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Physical Review Letters

Phonon-Assisted Damping of Rabi Oscillations in Semiconductor Quantum Dots

Jens Förstner, C. Weber, J. Danckwerts, A. Knorr

Published Sep 16, 2003• 283 citations
Publisher

Abstract

Electron-phonon interaction is a major source of optical dephasing in semiconductor quantum dots. Within a density matrix theory the electron-phonon interaction is considered up to the second order of a correlation expansion, allowing the calculation of the quantum kinetic dephasing dynamics of optically induced nonlinearities in GaAs quantum dots for arbitrary pulse strengths and shapes. We find Rabi oscillations renormalized and a damping that depends on the input pulse strength, a behavior not known from exponential dephasing mechanisms.

DOI
10.1103/physrevlett.91.127401

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Electron-phonon interaction is a major source of optical dephasing in semiconductor quantum dots. Within a density matrix theory the electron-phonon interaction is considered up to the second order of a correlation expansion, allowing the calculation of the quantum kinetic dephasing dynamics of optically induced nonlinearities in GaAs quantum dots for arbitrary pulse strengths and shapes. We find Rabi oscillations renormalized and a damping that depends on the input pulse strength, a behavior not known from exponential dephasing mechanisms.
A model of semiconductor quantum dots coupled to phonons and laser light, which is relevant in the limit of strong electronic confinement, is investigated. For an arbitrary sequence of excitations by ultrafast pulses, analytical solutions are obtained for all pertinent density-matrix elements. The results are nonperturbative with respect to the coupling to both phonons and laser light. The derivation depends neither on a particular choice of electronic wave functions nor on a particular wave-vector dependence of the phonon interaction or phonon dispersion. All components of the density matrix exhibit oscillatory dependences on the pulse areas of the exciting pulses analogously to the Rabi oscillations known from simple two-level systems. Three typical applications of the general results are worked out: (a) the influence of phonons on four-wave-mixing spectra, (b) the coherent control of electronic dot occupations in the presence of phonons, and (c) the dynamics of phonon correlations including the formation of a stable polaron spatially localized in the dot and the emission of a pulsed phonon wave packet that leaves the dot.
A systematic investigation is performed on the damping of Rabi oscillations induced by an external electromagnetic field interacting with a two-level semiconductor system. We have considered a coherently driven two-level system coupled to a dephasing reservoir and shown that, to explain the dependence of the dephasing rate on the driving intensity, it is essential to consider the non-Markovian character of the reservoir. Moreover, we have demonstrated that intensity-dependent damping may be induced by various dephasing mechanisms due to stationary as well as non-stationary effects caused by coupling with the environment. Finally, present results are able to explain a variety of experimental measurements available in the literature.
The dynamics in a GaAs-type quantum dot induced by excitation with Gaussian laser pulses of arbitrary duration are calculated in the density matrix formalism using the correlation expansion. In particular the back-action of nonequilibrium phonons, i.e., the coherent phonon amplitude and the nonequilibrium phonon occupation, on the electronic two-level system are studied. We find that especially for long pulses and low temperatures nonequilibrium phonons play an important role and cannot be neglected.