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Journal of Contemporary Physics (Armenian Academy of Sciences)

Influence of self-phase modulation on coherent effects in five-level system

E. A. Gazazyan, G. G. Grigoryan

Published Jul 1, 2016• 4 citations
Publisher

Abstract

The possibility of formation of a coherent dark state in the five-level system in the entire volume of the medium in an adiabatic pulse propagation is investigated. It is shown that the dark state formation is independent on the value of the first two-photon detuning from the resonance, which may be changed during the propagation in the medium. In the case of the M-type system with the equal strengths of oscillators at the extreme transitions it is shown that the self-phase modulation does not influence the coherent effects while in the ladder-type system it may lead to the destruction of the dark state. The estimation of the length of the medium in which the propagation effects are negligible is obtained.

DOI
10.3103/s1068337216030063

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The possibility of formation of a coherent dark state in the five-level system in the entire volume of the medium in an adiabatic pulse propagation is investigated. It is shown that the dark state formation is independent on the value of the first two-photon detuning from the resonance, which may be changed during the propagation in the medium. In the case of the M-type system with the equal strengths of oscillators at the extreme transitions it is shown that the self-phase modulation does not influence the coherent effects while in the ladder-type system it may lead to the destruction of the dark state. The estimation of the length of the medium in which the propagation effects are negligible is obtained.
We consider the propagation of two laser pulses in a medium of three-level $\ensuremath{\Lambda}$ atoms with nonvanishing two-photon detuning and different oscillator strengths of the transitions. We show that the two-photon detuning and the derivative of the mixing angle are described by one and the same equation. We analyze the solution of this equation and its physical consequences. In particular, we obtain the conditions and the distance where the nonadiabaticity and the two-photon detuning may be reduced. We derive a simple expression for the maximum length to which excitation in the medium may reach.
Propagation of four laser pulses in the five-level ladder system in the case of arbitrary intensities and the different strengths of oscillators is investigated, when one of the eigenstates of the interaction Hamiltonian is formed in the whole volume of the medium. Taking into account the first non-adiabatic correction, the equations of propagation are obtained. An analytical solution of these equations is obtained. The conditions for an effective excitation of the fifth level in the whole volume of medium and the limitations on the interaction parameters are obtained as well.
We consider adiabatic interaction of five-level atomic systems and their media with four short laser pulses under the condition of all two-photon detunings being zero. We derive analytical expressions for eigenvalues of the system's Hamiltonian and determine conditions of adiabaticity for both the atom and the medium. We analyze, in detail, the system's behavior when the eigenvalue with nonvanishing energy is realized. As distinct from the usual dark state of a five-level system (corresponding to zero eigenvalue), which is a superposition of three states, in our case the superposition of four states does work. We demonstrate that this seemingly unfavorable case nevertheless completely imitates a three-level system not only for a single atom but also in the medium, since the propagation equations are also split into those for three- and two-level media separately. We show that, under certain conditions, all the coherent effects observed in three-level media, such as population transfer, light slowing, light storage, and so on, may efficiently be realized in five-level media. This has an important advantage that the light storage can be performed twice in the same medium; i.e., the second pulse can be stored without retrieving the first one, and then the two pulses can be retrieved in any desired sequence.
Coherent propagation of a circularly polarized pulse which is two-photon quasi-resonant with a medium of multi-level atoms is considered in the adiabatic following limit. The relevant pair of non-linear coupled partial differential equations are solved exactly for arbitrary pulse shapes. The development of the envelope and the phase of the pulse as it propagates through the medium is described analytically. Perturbation theoretical results are shown to apply only for small intensity or small distance of propagation or both. Qualitatively different results apply for higher intensities and longer distances of propagation. These include strong self-phase-modulation effects as well as reshaping of the pulse envelope.
An analytic solution is obtained for the self-consistent equations describing propagation of an ultrashort pulse in a resonant two-level medium. The first approximation in respect of the dispersion is used to allow for phase modulation and for the dependence of the group velocity on the intensity and on the running value of the frequency. The conditions for the formation of a shock wave are established. It is shown that asymmetric broadening of the spectrum of a pulse results in coherent absorption, as a result of which the propagation of this pulse in such a medium leaves behind a polarization at the atomic transition frequency responsible for the radiation represented by the pulse.
The results of theoretical research of the propagation effect of an ultrashort optical pulse under the conditions of coherent interaction with two resonant transitions are presented. One of the transitions is tuned to exact resonance with the pulse carrier frequency; the other is distanced by much more than the pulse spectral width, thus the adiabatic following approximation may be applied to it. The interaction between the pulse and the far-from-resonance transition is described by the wave equation with the nonlinear index of refraction in the form of the Lorentz function of the field amplitude. This wave equation is solved together with the Bloch equations for the exact resonant transition. The solution in the form of the stationary phase-modulated pulse is obtained, and (pi) -pulse of self-induced transparency is the special case of this solution. The obtained solution has the area under the pulse envelope less than (pi) , and with increasing the absorption coefficient of the far-from-resonance transition the pulse area decreases. The effect can be used for reducing the transparency threshold of the resonant medium below (pi) .