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Physical Review B

Relaxation and dephasing quantum kinetics for a quantum dot in an optically excited quantum well

Q. T. Vu, H. Haug, S. W. Koch

Published May 9, 2006• 17 citations
Publisher

Abstract

We investigate the population and dephasing kinetics of a quantum dot coupled by Auger and phonon scattering processes with a femtosecond-pulse-excited electron-hole plasma in a quantum well or wetting layer. For the two-dimensional (2D) plasma we treat the quantum kinetics of the Coulomb scattering processes with a two-time-dependent screened Coulomb interaction potential. Additionally the scattering with LO phonons is included. For ultrashort pulse excitations close to the band edge of the plasma we obtain a slow decay of the polarization of the quantum dot with superimposed oscillations whose frequency is given by the energetic distance of the quantum dot levels and the 2D band edge. For two-pulse excitations we calculate the absorption spectrum of the probe pulse for various delay times and pump pulse intensities. One sees, e.g., the buildup of gain for a strong pump pulse in the spectral regions below the dot absorption line and below the band edge of the plasma. In the calculated four-wave-mixing signal we find in addition to long dephasing times, which decrease with increasing 2D plasma densities, also oscillations due to the beating of the quantum dot and the band edge transitions.

DOI
10.1103/physrevb.73.205317

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IEEE Journal of Selected Topics in Quantum Electronics•Sep 1, 2002•102 citations
We investigate the population and dephasing kinetics of a quantum dot coupled by Auger and phonon scattering processes with a femtosecond-pulse-excited electron-hole plasma in a quantum well or wetting layer. For the two-dimensional (2D) plasma we treat the quantum kinetics of the Coulomb scattering processes with a two-time-dependent screened Coulomb interaction potential. Additionally the scattering with LO phonons is included. For ultrashort pulse excitations close to the band edge of the plasma we obtain a slow decay of the polarization of the quantum dot with superimposed oscillations whose frequency is given by the energetic distance of the quantum dot levels and the 2D band edge. For two-pulse excitations we calculate the absorption spectrum of the probe pulse for various delay times and pump pulse intensities. One sees, e.g., the buildup of gain for a strong pump pulse in the spectral regions below the dot absorption line and below the band edge of the plasma. In the calculated four-wave-mixing signal we find in addition to long dephasing times, which decrease with increasing 2D plasma densities, also oscillations due to the beating of the quantum dot and the band edge transitions.
We investigate resonant time-resolved four-wave mixing on GaAs quantum wells at T=300KT=300\mathrm{K}T=300K and at elevated carrier densities using excitation with 11 fs optical pulses. The experiments are compared with non-Markovian quantum-kinetic calculations including carrier-carrier and carrier-LO-phonon scattering. A self-consistently determined two-time-dependent screened random-phase approximation Coulomb potential is used for the carrier-carrier scattering. In experiment and theory we find an unusual real-time response, which is far from an ideal photon echo. Surprisingly, we also find that the dependence of the decay time \ensuremath{\tau} of the four-wave-mixing signal versus the optically excited nonequilibrium electron-hole pair density neh{n}_{\mathrm{eh}}neh​ is quantitatively similar to the corresponding behavior of bulk GaAs. Thus both data sets can be fitted by the same form ${\ensuremath{\tau}}^{\ensuremath{-}1}={\ensuremath{\tau}}_{0}^{\ensuremath{-}1}{+cn}_{\mathrm{eh}}^{1/3}.$ This is not consistent with previous experimental work in a more limited range of carrier densities, which determined different behavior for quasi-two-dimensional (2D) and 3D, i.e., exponents of 0.3 and $0.55\ifmmode\pm\else\textpm\fi{}0.04,$ respectively.
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.
Femtosecond-pulse propagation in resonantly excited semiconductors is investigated by numerically solving the semiconductor Maxwell-Bloch equations for plane waves. For excitation at the exciton resonance, it is shown that the pulse absorption exhibits a strongly nonlinear dependence on the input pulse area. Very long propagation distances for strong pulses are observed, but even when all dephasing processes have been neglected, no lossless propagation (self-induced transparency) was found. The influence of the electron-hole many-body effects, nonequilibrium carrier relaxation, and optical dephasing on the pulse-propagation dynamics is studied. The exchange interaction in the electron-hole plasma is shown to support large propagation distances. For excitation of the continuum states, the dependence of the absorption on the intensity of the input pulse is reduced due to the rapid carrier relaxation into quasiequilibrium distributions.
Using laser pulses of duration comparable to semiconductor relaxation and dephasing times, the coherent phenomena common to two-level systems have been demonstrated in II-VI and III-V semiconductors. These light-matter interactions are characterized by electrons and holes in their initially excited states and/or a macroscopic polarization that persists after the excitation. A nonthermal carrier distribution was observed in bulk CdSe, demonstrating the extremely fast energy relaxation possible when carrier-LO-phonon scattering is included. Quantum-confined CdSe microcrystallites were then employed to limit the available decay avenues. The one and two-pair transitions were characterized, and using spectral hole-burning, energy relaxation was shown to be substantially slower than in bulk. Dipole dephasing remained very rapid. Persistent macroscopic polarization was demonstrated in semiconductors through pump and probe experiments conducted on time scales faster than the inverse linewidth of the exciton. In the first set of experiments, it was found that the exciton optical Stark shift deviates from that predicted by a steady-state theory. The shift is smaller than expected and lasts longer than the pump pulse. Both effects are explained by free evolution of the exciton's polarization. Transient exciton bleaching is observed and shown to be a result of adiabatic following. In a second study of coherent polarization, spectral oscillations at negative delay times were studied. Oscillations were measured in a wide variety of semiconductors, temporally preceding several different pump-probe phenomena. By comparison with a semiclassical theory, it was shown that spectral oscillations in the spectral region of the exciton are evidence of persistent exciton polarization. Oscillations in the band are due to four wave mixing of the pump and probe beams.
The polarization dephasing time has been measured across the gain region, at the transparency point, and into the absorption region of an optically excited GaAs multiple-quantum-well sample using spectral hole burning and degenerate four-wave mixing techniques. We observe strongly energy-dependent dephasing rates with a minimum at the crossover from gain to absorption. Numerical results for the microscopically calculated carrier-carrier scattering rates for a two-component electron-hole plasma in quantum wells show fair agreement with the experimental findings.
We present an extensive experimental study of the exciton relaxation and dephasing in InGaAs quantum dots (QDs) in the temperature range from 10 K to 295 K. The QDs are embedded in the active region of an electrically pumped semiconductor optical amplifier. Ultrafast four-wave mixing and differential transmission spectroscopy on the dot ground-state transition are performed with a sensitive heterodyne detection technique. The importance of the population relaxation dynamics to the dephasing is determined as a function of injection current and temperature. Above 150 K dephasing processes much faster than the population relaxation are present, due to both carrier-phonon scattering and Coulomb interaction with the injected carriers. Only at low temperatures (<30 K) does population relaxation of multiexcitons in the gain regime fully determine the dephasing.