Relativistic and QED effects in the fundamental vibration of T2_2

The hydrogen molecule has become a test ground for quantum electrodynamical calculations in molecules. Expanding beyond studies on stable hydrogenic species to the heavier radioactive tritium-bearing molecules, we report on a measurement of the fundamental T$_2$ vibrational splitting $(v= 0 \rightarrow 1)$ for $J=0-5$ rotational levels. Precision frequency metrology is performed with high-resolution coherent anti-Stokes Raman spectroscopy at an experimental uncertainty of $10-12$~MHz, where sub-Doppler saturation features are exploited for the strongest transition. The achieved accuracy corresponds to a fifty-fold improvement over a previous measurement, and allows for the extraction of relativistic and QED contributions to T$_2$ transition energies.Comment: 5 pages, 5 figure

Optimisation of on-line principal component analysis

Different techniques, used to optimise on-line principal component analysis, are investigated by methods of statistical mechanics. These include local and global optimisation of node-dependent learning-rates which are shown to be very efficient in speeding up the learning process. They are investigated further for gaining insight into the learning rates' time-dependence, which is then employed for devising simple practical methods to improve training performance. Simulations demonstrate the benefit gained from using the new methods.Comment: 10 pages, 5 figure

Acoustic characterization of Hofstadter butterfly with resonant scatterers

We are interested in the experimental characterization of the Hofstadter butterfly by means of acoustical waves. The transmission of an acoustic pulse through an array of 60 variable and resonant scatterers periodically distribued along a waveguide is studied. An arbitrary scattering arrangement is realized by using the variable length of each resonator cavity. For a periodic modulation, the structures of forbidden bands of the transmission reproduce the Hofstadter butterfly. We compare experimental, analytical, and computational realizations of the Hofstadter butterfly and we show the influence of the resonances of the scatterers on the structure of the butterfly

Hysteresis effect due to the exchange Coulomb interaction in short-period superlattices in tilted magnetic fields

We calculate the ground-state of a two-dimensional electron gas in a short-period lateral potential in magnetic field, with the Coulomb electron-electron interaction included in the Hartree-Fock approximation. For a sufficiently short period the dominant Coulomb effects are determined by the exchange interaction. We find numerical solutions of the self-consistent equations that have hysteresis properties when the magnetic field is tilted and increased, such that the perpendicular component is always constant. This behavior is a result of the interplay of the exchange interaction with the energy dispersion and the spin splitting. We suggest that hysteresis effects of this type could be observable in magneto-transport and magnetization experiments on quantum-wire and quantum-dot superlattices.Comment: 3 pages, 3 figures, Revtex, to appear in Phys. Rev.

Quantum Hall Effect on the Hofstadter Butterfly

Motivated by recent experimental attempts to detect the Hofstadter butterfly, we numerically calculate the Hall conductivity in a modulated two-dimensional electron system with disorder in the quantum Hall regime. We identify the critical energies where the states are extended for each of butterfly subbands, and obtain the trajectory as a function of the disorder. Remarkably, we find that when the modulation becomes anisotropic, the critical energy branches accompanying a change of the Hall conductivity.Comment: 4 pages, 6 figure

Ultra-stable implanted 83Rb/83mKr electron sources for the energy scale monitoring in the KATRIN experiment

The KATRIN experiment aims at the direct model-independent determination of the average electron neutrino mass via the measurement of the endpoint region of the tritium beta decay spectrum. The electron spectrometer of the MAC-E filter type is used, requiring very high stability of the electric filtering potential. This work proves the feasibility of implanted 83Rb/83mKr calibration electron sources which will be utilised in the additional monitor spectrometer sharing the high voltage with the main spectrometer of KATRIN. The source employs conversion electrons of 83mKr which is continuously generated by 83Rb. The K-32 conversion line (kinetic energy of 17.8 keV, natural line width of 2.7 eV) is shown to fulfill the KATRIN requirement of the relative energy stability of +/-1.6 ppm/month. The sources will serve as a standard tool for continuous monitoring of KATRIN's energy scale stability with sub-ppm precision. They may also be used in other applications where the precise conversion lines can be separated from the low energy spectrum caused by the electron inelastic scattering in the substrate.Comment: 30 pages, 10 figures, 1 table, minor revision of the preprint, accepted by JINST on 5.2.201

Monitoring of tritium purity during long-term circulation in the KATRIN test experiment LOOPINO using laser Raman spectroscopy

The gas circulation loop LOOPINO has been set up and commissioned at Tritium Laboratory Karlsruhe (TLK) to perform Raman measurements of circulating tritium mixtures under conditions similar to the inner loop system of the neutrino-mass experiment KATRIN, which is currently under construction. A custom-made interface is used to connect the tritium containing measurement cell, located inside a glove box, with the Raman setup standing on the outside. A tritium sample (purity > 95%, 20 kPa total pressure) was circulated in LOOPINO for more than three weeks with a total throughput of 770 g of tritium. Compositional changes in the sample and the formation of tritiated and deuterated methanes CT_(4-n)X_n (X=H,D; n=0,1) were observed. Both effects are caused by hydrogen isotope exchange reactions and gas-wall interactions, due to tritium {\beta} decay. A precision of 0.1% was achieved for the monitoring of the T_2 Q_1-branch, which fulfills the requirements for the KATRIN experiment and demonstrates the feasibility of high-precision Raman measurements with tritium inside a glove box

A Laterally Modulated 2D Electron System in the Extreme Quantum Limit

We report on magnetotransport of a two-dimensional electron system (2DES), located 32 nm below the surface, with a surface superlattice gate structure of periodicity 39 nm imposing a periodic modulation of its potential. For low Landau level fillings $\nu$, the diagonal resistivity displays a rich pattern of fluctuations, even though the disorder dominates over the periodic modulation. Theoretical arguments based on the combined effects of the long-wavelength, strong disorder and the short-wavelength, weak periodic modulation present in the 2DES qualitatively explain the data.Comment: 4 pages, 5 figures. to appear in Phys. Rev. Let

Quantum Hall effect in a p-type heterojunction with a lateral surface quantum dot superlattice

The quantization of Hall conductance in a p-type heterojunction with lateral surface quantum dot superlattice is investigated. The topological properties of the four-component hole wavefunction are studied both in r- and k-spaces. New method of calculation of the Hall conductance in a 2D hole gas described by the Luttinger Hamiltonian and affected by lateral periodic potential is proposed, based on the investigation of four-component wavefunction singularities in k-space. The deviations from the quantization rules for Hofstadter "butterfly" for electrons are found, and the explanation of this effect is proposed. For the case of strong periodic potential the mixing of magnetic subbands is taken into account, and the exchange of the Chern numbers between magnetic subands is discussed.Comment: 12 pages, 5 figures; reported at the 15th Int. Conf. on High Magnetic Fields in Semicond. Phys. (Oxford, UK, 2002