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European Journal of Physics

Understanding optical echoes using Schrodinger's equation: I. Echoes excited by two optical pulses

Alan V. Durrant, Joy Manners, Paul M. Clark

Published Oct 1, 1989• 6 citations
Publisher

Abstract

The mechanism of optical echo (photon echo) formation in solid and gas media is described. The treatment is based on solutions of Schrodinger's equation for the time evolution of atomic amplitudes during an optical excitation pulse sequence, and should be accessible to non-specialists and to students studying undergraduate quantum mechanics. Atomic amplitude evolution diagrams are developed to facilitate the analysis of the echo mechanism and the derivation of the echo time and propagation direction.

DOI
10.1088/0143-0807/10/4/009

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 14, 2000•0 citations
The mechanism of optical echo (photon echo) formation in solid and gas media is described. The treatment is based on solutions of Schrodinger's equation for the time evolution of atomic amplitudes during an optical excitation pulse sequence, and should be accessible to non-specialists and to students studying undergraduate quantum mechanics. Atomic amplitude evolution diagrams are developed to facilitate the analysis of the echo mechanism and the derivation of the echo time and propagation direction.
The authors derive analytical expressions for secondary echoes formed under the two-pulse excitation of the optically dense media developing McCall-Hahn area theorem for echo effects. They find that a series of self-reviving echo signals with a total area of 2$\ensuremath{\pi}$ or 0$\ensuremath{\pi}$ is excited and propagates deep in the media demonstrating strong non-linear nature of light-matter interaction at small changes of second pulse area. The pulse area approach paves the way for precise coherent spectroscopy, the study of different photon echoes and quantum control of light pulses in the optically dense media.
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.
The possibility of a class of optical echo-producing mechanisms is suggested that does not invoke the phase-reversal action of the second pulse. The mechanisms act selectively on the radiating atomic dipole moments, or on their radiation fields, with a periodic dependence on Δτ, where Δ is the angular frequency of the radiator relative to the central angular frequency of the distribution and τ the interpulse time. In the new formulation, the customary expression for the field radiated by an atomic dipole following a two-pulse excitation sequence is multiplied by a factor periodic in Δτ. It is shown that a sequence of echo pulses is predicted when the average over the radiators is calculated. One such mechanism is proposed: the selective absorption or amplification of the dephased free-induction decay field as they propagate through the sample.