Scaling Properties of Energy Gap in Dimerized Spinless Fermion Chains with Quasiperiodic Modulation

By employing the exact diagonalization method, we investigate the low-energy benavlour ot the almenzed spinless fermion chains with quasiperiodic modulation. It is found that for off-diagonal modulation, the energy gap with length N scales as exp（-cN^ω） with nonuniversal exponent ω if the dimerization is nonzero. However, for diagonal modulation, there may exist a critical dimerization δc beyond which the system exhibits a metal-insulator transition.     

A transportable optical calcium frequency standardDedicated to J. Helmcke on the occasion of his 60th birthday.

-12 . Received: 15 October 1998     

Wide- and narrow-band saturated fluorescence measurements of hydroxyl concentration in premixed flames from 1 bar to 10 bar

We have studied the use of wide-band detection in conjunction with saturation of a rovibronic transition of OH within itsA ^{2 +}–X ²(0,0) band. For wide-band detection, in which fluorescence is detected from the entire excited rotational manifold, the fluorescence yield is sensitive to collisions in two ways. First, it is sensitive to the ratio of rate coefficients describing rotational energy transfer and electronic quenching; this ratio determines the number of neighboring rotational levels that are populated during the laser pulse. Second, the fluorescence yield can vary with the total collisional rate coefficient; only after a sufficient number of collisions, corresponding to 2.5 ns in an atmospheric flame, does the rotational manifold reach steady state. We also compare measurements employing wide-band (detecting theR ₁ andR ₂ branches) and narrow-band (detecting a single transition) saturated fluorescence of OH. Over a wide range of conditions — obtained by varying the equivalence ratio, temperature, N₂ dilution, and pressure — the wide- and narrow-band fluorescence techniques compare well. Given this good agreement, wide-band saturated fluorescence could be especially useful for analyzing atmospheric flames with XeCl-excimer lasers; one can potentially obtain 2—D images of OH which have a high signal-to-noise ratio and a reduced sensitivity to laser irradiance and quenching.     

Minimum description of the onset of pipe turbulence

To demonstrate essentials of the mechanism for the onset of turbulence in a pipe at Re=2000, 48 degrees of freedom are enough. The derivation from the Navier-Stokes equation uses a novel type of modes which guarantee linear stability. For the reduction of the nonlinear interactions, the modes are grouped in 3 blocks. Facilitated by these simplifications the interdependence between linear and nonlinear processes is analysed, however, just for a special example. A phenomenon resembling backflow is identified. Received 20 October 1997     

Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation

The shortest pulses periodically emitted directly from a mode-locked Ti:sapphire laser are approaching the two-optical-cycle range. In this region, the phase of the optical carrier with respect to the pulse envelope becomes important in nonlinear optical processes such as high-harmonic generation. Because there are no locking mechanisms between envelope and carrier inside a laser, their relative phase offset experiences random fluctuations. Here, we propose several novel methods to measure and to stabilize this carrier-envelope offset (CEO) phase with sub-femtosecond uncertainty. The stabilization methods are an important prerequisite for attosecond pulse generation schemes. Short and highly periodic pulses of a two-cycle laser correspond to an extremely wide frequency comb of equally spaced lines, which can be used for absolute frequency measurements. Using the proposed phase-measurement methods, it will be possible to phase-coherently link any unknown optical frequency within the comb spectrum to a primary microwave standard. Experimental studies using a sub-6-fs Ti:sapphire laser suggesting the feasibility of carrier-envelope phase control are presented. Received: 19 August 1999 / Published online: 8 September 1999     

Cesium saturation spectroscopy revisited: How to reverse peaks and observe narrow resonances

The complex magnetic structure of the cesium atom is responsible for the interesting behaviour of its saturated absorption spectra, e.g., a two-fold sign reversal of a crossover resonance, under various polarization configurations with and without applied magnetic fields. We show that this morphology is a result of optical pumping processes including coherent population trapping which, under normal laboratory conditions, prevent the atoms from reaching an equilibrium situation. Our interpretation is useful for an intuitive and rapid understanding of this important tool in high-resolution spectroscopy.     

High-resolution spectroscopy with laser-cooled and trapped calcium atoms

We report on high-resolution spectroscopy with two different samples of calcium atoms, in a laser-cooled and deflected beam and in a magneto-optical trap. The atomic beam was excited by spatially separated laser fields. For spectroscopy with stored atoms in a magneto-optical trap we used a multiple-pulse excitation scheme. The resolution as low as 2.5 kHz was limited by residual frequency fluctuations of our dye-laser spectrometer. The results should allow to establish a frequency standard with a relative uncertainty below 10^–14.     

Instabilities developed in stratified flows over pronounced obstacles

In the present work we study numerical and experimentally the flow of a two-layer stratified fluid over a topographic obstacle. The problem reflects a wide number of oceanographic and meteorological situations, where the stratification plays an important role. We identify the different instabilities developed by studying the pycnocline deformation due to a pronounced obstacle. The numerical simulations were made using the model caffa3D.MB which works with a numerical model of Navier-Stokes equations with finite volume elements in curvilinear meshes. The experimental results are contrasted with numerical simulations. Linear stability analysis predictions are checked with particle image velocimetry (PIV) measurements.     

Absolute-frequency measurement of the iodine-based length standard at 514.67 nm

The absolute frequency of the length standard at 514.67 nm based on the molecular iodine (¹²⁷ I ₂) transition of the P(13) 43-0 component a₃ is measured using a self-referenced femtosecond optical comb. This frequency-based technique improves measurement precision more than 100 times compared with previous wavelength-based results. Power- and pressure-related frequency shifts have been carefully studied. The measured absolute frequency is 71.8±1.5 kHz higher than the internationally accepted value of 582490603.37±0.15 MHz, adopted by the Comité International des Poids et Mesures (CIPM) in 1997. Received: 7 March 2002 / Published online: 24 April 2002     

Absolute frequency measurements and comparisons in iodine at 735 nm and 772 nm

We report frequency measurements at the rovibronic transition P(42)1-14 (772 nm) and R(114)2-11 (735 nm) from the electronic transition of the iodine molecule ¹²⁷I₂ with the help of a frequency comb as a reference. By using Doppler-free saturation spectroscopy a frequency precision in the 7 × 10⁻¹⁰ region is reached and two iodine cells both operated at 550-600 °C are compared. To relate our results to other measurements, the absolute transition frequency of the hyperfine structure line P(148)1-14 a₁ at 780 nm with an already known transition frequency was also determined.