Tensors-structured numerical methods in scientific computing: Survey on recent advances

In the present paper, we give a survey of the recent results and outline future prospects of the tensor-structured numerical methods in applications to multidimensional problems in scientific computing. The guiding principle of the tensor methods is an approximation of multivariate functions and operators relying on a certain separation of variables. Along with the traditional canonical and Tucker models, we focus on the recent quantics-TT tensor approximation method that allows to represent N-d tensors with log-volume complexity, O(d log N). We outline how these methods can be applied in the framework of tensor truncated iteration for the solution of the high-dimensional elliptic/parabolic equations and parametric PDEs. Numerical examples demonstrate that the tensor-structured methods have proved their value in application to various computational problems arising in quantum chemistry and in the multi-dimensional/parametric FEM/BEM modeling—the tool apparently works and gives the promise for future use in challenging high-dimensional applications.     

14 MHz rate photon counting with room temperature InGaAs/InP avalanche photodiodes

Abstract

We have developed high speed gated-mode single-photon counters based on InGaAs/InP avalanche photodiodes for use at 1.55 μm wavelength. Operation at room temperature allows afterpulse probability to be below 0.2% for gate rates up to 14 MHz. We obtained optimum noise-equivalent power of 2.2 ×s; 10^?15 W Hz^?1/2 at 14% quantum efficiency with dark-count probability of 0.2%. We propose a metric (noise-equivalent power divided by gate frequency) for comparing high speed photon counters and show that for this metric our system outperforms previously reported counters at 1.55 μm wavelength. We demonstrate that for gate widths of a nanosecond or below, the differing amplitude distributions of dark versus light counts allow an optimal decision threshold to be set for a given bias voltage.     

Coherence properties of a continuous atom laser

Abstract

We investigate the coherence properties of an atomic beam evaporatively cooled in a magnetic guide, assuming thermal equilibrium in the quantum degenerate regime. The gas experiences two-dimensional, transverse Bose-Einstein condensation rather than a full three-dimensional condensation because of the very elongated geometry of the magnetic guide. First order and second order correlation functions of the atomic field are used to characterize the coherence properties of the gas along the axis of the guide. The coherence length of the gas is found to be much larger than the thermal de Broglie wavelength in the strongly quantum degenerate regime. Large intensity fluctuations present in the ideal Bose gas model are found to be strongly reduced by repulsive atomic interactions; this conclusion is obtained with a one-dimensional classical field approximation valid when the temperature of the gas is much higher than its chemical potential, k _B T » |μ|.     

Different realizations of the tomographic principle in quantum state measurement

Abstract

We establish a general principle for the tomographic approach to quantum state reconstruction, which until now has been based on a simple rotation transformation in the phase space; this allows us to consider other types of transformation. Then, we shall present different realizations of the principle in specific examples.     

Atomic motion in a standing-wave squeezed light field

Abstract

We investigate atomic motion in the standing-wave field of a cavity driven by coherent light plus broad-band-squeezed vacuum. We assume the bad-cavity limit and adiabatically eliminate the cavity mode, deriving a master equation for the atomic variables alone. From this master equation we study the (one-dimensional) atomic motion both in the semiclassical approximation and using quantum Monte Carlo wavefunction simulations. The light force and momentum diffusion are shown to be strongly dependent on the relative phase between the coherent and squeezed fields and, using a dressedstate analysis, we identify observable effects unique to the reduced quantum noise that characterizes squeezed-vacuum light.     

Validity of the cylindrical localized approximation for arbitrary shaped beams in generalized Lorenz-Mie theory for circular cylinders

Abstract

A so-called cylindrical localized approximation, allowing one to speed up the evaluation of beam shape distributions in generalized Lorenz-Mie theory for circular infinitely long cylinders, has been previously introduced and, in the case of Gaussian beams, rigorously justified. In this paper, we examine and demonstrate the validity of this approximation for arbitrary shaped beams.     

Analysis of Bragg reflectors by lateral photoluminescence spectroscopy

Abstract

A new method for the rapid determination of layer thicknesses in semiconductor Bragg mirrors for vertical cavity surface emitting lasers (VCSEL) has been developed. The photoluminescence spectrum of a complete VCSEL structure for a wavelength of 980 nm is measured in the wafer plane at room temperature with the excitation being normal to the specimen. In the spectrum from 850 to 1000 nm three regions can be distinguished; the long wavelength part of the spectrum (λ > 950 nm) gives iriformation about the quantum well emission, the shorter part (λ > 850 nm) stems from luminescence of heavily doped p type GaAs. A pronounced structure in the range from 900 to 950 nm arises from constructive interference of light generated in the GaAs layers and leaving the specimen parallel to the surface near the angle of total reflection. From the wavelength of these peaks the layer thicknesses within the Bragg mirror can be calculated with high precision.     

Dispersive Charge and Flux Qubit Readout as a Quantum Measurement Process

We analyze the dispersive readout of superconducting charge and flux qubits as a quantum measurement process. The measurement oscillator frequency is considered much lower than the qubit frequency. This regime is interesting because large detuning allows for strong coupling between the measurement oscillator and the signal transmission line, thus allowing for fast readout. Due to the large detuning we may not use the rotating wave approximation in the oscillator-qubit coupling. Instead we start from an approximation where the qubit follows the oscillator adiabatically, and show that non-adiabatic corrections are small. We find analytic expressions for the measurement time, as well as for the back-action, both while measuring and in the off-state. The quantum efficiency is found to be unity within our approximation, both for charge and flux qubit readout.      

Two-point optical resolution with homogeneous,evanescent and self field: Resolution criterion in near field imaging

Abstract

The radiative and non-radiative electromagnetic field of a quantum particle is studied. An optical resolution criterion is proposed in terms of the two-point resolution. Resolution of optical microscopes is limited either by homogeneous diffraction (conventional microscopes) or by evanescent diffraction (near-field microscopes). The evanescent diffraction limit is a function of the wavelength and the observation distance (a portion of the wavelength), which may be circumvented by measuring the non-radiative field, namely the self field in the quantum range of the objects. The resolution then becomes a function of the object size, and is no longer limited by the wavelength of light used. The two-level hydrogen atom is taken as an example.     

Kernel-based approximation for Cauchy problem of the time-fractional diffusion equation

We investigate in this paper a Cauchy problem for the time-fractional diffusion equation (TFDE). Based on the idea of kernel-based approximation, we construct an efficient numerical scheme for obtaining the solution of a Cauchy problem of TFDE. The use of M-Wright functions as the kernel functions for the approximation space allows us to express the solution in terms of M-Wright functions, whose numerical evaluation can be accurately achieved by applying the inverse Laplace transform technique. To handle the ill-posedness of the resultant coefficient matrix due to the noisy Cauchy data, we adapt the standard Tikhonov regularization technique with the L-curve method for obtaining the optimal regularization parameter to give a stable numerical reconstruction of the solution. Numerical results indicate the efficiency and effectiveness of the proposed scheme.     

Power Losses in Highly Conducting Lamellar Gratings

Abstract

We compare approaches based on a surface impedance approximation and a perturbation analysis with a rigorous modal technique for the calculation of the diffraction properties of highly conducting lamellar gratings. We show the surface impedance approximation to be inaccurate even for good metals at a wavelength of 10 μm. The perturbation theory results can be quite accurate, but their region of applicability is limited. We demonstrate that the rigorous technique can be used for lamellar gratings made of materials with a complex refractive index of very large modulus.     

Solar Cells,Photodetectors, and Optical Sources from Infrared Colloidal Quantum Dots

Optoelectronic devices made via spin‐coating of soft materials onto an arbitrary substrate enable ready integration, low cost, and physical flexibility. The use of solution‐processed colloidal quantum dots offers the added advantage of quantum‐size‐effect tuning of material bandgap. Tuning across the near‐ and short‐wavelength infrared (SWIR) spectral regions enables applications in fiber‐optic communications, night vision and biomedical imaging, and efficient solar energy collection. Here we review progress in infrared solar cells, light sensors, and optical sources based on solution‐processed materials. The latest solution‐processed photovoltaics now provide 4.2% power conversion efficiencies in the infrared, placing them a factor of three away from enabling a doubling in overall solar power conversion efficiency of visible‐wavelength solution‐processed photovoltaics. The best solution‐processed photodetectors now provide sensitivities of 10¹³ Jones D* (normalized detectivity), exceeding the sensitivity of the best epitaxially grown SWIR photodetectors. Infrared optical sources, both broadband light‐emitting diodes and, more recently, lasers, have now also been reported at 1.5 µm.     

Chromatic Dispersion Effects on Infrared Single-mode All-fibre Optic Double Fourier Interferometric Imaging

Abstract

In an infrared (IR) single-mode fibre-linked optical telescope array, not only the spatial but also the spectral resolution of a star can be simultaneously obtained as long as the fibre arms are stretched to generate the optical path difference (OPD) modulation. This imaging technique is called IR single-mode (SM) all-fibre optic (AFO) double Fourier interferometry (DFI). The fibre-stretching operation will inevitably introduce a chromatic dispersion problem and make the OPD wavelength dependent. In this paper, a point source response expression for the IR SM AFO DFI is first established. Accordingly, the recovered mutual spectral density (MSD) is deduced. One of the dispersion effects on MSD is a wavenumber shift; this and other effects on MSD are discussed. Then, we establish the final map expression for a point source and discuss the dispersion effects on it. One of these effects is a shift of the image position. Finally, we discuss the effects of the first-order approximation of the OPD. To reduce these effects, a method of dividing the whole spectral band into subbands is pointed out and discussed.     

Low-threshold quantum-dot injection heterolaser emitting at 1.84 μm

The use of InAs quantum dots in an InGaAs matrix lattice-matched with an InP substrate can appreciably increase the emission wavelength of quantum-dot lasers. Lasing via quantum-dot states at the 1.84 μm wavelength (77 K) was obtained for the first time at a threshold current density of 64 A/cm². Pis’ma Zh. Tekh. Fiz. 24, 49–54 (January 12, 1998)     

Quantum lost and found

Abstract

We consider the problem of correcting the errors incurred from sending classical or quantum information through a noisy quantum environment by schemes using classical information obtained from a measurement on the environment. We give conditions for quantum or classical information (prepared in a specified input basis B) to be corrigible based on a measurement M. Based on these criteria we give examples of noisy channels such that (1) no information can be corrected by such a scheme, (2) for some basis B there is a correcting measurement M, (3) for all bases B there is an M and (4) there is a measurement M which allows perfect correction for all bases B. The last case is equivalent to the possibility of correcting quantum information, and turns out to be equivalent to the channel allowing a representation as a convex combination of isometric channels. Such channels are doubly stochastic but not conversely.     

Investigation of the optical characteristics of a combination of InP/ZnS-quantum dots with MWCNTs in a PMMA matrix

In the present study we investigated a combination of quantum dots with multi-walled carbon nanotubes as a possible future additive to the active layer of polymer solar cells. In this case the quantum dots should serve to enhance the long wavelength response of the solar cell, while the nanotubes enhance the charge carrier collection efficiency by favoring charge carrier separation and enhancement of the lateral conduction of the films. In order to clarify the interplay of the nanoparticles only, we deposited them into a non-conducting and transparent polymethyl-methalacrylate (PMMA) matrix. InP/ZnS quantum dots with an emission peak wavelength of 660 nm have been chosen in this study, because their addition can enhance the long wavelength response of conventional poly(3-hexylthiophene) (P3HT): phenyl-C61-butyric acid methyl ester (PCBM) bulk heterostructure polymer solar cells. In our study we kept the quantum dot concentration constant and varied the concentration of the carbon nanotubes (CNTs) in the deposited films. The characterization of the film morphology by scanning electron microscopy (SEM) imaging and of the optical properties by photoluminescence and transmittance revealed a rather complex interplay between nanotubes and quantum dots. In particular we found a strong quenching of the photoluminescence and an inhomogeneous CNT distribution for carbon nanotube concentrations exceeding 1%. The decrease in optical transmittance of the films with increasing CNT concentration is less pronounced, when quantum dots (QDs) are added. The optical transmittance in a wavelength range between 380 nm and 800 nm of the composites could be expressed empirically as a simple second order polynomial function.     

Highly doped alkaline earth nanofluorides synthesized from ionic liquids

Bulk alkaline earth fluorides co-doped with optically active ions are prominent materials for luminescent applications. However, for phosphor materials the changeover to the nanoscale is a tightrope walk between achieving desirable features of small particles such as reduced light scattering and unwanted drawbacks such as a high surface defect concentration which is likely to result in quenching of luminescence. A new preparation route via ionic liquids allows obtaining pure and oxygen-free alkaline earth fluorides co-doped with Eu³⁺ and Gd³⁺ on the nanoscale with excellent quantum cutting abilities.     

Effect of strain rate sensitivity and cavity growth rate on failure of superplastic material

Abstract

Necking development and fracture strain of superplastic material under tensile load are analysed by introducing a model of cavity growth into the long wavelength approximation analysis which can describe the external neck development of specimens during deformation. The results show that both strain rate sensitivity m and cavity growth rate η have an important influence on the fracture strain of superplastic material. According to these results, a fracture diagram is presented in m–η coordinates, which is divided into three: a region in which material fails by macroscopic external necking, a region where cavity growth is predominant leading to fracture without pronounced external necking, and an intermediate region where both fracture modes occur. The prediction of fracture strain for various superplastic alloys exhibiting cavity growth during deformation is in good agreement with experimental results. The present analysis thus enables quantitative prediction of the effects of both strain rate sensitivity and cavity growth on superplastic fracture under uniaxial tension.

MST/491     

Quick Solution of Scattering Problems,from Very Short to Long Wavelengths

Abstract

An approximate method for the solution of scattering problems is presented: the plane approximation delta function boundary operator (PDBO) method. Numerical results based on the use of the fast Fourier transform show that this method, which takes into account the vector character of the light, is able to give reliable results both for short and for long wavelengths, provided the radius of curvature is large enough. The method is applied to diffraction gratings and to non-periodic rough surfaces. Comparison with rigorous results shows that the new method is much better than the classical Beckmann method.