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arXiv:cond-mat/0505059 · Physical Review Letters

Microscopic Measurement of Photon Echo Formation in Groups of Individual Excitonic Transitions

W. Langbein, Brian Patton

Published Jun 30, 2005• 57 citations
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Abstract

The third-order polarization emitted from groups of individual localized excitonic transitions after pulsed optical excitation is measured. We observe the evolution of the nonlinear response from the case of a free polarization decay for a single transition, to that of a photon echo for many transitions. The echo is shown to arise from the mutual rephasing of the emission from individual transitions.

DOI
10.1103/physrevlett.95.017403

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The third-order polarization emitted from groups of individual localized excitonic transitions after pulsed optical excitation is measured. We observe the evolution of the nonlinear response from the case of a free polarization decay for a single transition, to that of a photon echo for many transitions. The echo is shown to arise from the mutual rephasing of the emission from individual transitions.
Optical coherence time and nonlinear optical response of excitons localized to quantum dots in a GaAs/AlGaAs single quantum well are investigated by the three-pulse photon echo technique. At low temperature, the optical coherence time is estimated to be 1.8 ns from the decay curve of the photon echo signal. The decay profile for short time delay shows the strong dependence on the input pulse area of the third pulse. Rabi oscillations are also observed. The oscillations exhibit nonlinear behavior, which is affected by the pre-excited polarization. Such behavior can be qualitatively explained by the local field effect due to the exciton-exciton interaction between the excitons.
The phase relaxation of optically excited electronic states can be studied in fourwave mixing experiments where three excitation pulses at t = 0, t =t21, and t = T, respectively, interact via the third-order polarization of the medium to generate a nonlinear signal whose intensity depends on the dephasing time T2. For inhomogeneously broadened optical transitions the signal will be emitted as a time delayed photon echo pulse at t = T + t21 provided the pulse duration is short compared with T2. The echo amplitude decays as exp(−4t21/T2).1
In this article the third-order response of an excitonically coupled dimer is studied. The three-pulse photon echo signals were calculated by extracting polarization components from the total polarization in the corresponding phase-matched directions. The total nonlinear response was obtained by numeric propagation of the density matrix, with the exciton-vibrational coupling modeled via Redfield relaxation theory. The full two-dimensional three-pulse photon echo signals and the peak shift were analyzed in terms of the density-matrix dynamics of coherence dephasing and population relaxation. The location of the two-exciton state was found to be essential for proper modeling of the three-pulse photon echo. In particular, an oscillation in the three-pulse photon echo peak shift is found if the two-exciton state is displaced. The oscillations can be related to the dynamics of the one-exciton coherences.