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Physical Review B

Back action of nonequilibrium phonons on the optically induced dynamics in semiconductor quantum dots

A. Krügel, V. M. Axt, T. Kühn

Published Jan 3, 2006• 55 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.73.035302

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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.
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.
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.
Abstract We have simulated coherent control signals from quantum dots for carrier phonon interactions covering the low as well as the strong coupling limit. Calculations using the correlation expansion for phonon assisted density matrices are compared with numerically exact results obtained from a time dependent path‐integral approach. Even at elevated coupling strengths both calculations agree well for not too high temperatures. For pulse lengths and delay times shorter than the phonon induced memory time the correlation expansion gives good results in almost all cases. For strong coupling and/or high temperatures drastic discrepancies emerge. Interestingly, the correlation expansion works better at high pulse areas, which is related to a dynamic decoupling of electron and phonon dynamics in strongly confined systems.
This work is focused on the optical dynamics of mesoscopic semiconductor heterostructures, using as prototypes zero-dimensional quantum dots and quantum cascade lasers which consist of quasitwo-dimensional quantum wells. Within a density matrix theory, a microscopic many-particle theory is applied to study scattering effects in these structures: the coupling to external as well as local fields, electron-phonon coupling, coupling to impurities, and Coulomb coupling. For both systems, the investigated effects are compared to experimentally observed results obtained during the past years. In quantum dots, the three-dimensional spatial confinement leads to the necessity to consider a quantum kinetic description of the dynamics, resulting in non-Markovian electron-phonon effects. This can be seen in the spectral phonon sidebands due to interaction with acoustic phonons as well as a damping of nonlinear Rabi oscillations which shows a nonmonotonous intensity and pulse duration dependence. An analysis of the inclusion of the self-interaction of the quantum dot shows that no dynamical local field terms appear for the simple two-level model. Considering local fields which have their origin in many quantum dots, consequences for a two-level quantum dot such as a zero-phonon line broadening and an increasing signal in photon echo experiments are found. For the use of quantum dots in an optical spin control scheme, it is found that the dephasing due to the electron-phonon interaction can be dominant in certain regimes. Furthermore, soliton and breather solutions are studied analytically in nonlinear quantum dot ensembles. Generalizing to quasi-two-dimensional structures, the intersubband dynamics of quantum cascade laser structures is investigated. A dynamical theory is considered in which the temporal evolution of the subband populations and the current density as well as the influence of scattering effects is studied. In the nonlinear regime, the scattering dependence and the importance of coherence for Rabi oscillations is investigated. The optically induced charge dynamics is discussed with respect to coherent effects. Calculations of the electronic density and pump-probe signals within a microscopic theory of dephasing show coherent transport effects such as gain oscillations, in agreement with recent experimental results.
This paper studies the carrier-phonon dynamics in the optical control of the spin states in a single doped semiconductor quantum dot by means of a perturbation theory describing the open system evolution under arbitrary driving and a correlation expansion technique. This paper considers the phonon-induced decoherence accompanying a single-qubit gate: an arbitrary rotation between two selected electron spin states performed via stimulated adiabatic Raman transitions and virtual excitation of a trion state. The error of the quantum gate as well as the population and coherence dynamics is calculated depending on the driving duration and detuning and study the possible reduction of the phonon decoherence.