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physica status solidi (b)

Analytical results for nonlinear optical signals from quantum dots coupled to phonons

V. M. Axt, B. Krummheuer, Alexei Vagov, T. Kühn

Published Jul 21, 2003• 4 citations
Publisher

Abstract

Abstract The impact of pure dephasing processes on the optically induced nonlinear dynamics of quantum dots is analyzed. Concentrating on small dots pure dephasing can be studied analytically in the limit of ultrafast excitation. General conclusions from the analysis of the closed form formulas include the prediction that four‐wave‐mixing (FWM) spectra of single dots change from asymmetric to symmetric lineshapes with increasing pulse delay. Furthermore, in contrast to phenomenological dephasing models the delay dependence of the time integrated FWM amplitude |PFWM| generated by a strongly inhomogeneously broadened ensemble deviates from the real time dependence of |Plin|2, where Plin is the linear polarization emitted by a single dot. Numerical results are presented for FWM signals from dots coupled to bulk acoustic phonons. Surprisingly, the initial decay time of the signal depends non‐monotonously on the temperature. In addition, it is shown that for certain material parameters the coupling to the smooth continuum of acoustic phonons may result in pronounced oscillations.

DOI
10.1002/pssb.200303175

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Abstract Four wave mixing signals from single dots and dot ensembles involving excitonic and biexcitonic transitions are discussed. The results have been obtained analytically from a four level dot model coupled to longitudinal acoustic phonons. Time integrated four wave mixing amplitudes for quantum dot ensembles exhibit polarization dependent quantum beats that have already been found in experimental data. In four wave mixing signals of single quantum dots we find that the ground state to exciton transition has two contributions. One is identical to the known solution of the two level quantum dot model and leads to symmetric spectra for longer delay times, while the other comprises phase information from the biexciton and results in asymmetric spectra. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We report on four-wave-mixing experiments in self-assembled InAs/GaAs quantum dots and compare with a theory that accounts for the pure-dephasing induced by acoustic phonons. The measurements demonstrate an unusual non-monotonous temperature dependence of the initial decoherence time in full agreement with previous theoretical predictions made on the basis of a model that concentrates on the lowest electronic states. For samples exhibiting strong electronic confinement this model even yields a good quantitative agreement with the experiments while for less confined samples there are some systematic deviations although many qualitative features are still well reproduced by the model. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
The effect of phonons on a nonlinear optical response of a quantum dot-cavity system in quantum strong coupling regime can be accounted for by a fully analytical treatment, provided that the exciton-phonon dynamics is much faster than the exciton-cavity dynamics. Modern experiments involving semiconductor quantum dots embedded in optical microcavities typically meet this criterion. We find that, for a relatively small exciton-cavity coupling, the effect of phonons is concentrated mainly in the polaron shift of the exciton frequency and reduction of exciton-cavity coupling by the Huang-Rhys factor. We have generalized this result to an arbitrary optical nonlinearity and demonstrated a good agreement with the exact solution in a wide range of temperatures. This generalization provides access to higher rungs of the Jaynes-Cummings ladder, where exact numerical approaches are impractical or even impossible. At larger coupling strengths and low temperatures, our approximation is also in good agreement with the exact solution, which makes it a very useful tool for addressing the phonon contribution to the coherent dynamics of a nonlinear optical system. We demonstrate our results for third-order optical polarization with varying observation time and delay time between excitation pulses in the form of two-dimensional spectra. These spectra provide useful information about the coherent coupling between the exciton and the cavity modes. The presented analytical approach is also compared with another useful approximation, having the form of a matrix product, which is a special case of the asymptotically exact solution in the limit of a short phonon memory time.
Abstract Four‐wave mixing (FWM) optical response from a sample containing a non‐homogeneously broadened ensemble of vertically stacked pairs of quantum dots is studied theoretically. The effects of collective interaction between the dots and their electromagnetic environment are analyzed. It is shown that the shape of the FWM echo is affected by the coupling between the two dots and, to some extent, by the statistics of the ensemble. In the time‐integrated signal, oscillations on picosecond delay time scale appear which lead to a reduction of the coherent response for coupled dots. For longer delays, the evolution is dominated by radiative decay, with the decay rate increasing from Γ to 2Γ(superradiance effect) as the coupling becomes stronger. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)