Spectroscopic determination of the order parameter of coupled bilayers at =1

We report inelastic light scattering measurements of spin excitations on coupled electron bilayers with relatively large tunneling gaps at total filling factor ν_T=1. We show that the pseudospin polarization order parameter, where the pseudospin labels the occupation of symmetric and antisymmetric levels, can be determined from the energy of long wavelength spin excitations. Our experiments indicate that the order parameter in the quantum Hall ground state collapses at the incompressible–compressible phase transition. The latter is driven by decreasing the tunneling gap through the application of an in-plane magnetic field.     

Weak-localization-like temperature-dependent conductivity of a dilute two-dimensional hole gas in a parallel magnetic field

We have studied the magnetotransport properties of a high mobility two-dimensional hole gas (2DHG) in a 10 nm GaAs quantum well with densities in the range of (0.7-1.6) x 10(10) cm(-2) on the metallic side of the zero-field "metal-insulator transition." In a parallel field well above B(c) that suppresses the metallic conductivity, the 2DHG exhibits a conductivity Delta(g)(T) approximately (1/pi) (e(2)/h)lnT reminiscent of weak localization for Fermi liquids. The experiments are consistent with the coexistence of two phases in our system: a metallic phase and a weakly insulating Fermi liquid phase.     

Evidence of correlation in spin excitations of few-electron quantum dots

We report inelastic light scattering measurements of spin and charge excitations in nanofabricated AlGaAs/GaAs quantum dots with few electrons. A narrow spin excitation peak is observed and assigned to the intershell triplet-to-singlet monopole mode of dots with four electrons. Configuration-interaction theory provides precise quantitative interpretations that uncover large correlation effects that are comparable to exchange Coulomb interactions.     

Fabrication and microscopic characterization of a single quantum-wire laser with high uniformity

A T-shaped single quantum-wire laser with high spatial uniformity has been fabricated by a cleaved-edge overgrowth method with molecular beam epitaxy and a growth-interrupt annealing technique. Using micro-photoluminescence imaging and spectroscopy, we confirmed the formation of a spatially uniform quantum wire over 20 μm long without hetero-interface roughness. By optical pumping, we achieved single-mode lasing from the ground state of the single quantum wire at a threshold excitation power as low as 5 mW at 5 K.     

Higher-energy composite fermion levels in the fractional quantum Hall effect

Even though composite fermions in the fractional quantum Hall liquid are well established, it is not yet known up to what energies they remain intact. We probe the high-energy spectrum of the 1/3 liquid directly by resonant inelastic light scattering, and report the observation of a large number of new collective modes. Supported by our theoretical calculations, we associate these with transitions across two or more composite fermions levels. The formation of quasiparticle levels up to high energies is direct evidence for the robustness of topological order in the fractional quantum Hall effect.     

On the convergence of the ensemble Kalman filter

Convergence of the ensemble Kalman filter in the limit for large ensembles to the Kalman filter is proved. In each step of the filter, convergence of the ensemble sample covariance follows from a weak law of large numbers for exchangeable random variables, the continuous mapping theorem gives convergence in probability of the ensemble members, and L ^p bounds on the ensemble then give L ^p convergence.     

Quantum wire lasers with high uniformity formed by cleaved-edge overgrowth with growth-interrupt anneal

High-quality T-shaped quantum wire lasers are fabricated by cleaved-edge overgrowth with the molecular beam epitaxy on the interface improved by a growth-interrupt high-temperature anneal. Micro-photoluminescence (PL) and PL excitation spectroscopy reveals unprecedented high quality of the wires, and structures of one-dimensional (1D) free excitons and 1D continuum states. At high pumping levels, PL evolves from a sharp free exciton peak via a biexciton peak to a red-shifted broad band. Lasing has been achieved with low lasing threshold. The lasing energy is on the red-shifted broad band and is about 5 meV below the free exciton. The observed shift excludes free excitons in lasing, and suggests contribution of highly Coulomb-correlated electron-hole plasma.     

Spin excitations in few-electrons AlGaAs/GaAs quantum dots probed by inelastic light scattering

We present recent studies of electronic excitations in nanofabricated AlGaAs/GaAs semiconductor quantum dots (QDs) by resonant inelastic light scattering. The resonant light scattering spectra are dominated by excitations from parity-allowed inter-shell transitions between Fock–Darwin levels. In QDs with very few electrons the resonant spectra are characterized by distinct charge and spin excitations that reveal the strong impact of both exchange and correlation effects. A sharp inter-shell spin excitation of the triplet spin QD state with four electrons is identified.     

Resonant rayleigh scattering from bilayer quantum Hall phases

We observe resonant Rayleigh scattering of light from quantum Hall bilayers at Landau level filling factor nu = 1. The effect arises below 1 Kelvin when electrons are in the incompressible quantum Hall phase with strong interlayer correlations. Marked changes in the Rayleigh scattering signal in response to application of an in-plane magnetic field indicate that the unexpected temperature dependence is linked to formation of a nonuniform electron fluid close to the phase transition towards the compressible state. These results demonstrate a new realm of study in which resonant Rayleigh scattering methods probe quantum phases of electrons in semiconductor heterostructures.     

Large Time Asymptotics for Brownian Hitting Densities of Transient Concave Curves

With appropriate regularity assumptions on the increasing concave function x=(t)<0, the hitting time density p(t) for a transient curve x=(t) by a 1-dimensional Brownian motion is shown to satisfy Here r is the probability of eventually hitting the curve and (t)=t ^–1/2(t).