dark state geometry, i.e. the system can be trapped in the dark state even when the initial state is not the dark state. Meanwhile, it is found that the phase can adjust the time needed by the system to reach the steady state in a quite wide range.
The effect of a dark state on the entanglement properties of the two-mode field from a laser-driven Λ-type three-level atomic system is investigated by taking into account the spontaneously generated coherence (SGC). When the dark state is present, it is found that the entanglement between the two cavity modes can be significantly enhanced compared to the case without the dark state. When the value of SGC is maximal, the dark state population depending on the initial values of the system can affect the entanglement dramatically. Moreover, the effects of a squeezed parameter and Rabi frequency on entanglement evolution are also presented in the presence of a dark state.
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 derive the equations describing the dynamics of an ensemble of atoms with (Lambda) - scheme of levels driven by two coherent resonant fields in a case when cooperative relaxation prevails over usual incoherent spontaneous emission. We investigate numerically temporal dynamics of mean values of the collective atomic operators. When the two-photon resonance condition is fulfilled then all atoms tend to be trapped in a coherent dark state, so coherent population trapping arises in a case of cooperative decay. Most important values characterizing this phenomenon such as the width of the black line and the time of initial transient stage of evolution are evaluated.
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We consider the coherent population trapping effect with a train of ultrashort pulses in a $\ensuremath{\Lambda}$-type system with two bound states and a continuum replacing the upper state. Population transfer to the continuum can be totally suppressed provided that the splitting between the bound states is a multiple of the pulse repetition rate. Compared to the traditional case with only two laser fields coupling the bound states to the continuum, CPT with a pulse train allows one to avoid incoherent population losses due to interaction of the fields with ``wrong'' transitions, which results in only partial suppression of ionization. A method of suppression of excited-state absorption of pumping radiation in laser crystals, with pumping in the form of the pulse train, is proposed. As a particular example pumping dynamics of a Ti3+:YAlO3{\mathrm{Ti}}^{3+}:{\mathrm{YAlO}}_{3}Ti3+:YAlO3​ crystal using this technique is numerically analyzed.
Abstract Owing to interference induced by spontaneous emission, the density-matrix equations in a three-level Λ-type system have an additional coherence term, which plays a critical role in modulating the inversionless gain and electromagnetically induced transparency effect. In addition, it is shown that spontaneously generated coherence (SGC) has an effect on the entanglement between an atom and a photon of the coupling laser field by calculating the degree of entanglement (DEM) of the atomic system. In this paper, we investigate the influence of the SGC effect on atom-photon entanglement in a Λ-type system, which generally remains a high entangled state. When an incoherent pump source is introduced, we find that the SGC effect could exert considerable influence on the atom reduced entropy under certain conditions for both transient and steady states. More interestingly, such an incoherent pump field could actively affect the short-time dynamic behaviors of the transient quantum entangled state at a certain range of pump rate as a typical coherent case.