Calculation of pure dephasing for excitons in quantum dots

Pure dephasing of an exciton in a small quantum dot by optical and acoustic phonons is calculated using the ``independent boson model''. Considering the case of zero temperature the dephasing is shown to be only partial which manifests itself in the polarization decaying to a finite value. Typical dephasing times can be assigned even though the spectra exhibits strongly non-Lorentzian line shapes. We show that the dephasing from LO phonon scattering, occurs on a much larger time scale than that of dephasing due to acoustic phonons which for low temperatures are also a more efficient dephasing mechanism. The typical dephasing time is shown to strongly depend on the quantum dot size whereas the electron phonon ``coupling strength'' and external electric fields tend mostly to effect the residual coherence. The relevance of the dephasing times for current quantum information processing implementation schemes in quantum dots is discussed

A Statistical Test of Heterogeneous Subgraph Densities to Assess Clusterability

Determining if a graph displays a clustered structure prior to subjecting it to any cluster detection technique has recently gained attention in the literature. Attempts to group graph vertices into clusters when a graph does not have a clustered structure is not only a waste of time; it will also lead to misleading conclusions. To address this problem, we introduce a novel statistical test, the-test, which is based on comparisons of local and global densities. Our goal is to assess whether a given graph meets the necessary conditions to be meaningfully summarized by clusters of vertices. We empirically explore our test’s behavior under a number of graph structures. We also compare it to other recently published tests. From a theoretical standpoint, our test is more general, versatile and transparent than recently published competing techniques. It is based on the examination of intuitive quantities, applies equally to weighted and unweighted graphs and allows comparisons across graphs. More importantly, it does not rely on any distributional assumptions, other than the universally accepted definition of a clustered graph. Empirically, our test is shown to be more responsive to graph structure than other competing tests

Revisiting clustering as matrix factorisation on the Stiefel manifold

International audienceThis paper studies clustering for possibly high dimensional data (e.g. images, time series, gene expression data, and many other settings), and rephrase it as low rank matrix estimation in the PAC-Bayesian framework. Our approach leverages the well known Burer-Monteiro factorisation strategy from large scale optimisation, in the context of low rank estimation. Moreover, our Burer-Monteiro factors are shown to lie on a Stiefel manifold. We propose a new generalized Bayesian estimator for this problem and prove novel prediction bounds for clustering. We also devise a componentwise Langevin sampler on the Stiefel manifold to compute this estimator

Unbound states in quantum heterostructures

We report in this review on the electronic continuum states of semiconductor Quantum Wells and Quantum Dots and highlight the decisive part played by the virtual bound states in the optical properties of these structures. The two particles continuum states of Quantum Dots control the decoherence of the excited electron – hole states. The part played by Auger scattering in Quantum Dots is also discussed

Polaron states in InAs/GaAs quantum dots: strong electron-phonon coupling regime

We report on the magneto-optical evidence and theoretical modelling of polaron effects in self-assembled InAs/GaAs quantum dots, Using far-infrared magneto-transmission experiments performed up to 28 T at T = 2 K in doped QDs samples.. we investigate the electronic transitions between the ground and first excited states. We observe very large anticrossings in the B-dispersion of the magneto-optical transitions. whose existence cannot be explained by a purely electronic model. We thus calculate the coupling between the mixed electron-lattice states using the Frohlich Hamiltonian and determine the polaron states and the energies of the dipolar electric transitions. An excellent agreement between the calculations and the experimental data is obtained, demonstrating that the magneto-optical transitions occur between polaron states. The time dependence of the survival probability is calculated for the various non-interacting electron-phonon states, Such probabilities are found to oscillate and do not show an exponential decay as it would be the case for a weak coupling regime, This last argument confirms that the electrons and the LO-phonons experience a strong coupling regime in QDs. (C) 2002 Elsevier Science B.V. All rights reserved

Far-infrared magnetospectroscopy of polaron states in self- assembled InAs/GaAs quantum dots

We investigate the far infrared magneto-optical transitions in self-assembled InAs quantum dots with different. lateral diameters and we show that a purely electronic model is unable to account for the experimental data. We calculate them coupling between the mixed electron-LO-phonon states using the, Frohlich Hamiltonian, from which we determine the polaron states as well as the energies of the dipolar electric transitions. The excellent agreement between the experiments and the calculations obtained for the different samples provides strong evidence that the magneto-optical transitions arise between polaron states and that the electrons and LO phonons experience a strong coupling regime