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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Cooperative dynamics of an ensemble of atoms with Λ-scheme of levels driven by two resonant laser fields

I. A. Grigorenko, Boris G. Matisov

Published Jan 1, 1998• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.299585

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arXiv:quant-ph/0103130•Physical Review A•Oct 12, 2001•20 citations
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.
Equations are derived which describe the dynamics of three-level atoms with a Λ level scheme, interacting with two coherent resonance fields under conditions such that cooperative relaxation predominates over incoherent spontaneous emission. A numerical calculation of the temporal dynamics of the values of the atomic populations is performed. It is shown that coherent population trapping in the presence of cooperative decay is possible. The quantities characterizing this phenomenon are calculated—the width of the black line and the transition time to coherent trapping in this scheme.
We derive equations that describe the dynamics of three-level atoms with a cascade system of levels interacting with two resonant coherent fields in conditions where cooperative relaxation dominates over incoherent spontaneous emission. We calculate the temporal dynamics of the values of the atomic populations. The possibility of coherent population trapping in the presence of the cooperative decay is established. Finally, we calculate the averaged population of the intermediate level as a function of detuning for different values of the coupling constant.
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 present report deals with the condition under which an ensemble of atoms goes over into a regime of collective two-photon nutation, and with the behavior of Rabi frequency as function of external light. To simplify this problem, we consider a system of Λ-type atoms that enters into two-photon resonance with an external squeezed electromagnetic field relative to the forbidden transition ∣1> ∣2> , where ∣1> and ∣2> are ground and first exited states [1,2] The situation is examining, when the values of quantum fluctuations of electromagnetic field intensity have the same value as the mean value of electromagnetic field intensity. This is one of main difference between the our paper and [2]. The proposed mathematical model permits to take into account all the two-photon diagrams. These diagrams describe not only resonance two-photon transitions but two-photon scattering processes between ∣1> and ∣2> levels too. Using mathematical method which is proposed in [1,2] it is obtained the master equation for the atom subsystem. Two stationary solutions for the case when Rabi frequency is larger than the inverse value of the collective two-photon decay time and the case when external light is coherent are examined. It is showing that the absorption rate of an phase squeezed field is larger than the absorption rate of an amplitude squeezed light. We also obtained the behavior of inversion between the levels ∣1> and ∣2>, when the collective of atoms enters into two-photon resonance with external field.
We study the features of spatial and temporal evolution of two powerful short different-wavelength laser pulses interacting with optical dense three-level Lambda-type medium under condition of coherent population trapping for the general case of unequal transition oscillator strengths. The pulses are simultaneously sent into an atom. The durations of probe and coupling pulses T1,2T_{1,2}T1,2​ (T2>T1T_2>T_1T2​>T1​) are supposed to be shorter than all relaxation times in the medium. We present analytical and numerical solutions of the self-consistent set of coupled Schr\\"{o}dinger equations and reduced wave equations in adiabatic limit with taking into account the first non-adiabatic correction. The adiabaticity criterion with account of pulse propagation is studied. We find that propagation dynamics depends on the relationship between the transition oscillator strengths. It is shown that at the initial stage of propagation the envelopes of the pulses slightly change along the length of the medium. This distance can be large compared to one-photon resonant absorption length of the medium. Also it is possible a regime of complete reemitting of the probe pulse into the coupling one during propagation. A spatial evolution of the atomic Raman coherence is investigated in detail too.
The spatial and temporal evolution is studied of two powerful short laser pulses having different wavelengths and interacting with a dense three-level \ensuremath{\Lambda}-type optical medium under coherent population trapping. The general case of unequal oscillator strengths of the transitions is considered. The durations of the probe pulse and the coupling pulse T1,2(T2>T1){T}_{1,2} {(T}_{2}>{T}_{1})T1,2​(T2​>T1​) are assumed to be shorter than any of the relevant atomic relaxation times. We propose analytical and numerical solutions of a self-consistent set of coupled Schr\"odinger equations and reduced wave equations in the adiabatic limit taking account of the first nonadiabatic correction. The adiabaticity criterion is also discussed taking account of pulse propagation. The dynamics of propagation is found to be strongly dependent on the ratio of the transition oscillator strengths. It is shown that the envelopes of the pulses slightly change throughout the medium length in the initial stage of propagation. This distance can be large compared to the one-photon resonant absorption length. Eventually, the probe pulse is completely reemitted into the coupling pulse during propagation. An effect of localization of the atomic coherence was observed similar to the one predicted by Fleischhauer and Lukin [Phys. Rev. Lett. 84, 5094 (2000)].