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Optics and Spectroscopy

Self-induced three-level echo

Ashat M. Basharov

Published Sep 1, 2006• 7 citations
Publisher

Abstract

A new type of three-level photon echo has been predicted and analytically described. In contrast to the conventional three-level echo, whose formation involves three resonant ultrashort excitation pulses spaced in time, two of which are resonant to different optically allowed and adjacent transitions with different frequencies, the echo predicted arises under the conditions of formation of the conventional two-pulse echo and requires only two pump pulses of the same frequency. A theory is developed for the conditions of experiments on generation of a superradiance pulse at the 3 P 0-3 H 6 transition in impurity praseodymium ions in the LaF3 matrix upon ultrashort coherent excitation of the adjacent optically allowed 3 H 4-3 P 0 transition in praseodymium. It is shown that the superradiance pulse after its deexcitation does not polarize the medium at the 3 P 0-3 H 6 generation transition and completely eliminates polarization at the 3 H 4-3 P 0 excitation transition. However, simultaneously, the superradiance pulse transfers the optical coherence from the excitation transition to the optically forbidden 3 H 6-3 H 4 transition. Thus, the phase memory about the effect of the excitation superradiance pulse is retained in the medium within a time interval that is shorter than the irreversible relaxation time of the optically forbidden transition.

DOI
10.1134/s0030400x06090153

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A new type of three-level photon echo has been predicted and analytically described. In contrast to the conventional three-level echo, whose formation involves three resonant ultrashort excitation pulses spaced in time, two of which are resonant to different optically allowed and adjacent transitions with different frequencies, the echo predicted arises under the conditions of formation of the conventional two-pulse echo and requires only two pump pulses of the same frequency. A theory is developed for the conditions of experiments on generation of a superradiance pulse at the 3 P 0-3 H 6 transition in impurity praseodymium ions in the LaF3 matrix upon ultrashort coherent excitation of the adjacent optically allowed 3 H 4-3 P 0 transition in praseodymium. It is shown that the superradiance pulse after its deexcitation does not polarize the medium at the 3 P 0-3 H 6 generation transition and completely eliminates polarization at the 3 H 4-3 P 0 excitation transition. However, simultaneously, the superradiance pulse transfers the optical coherence from the excitation transition to the optically forbidden 3 H 6-3 H 4 transition. Thus, the phase memory about the effect of the excitation superradiance pulse is retained in the medium within a time interval that is shorter than the irreversible relaxation time of the optically forbidden transition.
An analytical study of the photon echoes associated with the three-level system interacting resonantly with optical pulses possessing two different frequencies is performed. It is predicted that photon echoes arise at anomalous times corresponding to the correlation between the inhomogeneous broadenings for the different spectral lines as well as at the normal time expected in a simple two-level system. This new effect is caused by the coupling of the two resonant transitions through the common energy level. Furthermore, if the particle does not have inversion symmetry, the echoes with the sum or difference frequency of the exciting optical pulses can be observed in such a system. The quantitative analysis is also given for intensities, direction of propagation and polarizations of the anomalous echoes which depend upon the exciting pulses with different frequency.
Regularities of the optical coherence transformation in three-level systems, resulting from instability development and superradiance, are considered. It is shown that the superradiance eliminates optical coherence on the adjacent optically allowed transitions and induces optical coherence on the optically forbidden transition. This, in turn, makes it possible to observe new effects of photon-echo type. In such a way the known cases of supperradiant emission from the LaF3:Pr3+ medium admit the described phase memory effect.
A theory of photon echoes using double-resonance optical pulses (PEDROP) is presented. Two double-resonance pulses, separated by a time interval T, are used to cause transitions among three states of an atom. Each double-resonance pulse consists of two simultaneously applied laser pulses that drive coupled transitions in the atom. It is shown that for time t > T, six photon echoes are produced (three on each of the coupled transitions) at five distinct times. Moreover, a nonradiating macroscopic coherence is also produced between states of the same parity. With the use of an interrogation pulse to monitor this coherence, three additional photon echoes can be produced on either of the coupled transitions. A Doppler phase diagram is constructed that enables one easily to predict the times and conditions of echo formation. PEDROP combines features of both two-photon and trilevel echoes but offers advantages over these methods for studying relaxation phenomena.
In the limit of small exciting light-pulse areas the amplitude and polarization of the tri-level photon echo in gases formed by the exciting pulses with arbitrary shapes are obtained. It is shown that the dependence of the tri-level photon echo signal on the mutual orientation of the exciting pulse polarization vectors may be used to determine the optical coherence-matrix relaxation characteristics for an optically forbidden transition. The conditions under which a tri-level photon echo pulse repeats the shape of each of the exciting pulses are defined. It is proved that the tri-level photon-echo polarization properties do not depend on the shapes of the exciting pulses, either for small light-pulse areas or for the tri-level echo formation on narrow spectral lines.