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arXiv:1110.4538 · Physical Review A

Nonlinear temporal dynamics of a strongly coupled quantum-dot–cavity system

Arka Majumdar, Dirk Englund, Michal Bajcsy, Jelena Vuckovic A

Published Mar 5, 2012• 53 citations
arXivHTMLPDF

Abstract

We theoretically analyze the temporal dynamics of strongly coupled quantum-dot--cavity system driven by a resonant laser pulse and observe the signature of Rabi oscillation in the time-resolved response of the system (i.e., in the numerically calculated cavity output). We derive simplified linear and nonlinear semiclassical models that approximate well the system's behavior in the limits of high- and low-power driving pulses and describe the role of quantum coherence in the exact dynamics of the system. Finally, we also present time-resolved transmission measurements showing the dynamics of a quantum-dot--cavity system in the presence of a short laser pulse.

DOI
10.1103/physreva.85.033802

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We theoretically analyze the temporal dynamics of strongly coupled quantum-dot--cavity system driven by a resonant laser pulse and observe the signature of Rabi oscillation in the time-resolved response of the system (i.e., in the numerically calculated cavity output). We derive simplified linear and nonlinear semiclassical models that approximate well the system's behavior in the limits of high- and low-power driving pulses and describe the role of quantum coherence in the exact dynamics of the system. Finally, we also present time-resolved transmission measurements showing the dynamics of a quantum-dot--cavity system in the presence of a short laser pulse.
We report time domain observation of vacuum Rabi oscillations in a single quantum dot strongly coupled to a nanocavity under incoherent optical carrier injection. We realize a photonic crystal nanocavity with a very high quality factor of >80000>80\phantom{\rule{0.16em}{0ex}}000>80000 and employ it to clearly resolve the ultrafast vacuum Rabi oscillations by simple photoluminescence-based experiments. We found that the time domain vacuum Rabi oscillations were largely modified when changing the pump wavelength and intensity, even when marginal changes were detected in the corresponding photoluminescence spectra. We analyze the measured time domain oscillations by fitting to simulation curves obtained with a cavity quantum electrodynamics model. The observed modifications of the oscillation curves were mainly induced by the change in the carrier capture and dephasing dynamics in the quantum dot, as well as the change in bare-cavity emission. This result suggests that vacuum Rabi oscillations can be utilized as a highly sensitive probe for the quantum-dot dynamics. Our work points out a powerful alternative to conventional spectral-domain measurements for a deeper understanding of the vacuum Rabi dynamics in quantum-dot-based--cavity quantum electrodynamics systems.
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Optical Rabi oscillations are coherent population oscillations of a two-level system coupled by an electric dipole transition when driven by a strong nearly resonant optical field. In quantum dot structures, these measurements have typically been performed as a function of the total pulse area $\ensuremath{\int}{\ensuremath{\Omega}}_{0}(t)\phantom{\rule{0.16em}{0ex}}\mathrm{d}t$ where the pulse area varies as a function of Rabi frequency. Here, we report direct detection of the time-resolved coherent transient response of the resonance fluorescence to measure the time evolution of the optical Rabi oscillations in a single charged InAs quantum dot. We extract a decoherence rate consistent with the limit from the excited state lifetime.
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.
Summary form only given. Recent studies have been carried out on the resonant response from single interface fluctuation quantum dots. Such a discrete-level model yields unique signatures under strong resonant driving, including Rabi oscillations. To date, Rabi oscillations (excluding microcavity studies) have only been reported for two-dimensional excitonic systems. We present data showing the nonlinear response from an ensemble of interface fluctuation quantum dots. This data is consistent with Rabi oscillations for moderate driving fields (that is, for /spl Theta//spl sim/2/spl pi/, where /spl Theta/ is the pulse area). The sample under investigation is a single thin (62 /spl Aring/) GaAs/Al/sub 0.3/Ga/sub 0.7/As quantum well grown with growth interruptions and is studied at 5 K. The laser is tuned to the lower energy excitonic resonance, corresponding to an inhomogeneously broadened distribution of excitons localized due to well width fluctuations. The time-integrated PL is collected with a spectrometer tuned 2.5 meV below the excitonic resonance.