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Physical Review A

Spontaneous emission properties of a quantum dot in an ultrahigh- Q cavity: Crossover from weak- to strong-coupling states and robust quantum interference

Jun-ichi Inoue, Tetsuyuki Ochiai, Kazuaki Sakoda

Published Jan 10, 2008• 8 citations
Publisher

Abstract

We theoretically discuss spontaneous emission properties of a quantum dot embedded in an ultrahigh-$Q$ microcavity, where a detuning between an excitation in the quantum dot and the cavity mode is taken into account. Both weak- and strong-coupling states are obtained under the ultrahigh-$Q$ condition. In the high-$Q$ weak-coupling case, the spontaneous emission spectrum shows a sharp dip, whose origin is a quantum interference. In the strong-coupling case, there is a region where both the Rabi splitting and the quantum interference contribute on an equal footing, referred to as a crossover region, where the spontaneous emission spectral shape is quite similar to that of the high-$Q$ weak-coupling state. The quantum interference is robust against the detuning.

DOI
10.1103/physreva.77.015806

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Spontaneous emission spectra from a single quantum dot embedded in a microcavity characterized by the quality factor ( Q ) are theoretically discussed in the high Q weak coupling region. It is shown that the region should be divided into two subregions in terms of the spectral shape. The spontaneous emission spectrum in one subregion has the Lorentzian line shape, which shows a cavity effect in the line width characterized by Q -1 dependence. In the other subregion, the spectral line shape is found to have a "doublet" structure, although it is in the weak coupling region. This doublet is caused by a quantum interference effect.
We discuss the spectral line shapes of NNN quantum dots in strong coupling with the single mode of a microcavity in the presence of a continuous, incoherent pumping. Nontrivial features in the response of the system are induced by detuning the emitters or probing the direct exciton emission spectrum. We describe dark states, quantum nonlinearities, emission dips, and interferences and show how these various effects may coexist, giving rise to highly peculiar line shapes.
The spontaneous emission spectrum from two quantum dots (QDs) that are strongly coupled with a single-mode nanocavity is investigated using rigorous numerical calculations and simple analytical solutions of quantum dynamics. The emission spectra both from the side and along the axis of the cavity are considered. Modification of two parameters, the coupling strength and the detuning between the transition frequencies of the two quantum dots, allows us to efficiently control the shape of the spontaneous emission spectrum. Different profiles and their physical origins can be well understood in the dressed-state picture for the light—QD interaction in the on-resonance and off-resonance situations. In the on-resonance situation, the emission spectra exhibit symmetric features, and they are not altered by the asymmetry in the coupling parameters. The axis spectra show two emission peaks while the side spectra have three emission peaks. In the off-resonance situation, the emission spectra always show an asymmetrical three-peak feature. When the two QDs have different decay parameters, singular features (a peak or a dip) can take place at the frequency of the cavity mode, and this is attributed to the unbalanced process of the emission and absorption of a single photon.
We study the dynamics of a quantum dot embedded in a three-dimensional microcavity in the strong coupling regime in which the quantum dot exciton has an energy close to the frequency of a confined cavity mode. Under the continuous pumping of the system, the confined electron and hole can recombine either by spontaneous emission through a leaky mode or by stimulated emission of a cavity mode that can escape from the cavity. The numerical integration of a master equation including all these effects gives the dynamics of the density matrix. By using the quantum regression theorem, we compute the first- and second-order coherence functions required to calculate the photon statistics and the spectrum of the emitted light. Our main result is the determination of a range of parameters in which a state of cavity modes with Poissonian or sub-Poissonian (nonclassical) statistics can be built up within the microcavity. Depending on the relative values of pumping and rate of stimulated emission, either one or two peaks close to the excitation energy of the dot and/or to the natural frequency of the cavity are observed in the emission spectrum. The physics behind these results is discussed.
We have investigated theoretically and experimentally the emission of (quantum dot-cavity) systems for different coupling strength and a wide range of exciton-photon mode detunings controlled by temperature variation in the range 10–45 K. Under close to resonance conditions, the radiation spectrum from the cavity emission becomes essentially dependent on the primary excitation path, which can be either via resonant quantum-dot exciton or via cavity mode. Particularly, in the case of nonresonant cavity mode excitation, the emission line becomes split into two asymmetric lines already in the weak coupling regime.