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Optics and Spectroscopy

Photon echo excited in multilevel quantum media by ultimately short pulses

A. Yu. Parkhomenko, С. В. Сазонов

Published May 1, 2001• 11 citations
Publisher

Abstract

The photon echo excitated in a multilevel quantum medium by two or more ultimately short pulses with duration down to one period of optical oscillations is studied theoretically. It is shown that the number of echo responses formed in the system depends on the number of quantum levels covered by the spectrum of the exciting pulses and strongly increases with this number. General equations for the spatio-temporal characteristics of the multipulse echo signals are obtained.

DOI
10.1134/1.1374659

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Quantum Electronics•Oct 31, 1997•1 citation
The photon echo excitated in a multilevel quantum medium by two or more ultimately short pulses with duration down to one period of optical oscillations is studied theoretically. It is shown that the number of echo responses formed in the system depends on the number of quantum levels covered by the spectrum of the exciting pulses and strongly increases with this number. General equations for the spatio-temporal characteristics of the multipulse echo signals are obtained.
A photon echo in a multilevel quantum medium excited by two extremely short pulses with durations of less than one period of oscillation of the light is investigated theoretically. It is shown thatQ echo signals (Q is the number of allowed transitions) can form at each frequency of the allowed transitions, and the number of echo responses for all the allowed transitions equalsQ 2. Of these,Q(Q−1) signals are separated in both time and space. The otherQ echo signals of all the allowed frequencies all arise at the time 2τ 21 (τ 21 is the time interval between application of the first and second pulses to the medium) and are collinear with one another.
Echo responses of a three-level medium formed by the λ-scheme of quantum transitions under exposure to optical pulses consisting of an arbitrary number of oscillations have been studied theoretically. The cases of pulses consisting of few optical oscillations (for which the concept of an envelope cannot be used) and combinations of such pulses and quasi-monochromatic resonance signals have been considered. The approach used can be reduced to the renormalization of dipole moments of allowed quantum transitions through their multiplication by coefficients depending on the shape and duration of pump pulses and having absolute values in the range from zero (for nonresonance pulses) to unity (for resonance quasi-monochromatic pulses and broadband pulses consisting of few oscillations, whose spectrum covers the quantum transitions). A general equation has been proposed for the pulse area. In the limit of a large number of oscillations, it transforms into the well-known definition of the area of a quasi-monochromatic signal. The characteristics of primary and longlived photon echoes have been analyzed in detail. It has been shown that, when a medium is exposed to only pulses consisting of a few oscillations, three echo responses of both types can be principally generated at each frequency of the λ-scheme. Introduction of quasi-monochromatic pulses in pump pulse series decreases the number of echoes, and their qualitative character has a non-commutative property with respect to pulse permutation in a series. The extension of the proposed approach to more complex schemes of quantum transitions with the large number of quantum levels faces no principal difficulties.
On the basis of quantum-mechanical approach, a theoretical study of the primary Raman photon echo was carried out under conditions of excitation of a medium by pulses with a duration on the order of one period of electromagnetic oscillations (ultimately short pulses) and by strong quasi-monochromatic nonresonant pumping. It is shown that the intensities of the pumps determine to a considerable extent the time of formation of the echo signal, its duration, the direction of emission, and the power and that the use of ultimately short pulses promotes the substantial simplification of the schemes of prospective experiments. The possibilities of echo generation at the Stokes and anti-Stokes frequencies in the regimes of two-, one-, and zero-pulse excitations are revealed. In the last case, the Raman-active transitions are excited by two pumps with different intensities.
The effect of two-pulse photon echoes at the complicated action on a two-level medium with large inhomogeneous broadening of supremely short and quasiresonant pulses is investigated. Two versions of the action sequence of both pulses are considered. It is shown that the temporal properties of the echo signal are depended largely on the action order of indicated pulses. The effect of suppression of the optical echoes in the both cases at the action on a medium of the supremely short zeroth 'area' pulse is predicted. The qualitative procedure of definition of the complicated echoes spatial properties has been proposed and applied. It is shown that in indicated cases the diagrams of the echo signal intensity direction are not so peaked as in the case of common light echo.
Two-frequency correlation between the profiles of signals of the primary and long-lived (stimulated) photon echos in a three-level medium excited by combined sequences of resonance quasimonochromatic (encoding) signals and femtosecond pulses consisting of a few optical oscillations (down to one) is predicted. It is shown that the profiles of echo responses of both frequencies correlate with each other and with the profiles of encoding pulses, copy them, and induce mirror rotations, as well as scaling transformations in time in dependence on the methods of forming exciting sequences.
An investigation is made of a two-pulse photon echo in a two-level medium with strong inhomogeneous broadening, which is subjected simultaneously to extremely short and quasiresonant pulses. Two variants of the sequence of application of the two pulses are considered and it is shown that the kinetics of an echo signal depends largely on the sequence in which the pulses are applied. Suppression of the photon echo is predicted for both variants when a zero-are extremely short pulse is applied to a medium. A qualitative method for determination of the spatial characteristics of such a combined echo is proposed and used. It is shown that, in the investigated cases, the angular distributions of the echo-signal intensity in an extended medium are not as peaked as in the case of a conventional photon echo.