Aspects of the internal physics of InGaAs/InAlAs quantum cascade lasers

We report on the results of our simulations of an InGaAs/InAlAs midinfrared quantum cascade laser (QCL) designed to operate in continuous wave mode at room temperature [Beck et al., Science 295, 301 (2002)]. Our physical model of the device consists of a self-consistent solution of the subband population rate equations and accounts for all electron-longitudinal-optical phonon and electron-electron scattering rates, as well as an evaluation of the temperature of the nonequilibrium electron distribution. We also consider the role of the doping density and its influence on the electron dynamics. We found that the temperature of the nonequilibrium electron distribution differed significantly from the lattice temperature and that this temperature increased with applied electric field and current density, with coupling constants somewhat larger than analogous GaAs based midinfrared QCLs. Our simulations also reveal physical processes of the device that are not apparent from the experimental measurements, such as the role of electron-electron scattering. © 2006 American Institute of Physic

A Graphical Language for Proof Strategies

Complex automated proof strategies are often difficult to extract, visualise, modify, and debug. Traditional tactic languages, often based on stack-based goal propagation, make it easy to write proofs that obscure the flow of goals between tactics and are fragile to minor changes in input, proof structure or changes to tactics themselves. Here, we address this by introducing a graphical language called PSGraph for writing proof strategies. Strategies are constructed visually by "wiring together" collections of tactics and evaluated by propagating goal nodes through the diagram via graph rewriting. Tactic nodes can have many output wires, and use a filtering procedure based on goal-types (predicates describing the features of a goal) to decide where best to send newly-generated sub-goals. In addition to making the flow of goal information explicit, the graphical language can fulfil the role of many tacticals using visual idioms like branching, merging, and feedback loops. We argue that this language enables development of more robust proof strategies and provide several examples, along with a prototype implementation in Isabelle

A new quantum fluid at high magnetic fields in the marginal charge-density-wave system α\alpha-(BEDT-TTF)2M_2MHg(SCN)4_4 (where M=M=~K and Rb)

Single crystals of the organic charge-transfer salts $\alpha$-(BEDT-TTF)$_2M$Hg(SCN)$_4$ have been studied using Hall-potential measurements ($M=$K) and magnetization experiments ($M$ = K, Rb). The data show that two types of screening currents occur within the high-field, low-temperature CDW$_x$ phases of these salts in response to time-dependent magnetic fields. The first, which gives rise to the induced Hall potential, is a free current (${\bf j}_{\rm free}$), present at the surface of the sample. The time constant for the decay of these currents is much longer than that expected from the sample resistivity. The second component of the current appears to be magnetic (${\bf j}_{\rm mag}$), in that it is a microscopic, quasi-orbital effect; it is evenly distributed within the bulk of the sample upon saturation. To explain these data, we propose a simple model invoking a new type of quantum fluid comprising a CDW coexisting with a two-dimensional Fermi-surface pocket which describes the two types of current. The model and data are able to account for the body of previous experimental data which had generated apparently contradictory interpretations in terms of the quantum Hall effect or superconductivity.Comment: 13 pages, 11 figure

Photoreflectance and surface photovoltage spectroscopy of beryllium-doped GaAs/AlAs multiple quantum wells

We present an optical study of beryllium delta-doped GaAs/AlAs multiple quantum well (QW) structures designed for sensing terahertz (THz) radiation. Photoreflectance (PR), surface photovoltage (SPV), and wavelength-modulated differential surface photovoltage (DSPV) spectra were measured in the structures with QW widths ranging from 3 to 20 nm and doping densities from 2×10(10) to 5×10(12) cm(–2) at room temperature. The PR spectra displayed Franz-Keldysh oscillations which enabled an estimation of the electric-field strength of ~20 kV/cm at the sample surface. By analyzing the SPV spectra we have determined that a buried interface rather than the sample surface mainly governs the SPV effect. The DSPV spectra revealed sharp features associated with excitonic interband transitions which energies were found to be in a good agreement with those calculated including the nonparabolicity of the energy bands. The dependence of the exciton linewidth broadening on the well width and the quantum index has shown that an average half monolayer well width fluctuations is mostly predominant broadening mechanism for QWs thinner than 10 nm. The line broadening in lightly doped QWs, thicker than 10 nm, was found to arise from thermal broadening with the contribution from Stark broadening due to random electric fields of the ionized impurities in the structures. We finally consider the possible influence of strong internal electric fields, QW imperfections, and doping level on the operation of THz sensors fabricated using the studied structures. © 2005 American Institute of Physic

Finite pseudo orbit expansions for spectral quantities of quantum graphs

We investigate spectral quantities of quantum graphs by expanding them as sums over pseudo orbits, sets of periodic orbits. Only a finite collection of pseudo orbits which are irreducible and where the total number of bonds is less than or equal to the number of bonds of the graph appear, analogous to a cut off at half the Heisenberg time. The calculation simplifies previous approaches to pseudo orbit expansions on graphs. We formulate coefficients of the characteristic polynomial and derive a secular equation in terms of the irreducible pseudo orbits. From the secular equation, whose roots provide the graph spectrum, the zeta function is derived using the argument principle. The spectral zeta function enables quantities, such as the spectral determinant and vacuum energy, to be obtained directly as finite expansions over the set of short irreducible pseudo orbits.Comment: 23 pages, 4 figures, typos corrected, references added, vacuum energy calculation expande

Quantum statistics on graphs

Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph, concentrating on the simplest case of abelian statistics for two particles. In spite of the fact that graphs are locally one-dimensional, anyon statistics emerge in a generalized form. A given graph may support a family of independent anyon phases associated with topologically inequivalent exchange processes. In addition, for sufficiently complex graphs, there appear new discrete-valued phases. Our analysis is simplified by considering combinatorial rather than metric graphs -- equivalently, a many-particle tight-binding model. The results demonstrate that graphs provide an arena in which to study new manifestations of quantum statistics. Possible applications include topological quantum computing, topological insulators, the fractional quantum Hall effect, superconductivity and molecular physics.Comment: 21 pages, 6 figure

Time delay in thin slabs with self-focusing Kerr-type nonlinearity

Time delays for an intense transverse electric (TE) wave propagating through a Kerr-type nonlinear slab are investigated. The relation between the bidirectional group delay and the dwell time is derived and it is shown that the difference between them can be separated into three terms. The first one is the familiar self interference time, due to the dispersion of the medium surrounding the slab. The other two terms are caused by the nonlinearity and oblique incidence of the TE wave. It is shown that the electric field distribution along the slab may be expressed in terms of Jacobi elliptic functions while the phase difference introduced by the slab is given in terms of incomplete elliptic integrals. The expressions for the field intensity dependent complex reflection and transmission coefficients are derived and the multivalued oscillatory behavior of the delay times for the case of a thin slab is demonstrated