Involutivity of integrals for sine-Gordon, modified KdV and potential KdV maps

Closed form expressions in terms of multi-sums of products have been given in \cite{Tranclosedform, KRQ} of integrals of sine-Gordon, modified Korteweg-de Vries and potential Korteweg-de Vries maps obtained as so-called $(p,-1)$-traveling wave reductions of the corresponding partial difference equations. We prove the involutivity of these integrals with respect to recently found symplectic structures for those maps. The proof is based on explicit formulae for the Poisson brackets between multi-sums of products.Comment: 24 page

Decay dynamics of quantum dots influenced by the local density of optical states of two-dimensional photonic crystal membranes

We have performed time-resolved spectroscopy on InAs quantum dot ensembles in photonic crystal membranes. The influence of the photonic crystal is investigated by varying the lattice constant systematically. We observe a strong slow down of the quantum dots' spontaneous emission rates as the two-dimensional bandgap is tuned through their emission frequencies. The measured band edges are in full agreement with theoretical predictions. We characterize the multi-exponential decay curves by their mean decay time and find enhancement of the spontaneous emission at the bandgap edges and strong inhibition inside the bandgap in good agreement with local density of states calculations.Comment: 9 pages (preprint), 3 figure

Modally Resolved Fabry-Perot Experiment with Semiconductor Waveguides

Based on the interaction between different spatial modes, semiconductor Bragg-reflection waveguides provide a highly functional platform for non-linear optics. Therefore, the control and engineering of the properties of each spatial mode is essential. Despite the multimodeness of our waveguide, the well-established Fabry-Perot technique for recording fringes in the optical transmission spectrum can successfully be employed for a detailed linear optical characterization when combined with Fourier analysis. A prerequisite for the modal sensitivity is a finely resolved transmission spectrum that is recorded over a broad frequency band. Our results highlight how the features of different spatial modes, such as their loss characteristics and dispersion properties, can be separated from each other allowing their comparison. The mode-resolved measurements are important for optimizing the performance of such multimode waveguides by tailoring the properties of their spatial modes.Comment: 8 pages, 7 figure

Near-field imaging and frequency tuning of a high-Q photonic crystal membrane microcavity

We discuss experimental studies of the interaction between a nanoscopic object and a photonic crystal membrane resonator of quality factor Q=55000. By controlled actuation of a glass fiber tip in the near-field of a photonic crystal, we constructed a complete spatio-spectral map of the resonator mode and its coupling with the fiber-tip. On the one hand, our findings demonstrate that scanning probes can profoundly influence the optical characteristics and the near-field images of photonic devices. On the other hand, we show that the introduction of a nanoscopic object provides a low-loss method for on-command tuning of a photonic crystal resonator frequency. Our results are in a very good agreement with the predictions of a combined numerical/analytical theory.Comment: 9 pages, 4 figure

Memristive operation mode of a site-controlled quantum dot floating gate transistor

The authors gratefully acknowledge financial support from the European Union (FPVII (2007-2013) under Grant Agreement No. 318287 Landauer) as well as the state of Bavaria.We have realized a floating gate transistor based on a GaAs/AlGaAs heterostructure with site-controlled InAs quantum dots. By short-circuiting the source contact with the lateral gates and performing closed voltage sweep cycles, we observe a memristive operation mode with pinched hysteresis loops and two clearly distinguishable conductive states. The conductance depends on the quantum dot charge which can be altered in a controllable manner by the voltage value and time interval spent in the charging region. The quantum dot memristor has the potential to realize artificial synapses in a state-of-the-art opto-electronic semiconductor platform by charge localization and Coulomb coupling.Publisher PDFPeer reviewe

Integrable and superintegrable systems associated with multi-sums of products

We construct and study certain Liouville integrable, superintegrable, and non-commutative integrable systems, which are associated with multi-sums of products.Comment: 26 pages, submitted to Proceedings of the royal society