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arXiv:1207.6124 · Acta Physica Polonica A

Collective Spontaneous Emission from a System of Quantum Dots

Wildan Abdussalam, Paweł Machnikowski

Published Dec 1, 2012• 1 citation
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Abstract

We study the spontaneous emission from a regular lateral array or a randomly distributed ensemble of quantum dots under strong excitation (full inversion) conditions.We focus on the similarities and dierences between the cases of random and regular arrangement of the dots and show that there is very little dierence between the evolution of luminescence in these two cases, both for identical dots and for a realistically inhomogeneously broadened ensemble.This means that the enhanced emission or superradiance eect is not due to accidental clustering of pairs of dots.Moreover, we point out that observation of an enhanced emission under weak excitation does not prove that true superradiance will develop in a fully inverted system.

DOI
10.12693/aphyspola.122.994

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We study the spontaneous emission from a regular lateral array or a randomly distributed ensemble of quantum dots under strong excitation (full inversion) conditions.We focus on the similarities and dierences between the cases of random and regular arrangement of the dots and show that there is very little dierence between the evolution of luminescence in these two cases, both for identical dots and for a realistically inhomogeneously broadened ensemble.This means that the enhanced emission or superradiance eect is not due to accidental clustering of pairs of dots.Moreover, we point out that observation of an enhanced emission under weak excitation does not prove that true superradiance will develop in a fully inverted system.
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The collective spontaneous emission of a fully inverted inhomogeneously broadened ensemble of N two-level systems coupled to a single-mode low-Q cavity is investigated numerically using Monte Carlo wave function technique. An intrinsically bi-exponential emission dynamics is found when the time scales of superradiance tau(sr) and inhomogeneous dephasing T2* approximately 1/Deltaomega(inh) become comparable: a fast superradiant is followed by a slow subradiant decay. Experimental configurations using ensembles of quantum dots coupled to optical microcavities are proposed as possible candidates to observe the combined superradiant and subradiant energy relaxation.
We study collective spontaneous emission from a linear array of N two-state atoms using quantum trajectory theory and without an a priori single-mode assumption. Assuming a fully excited initial state, we calculate the angular distribution of the kthk\mathrm{th}kth emitted photon, k=1,…,N.k=1,\dots{},N.k=1,…,N. We investigate the evolution of the distribution from a dipole radiation pattern for the first photon emission to a distribution characteristic of directional superradiance. The formalism is developed around an unravelling of the master equation in terms of source-mode quantum jumps. Exact calculations for 11 and fewer atoms do not show directional superradiance, but are characterized by delayed (subradiant) photon emissions directed along the axis of the linear array. A modified boson approximation is made to treat the many-atom case, where it is found that strong directional superradiance occurs for a few hundred atoms; the decay of subradiant excitations is preserved in the tail of the superradiant pulse.
We investigate the collective spontaneous emission in a system of two identical quantum dots (QDs) strongly coupled through the dipole-dipole ($d\ensuremath{-}d$) interaction. The QDs are modeled as two-level quantum objects, while the $d\ensuremath{-}d$ interaction is described as the exchange of a virtual photon through the photonic reservoir. The master equation approach is used in the analysis. The main attention is focused on antenna characteristics of the two-QD system---the radiation intensity dependence on the meridian and azimuthal angles of observation. We show that the radiation pattern of such a system is nonstationary and its temporal behavior depends on the initial quantum state. In particular, for entangled initial states the radiative pattern exhibits oscillations on the frequency which corresponds to the $d\ensuremath{-}d$ interaction energy. We also analyze spectral properties of the directional diagram. The comparison of radiation patterns is carried out for two QDs and two classical dipoles. The concept of quantum nanoantenna is proposed based on collective spontaneous emission in QD ensembles.
We present a theoretical analysis of the intensity correlation functions for the spontaneous emission from a planar ensemble of self-assembled quantum dots. Using the quantum jump approach, we numerically simulate the evolution of the system and construct photon-photon delay time statistics that approximates the second-order correlation functions of the field. The form of this correlation function in the case of collective emission from a highly homogeneous ensemble qualitatively differs from that characterizing an ensemble of independent emitters (inhomogeneous ensemble of uncoupled dots). The signatures of collective emission are observed also in the case of an inhomogeneous but sufficiently strongly coupled ensemble. Different forms of the correlation functions are observed in the intensity autocorrelations and in cross correlations between various spectral ranges, revealing the quantum state projection associated with the detection event and the subsequent interaction-induced redistribution of occupations. The predicted effect of collective dynamics on the correlation functions appears under various excitation conditions. Thus, we show that the second-order correlation function of the emitted field provides a sensitive test of cooperative effects.