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arXiv:0910.3749 · Physical Review B

Phonon-assisted transitions from quantum dot excitons to cavity photons

Ulrich Hohenester, Arne Laucht, M. Kaniber, Norman Hauke, Andre Neumann, Abbas Mohtashami, Marek Seliger, Max Bichler A, Jonathan James Finley

Published Nov 18, 2009• 151 citations
arXivHTMLPDF

Abstract

For a single semiconductor quantum dot embedded in a microcavity, we theoretically and experimentally investigate phonon-assisted transitions between excitons and the cavity mode. Within the framework of the independent boson model we find that such transitions can be very efficient, even for relatively large exciton-cavity detunings of several millielectron volts. Furthermore, we predict a strong detuning asymmetry for the exciton lifetime that vanishes for elevated lattice temperature. Our findings are corroborated by experiment, which turns out to be in good quantitative and qualitative agreement with theory.

DOI
10.1103/physrevb.80.201311

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For a single semiconductor quantum dot embedded in a microcavity, we theoretically and experimentally investigate phonon-assisted transitions between excitons and the cavity mode. Within the framework of the independent boson model we find that such transitions can be very efficient, even for relatively large exciton-cavity detunings of several millielectron volts. Furthermore, we predict a strong detuning asymmetry for the exciton lifetime that vanishes for elevated lattice temperature. Our findings are corroborated by experiment, which turns out to be in good quantitative and qualitative agreement with theory.
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We develop a theory of exciton energy transfer dynamics between two quantum dots in a planar microcavity. We study the dynamics of quantum dot excitons in three different cases: (i) a single dot coupled only to cavity modes, (ii) two dots coupled to cavity modes, and (iii) two dots coupled to cavity modes and to acoustic phonons. In the latter case, we focus on the process of phonon-assisted inelastic exciton energy transfer between the quantum dots. We take into account phonon effects by introducing a light-matter Hamiltonian with operators describing the exciton-photon-phonon coupling and we truncate the Hilbert space by assuming that at most one excitation is present in the system. Using this approach we simulate the exciton dynamics with realistic parameters in the zero temperature limit. From the dynamics we extract the dependence of the characteristic energy transfer rate as a function of the interdot separation. This theoretical approach can be used to optimize exciton energy transfer by designing structures with engineered photon and phonon density of states.
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.
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The excitonic dynamics in a single quantum dot within a microcavity is investigated theoretically in terms of the perturbation treatment based on a unitary transformation. The excitonic Rabi oscillations with a damping rate are obtained explicitly. It is shown that the damping rate depends on exciton-phonon coupling constant and the vacuum Rabi frequency. Even at absolute zero temperature and in the vacuum cavity, the exciton-phonon interaction and exciton-photon interaction still cause excitonic decoherence. We also predict that under strong control fields the collapse and revival of excitonic Rabi oscillation may be observed for the quantum dots with small exciton-phonon coupling in the $T\ensuremath{\rightarrow}0$ limit.
This thesis reports a theoretical investigation of the influence of the electronphonon interaction on semiconductor cavity quantum electrodynamical systems, specifically a quantum dot coupled to an optical microcavity. We develop a theoretical description of the decay dynamics of the quantum dot interacting with the cavity and the phonons. It is shown that the presence of the phonon interaction, fundamentally changes the spontaneous emission decay behavior of the quantum dot. Especially in the regime where the quantum dotcavity spectral detuning is significantly larger than any linewidth of the system, the effect of the phonon interaction is very pronounced. A simple approximate analytical expression for the quantum dot decay rate is derived, which predicts a strong asymmetry with respect to the quantum dot-cavity detuning at low temperatures, and allows for a clear interpretation of the physics. Furthermore, a study of the indistinguishability of single photons emitted from the coupled quantum dot-cavity system is performed, with special emphasis on non-Markovian decoherence due to the phonon interaction. We show that common theoretical approaches fail to predict the degree of indistinguishability, on both a qualitative and quantitative level, for experimentally relevant parameters regimes. The important role of non-Markovian effects in the shorttime regime, where virtual processes dominate the decoherence of the quantum dot-cavity system, is emphasized. Importantly, our investigations lead to a maximum achievable degree of indistinguishability, a prediction which eludes common approaches.