An EPTAS for Scheduling on Unrelated Machines of Few Different Types

In the classical problem of scheduling on unrelated parallel machines, a set of jobs has to be assigned to a set of machines. The jobs have a processing time depending on the machine and the goal is to minimize the makespan, that is the maximum machine load. It is well known that this problem is NP-hard and does not allow polynomial time approximation algorithms with approximation guarantees smaller than $1.5$ unless P$=$NP. We consider the case that there are only a constant number $K$ of machine types. Two machines have the same type if all jobs have the same processing time for them. This variant of the problem is strongly NP-hard already for $K=1$. We present an efficient polynomial time approximation scheme (EPTAS) for the problem, that is, for any $\varepsilon > 0$ an assignment with makespan of length at most $(1+\varepsilon)$ times the optimum can be found in polynomial time in the input length and the exponent is independent of $1/\varepsilon$. In particular we achieve a running time of $2^{\mathcal{O}(K\log(K) \frac{1}{\varepsilon}\log^4 \frac{1}{\varepsilon})}+\mathrm{poly}(|I|)$, where $|I|$ denotes the input length. Furthermore, we study three other problem variants and present an EPTAS for each of them: The Santa Claus problem, where the minimum machine load has to be maximized; the case of scheduling on unrelated parallel machines with a constant number of uniform types, where machines of the same type behave like uniformly related machines; and the multidimensional vector scheduling variant of the problem where both the dimension and the number of machine types are constant. For the Santa Claus problem we achieve the same running time. The results are achieved, using mixed integer linear programming and rounding techniques

Linear optical absorption spectra of mesoscopic structures in intense THz fields: free particle properties

We theoretically study the effect of THz radiation on the linear optical absorption spectra of semiconductor structures. A general theoretical framework, based on non-equilibrium Green functions, is formulated, and applied to the calculation of linear optical absorption spectrum for several non-equilibrium mesoscopic structures. We show that a blue-shift occurs and sidebands appear in bulk-like structures, i.e., the dynamical Franz-Keldysh effect [A.-P. Jauho and K. Johnsen, Phys. Rev. Lett. 76, 4576 (1996)]. An analytic calculation leads to the prediction that in the case of superlattices distinct stable steps appear in the absorption spectrum when conditions for dynamical localization are met.Comment: 13 Pages, RevTex using epsf to include 8 ps figures. Submitted to Phys. Rev. B (3 April 97

Field-induced delocalization and Zener breakdown in semiconductor superlattices

We investigate the energy spectrum and the electron dynamics of a band in a semiconductor superlattice as a function of the electric field. Linear optical spectroscopy shows that, for high fields, the well-known localization of the Bloch states is followed by a field-induced delocalization, associated with Zener breakdown. Using time-resolved measurements, we observe Bloch oscillations in a regime where they are damped by Zener breakdown

Waveguide Coupled Resonance Fluorescence from On-Chip Quantum Emitter

Resonantly driven quantum emitters offer a very promising route to obtain highly coherent sources of single photons required for applications in quantum information processing (QIP). Realizing this for on-chip scalable devices would be important for scientific advances and practical applications in the field of integrated quantum optics. Here we report on-chip quantum dot (QD) resonance fluorescence (RF) efficiently coupled into a single-mode waveguide, a key component of a photonic integrated circuit, with a negligible resonant laser background and show that the QD coherence is enhanced by more than a factor of 4 compared to off-resonant excitation. Single-photon behavior is confirmed under resonant excitation, and fast fluctuating charge dynamics are revealed in autocorrelation g(2) measurements. The potential for triggered operation is verified in pulsed RF. These results pave the way to a novel class of integrated quantum-optical devices for on-chip quantum information processing with embedded resonantly driven quantum emitters

CdSe-single-nanoparticle based active tips for near-field optical microscopy

We present a method to realize active optical tips for use in near-field optics that can operate at room temperature. A metal-coated optical tip is covered with a thin polymer layer stained with CdSe nanocrystals or nanorods at low density. The time analysis of the emission rate and emission spectra of the active tips reveal that a very small number of particles - possibly down to only one - can be made active at the tip apex. This opens the way to near-field optics with a single inorganic nanoparticle as a light source

Multifrequency broadband tapered plasmonic nanoantennas

We suggest a novel multifrequency broadband plasmonic Yagi-Uda-type nanoantenna equipped with an array of tapered directors. Each director can be used for the excitation of the antenna by nanoemitters matched spectrally with the director resonant frequency and placed in the director near-field region. Multifrequency op- eration of nanoantennas provides tremendous opportunities for broadband emission enhancement, spectroscopy and sensing. By the principle of reciprocity, the same tapered nanoantenna architecture can be used both as a transmitter and/or as a receiver, thus being useful for creating a broadband wireless communication system

Miniband-related 1.4–1.8 μm luminescence of Ge/Si quantum dot superlattices

The luminescence properties of highly strained, Sb-doped Ge/Si multi-layer heterostructures with incorporated Ge quantum dots (QDs) are studied. Calculations of the electronic band structure and luminescence measurements prove the existence of an electron miniband within the columns of the QDs. Miniband formation results in a conversion of the indirect to a quasi-direct excitons takes place. The optical transitions between electron states within the miniband and hole states within QDs are responsible for an intense luminescence in the 1.4–1.8 µm range, which is maintained up to room temperature. At 300 K, a light emitting diode based on such Ge/Si QD superlattices demonstrates an external quantum efficiency of 0.04% at a wavelength of 1.55 µm

Linearly Polarized Emission from an Embedded Quantum Dot Using Nanowire Morphology Control

GaAs nanowires with elongated cross sections are formed using a catalyst-free growth technique. This is achieved by patterning elongated nanoscale openings within a silicon dioxide growth mask on a (111)B GaAs substrate. It is observed that MOVPE-grown vertical nanowires with cross section elongated in the [21̅1̅] and [1̅12] directions remain faithful to the geometry of the openings. An InGaAs quantum dot with weak radial confinement is realized within each nanowire by briefly introducing indium into the reactor during nanowire growth. Photoluminescence emission from an embedded nanowire quantum dot is strongly linearly polarized (typically >90%) with the polarization direction coincident with the axis of elongation. Linearly polarized PL emission is a result of embedding the quantum dot in an anisotropic nanowire structure that supports a single strongly confined, linearly polarized optical mode. This research provides a route to the bottom-up growth of linearly polarized single photon sources of interest for quantum information applications