We have studied quantum coherence and interference phenomena in a quantum dot (QD)-metallic nanorod (MNR) hybrid system. Probe and control laser fields are applied to the hybrid system. Induced dipole moments are created in the QD and the MNR, and they interact with each other via the dipole-dipole interaction. Using the density matrix method, it was found that the power spectrum of MNR has two transparent, states and they can be switched to one transparent state by the control field. Ultrafast switching and sensing nanodevices could be produced using this model.

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All 8th order Franklin bent diagonal squares with distinct elements 1, …, 64 have been constructed by an exact backtracking method. Our count of 1, 105, 920 dramatically increases the handful of known examples, and is some eight orders of magnitude less than a recent upper bound. Exactly one-third of these squares are pandiagonal, and therefore magic. Moreover, these pandiagonal Franklin squares have the same population count as the eighth order ‘complete’, or ‘most-perfect pandiagonal magic’, squares. However, while distinct, both types of squares are related by a simple transformation. The situation for other orders is also discussed.

Large unit cell calculations of the properties of charged point defects in insulators largely neglect dielectric polarization of the crystal, because the periodically repeated cells are so small. Embedded quantum cluster calculations with shell-model crystals, representing a single defect in a large crystal, are able to represent the polarization more realistically. For such embedded quantum clusters, we evaluate the optical excitation energy for the nitrogen vacancy in charge state (+3): v 3+ N in AlN. This is done with and without dielectric polarization of the embedding crystal. A discrepancy of a few per cent is found, when both ground and excited state orbitals are well-localized within the vacancy. We show that the discrepancy rises rapidly as the excited state becomes more diffuse. We conclude that an embedded cluster approach will be required for transitions that involve even somewhat diffuse states. The investigation is based on a new model for AlN that shows promise for quantitative accuracy.

We have studied energy absorption rate in a quantum dot-metallic nanosphere system embedded on a dielectric substrate. We applied a control field to induce dipole moments in the quantum dot and the metal nanosphere, and monitored the energy absorption using a probe field. These external fields induce dipole moments in the metal nanosphere and the quantum dot, and these two structures interact with one another via the dipole-dipole interaction. The density matrix method was used to evaluate the absorption, indicating that it can be shifted by moving the metal nanosphere close to the quantum dot. Also, absorption efficiency can either be quenched or enhanced by the addition of a metal nanosphere. This hybrid system can be used to create ultrafast switching and sensing nanodevices.