Martin Holthaus

Near-field heat transfer in a scanning thermal microscope

We present measurements of the near-field heat transfer between the tip of a thermal profiler and planar material surfaces under ultrahigh vacuum conditions. For tip-sample distances below 10(-8) m, our results differ markedly from the prediction of fluctuating electrodynamics. We argue that these differences are due to the existence of a material-dependent small length scale below which the macroscopic description of the dielectric properties fails, and discuss a heuristic model which yields fair agreement with the available data. These results are of importance for the quantitative interpretation of signals obtained by scanning thermal microscopes capable of detecting local temperature variations on surfaces.

Superfluid-insulator transition in a periodically driven optical lattice.

We demonstrate that the transition from a superfluid to a Mott insulator in the Bose-Hubbard model can be induced by an oscillating force through an effective renormalization of the tunneling matrix element. The mechanism involves adiabatic following of Floquet states, and can be tested experimentally with Bose-Einstein condensates in periodically driven optical lattices. Its extension from small to very large systems yields nontrivial information on the condensate dynamics.

ON BOSE-EINSTEIN CONDENSATION IN HARMONIC TRAPS

Abstract Assuming the validity of grand canonical statistics, we study Bose-Einstein condensation of relatively small numbers of particles confined by a harmonic potential. Corrections to the case of large particle numbers appear as a downward shift of the condensation temperature T C and an enhancement of the specific heat capacity below T C . Even if the particle number is merely of order 10 4 , the specific heat capacity exhibits a sharp drop at the onset of condensation, reminiscent of the heat capacity of liquid 4 He at the λ-point.

Analog of photon-assisted tunneling in a Bose-Einstein condensate.

We study many-body tunneling of a small Bose-Einstein condensate in a periodically modulated, tilted double-well potential. Periodic modulation of the trapping potential leads to an analog of photon-assisted tunneling, with distinct signatures of the interparticle interaction visible in the amount of particles transferred from one well to the other. In particular, under experimentally accessible conditions there exist well-developed half-integer Shapiro-like resonances.

Exploring dynamic localization with a Bose-Einstein condensate

We report on the experimental observation of dynamic localization of a Bose-Einstein condensate in a shaken optical lattice, both for sinusoidal and square-wave forcing. The formulation of this effect in terms of a quasienergy band collapse, backed by the excellent agreement of the observed collapse points with the theoretical predictions, suggests the feasibility of systematic quasienergy band engineering.

Improved variational principle for bounds on energy dissipation in turbulent shear flow

We extend the Doering-Constantin approach to upper bounds on energy dissipation in turbulent flows by introducing a balance parameter into the variational principle. This parameter governs the relative weight of different contributions to the dissipation rate. Its optimization leads to improved bounds without entailing additional technical difficulties. For plane Couette flow, the high-Re-bounds obtainable with one-dimensional background flows are methodically lowered by a factor of 2732.

Adiabatic processes in the ionization of highly excited hydrogen atoms

Adiabatic and non-adiabatic processes in the dynamics of periodically driven quantum systems are studied employing the Floquet picture of quantum mechanics. The validity ofN-niveau approximations in the Floquet theory is investigated. A method is described which allows the separation of fast (periodic) and slow (parametric) time-dependence and which yields a transparent description of the dynamical Landau-Zener mechanism. Using the model of surface-state electrons it is demonstrated that adiabaticity is decisive for the description of ionization experiments on highly excited hydrogen atoms; furthermore, an ionization mechanism based on the sudden onset of Landau-Zener transitions is proposed and shown to yield values for the ionization threshold which are in good agreement with experimental data. The connection to classical mechanics is considered by establishing the semiclassical limit of Floquet dynamics.

The quantum theory of an ideal superlattice responding to far-infrared laser radiation

Minibands of quasienergies can be defined for a superlattice interacting with far-infrared laser radiation. It is demonstrated that the width of these quasienergy minibands depends not only on the parameters of the superlattice, but also on strength and frequency of the driving laser field. In particular, the width approaches zero at certain values of these parameters. A strong coupling ansatz, combined with perturbation theory for degenerate quasienergy states, leads to a detailed understanding of these results.

A semiclassical theory of quasienergies and Floquet wave functions

Abstract Employing the Maslov construction of the canonical operator, we derive semiclassical quantization rules for quasienergies and Floquet states of periodically time-dependent systems. The method is applied to a class of strongly driven anharmonic oscillators which, on the classical level, show a sharp division of the phase space into an almost regular and a stochastic region. For the almost regular part of motion the semiclassical quantization rules are shown to yield excellent approximations to the exact quantum mechanical quasienergies and Floquet states. The influence of resonances and stochastic motion on quasienergy spectra and Floquet wave functions is discussed. We demonstrate that an exact scaling relation valid for the classical Hamiltonian leads to an approximate scaling relation for the quasienergies which is broken in a characteristic manner by quantum effects.

Thermal radiation and near-field energy density of thin metallic films

Abstract. We study the properties of thermal radiation emitted by a thin dielectric slab, employing the framework of macroscopic fluctuational electrodynamics. Particular emphasis is given to the analytical construction of the required dyadic Greens functions. Based on these, general expressions are derived for both the systems Poynting vector, describing the intensity of propagating radiation, and its energy density, containing contributions from non-propagating modes which dominate the near-field regime. An extensive discussion is then given for thin metal films. It is shown that the radiative intensity is maximized for a certain film thickness, due to Fabry-Perot-like multiple reflections inside the film. The dependence of the near-field energy density on the distance from the films surface is governed by an interplay of several length scales, and characterized by different exponents in different regimes. In particular, this energy density remains finite even for arbitrarily thin films. This unexpected feature is associated with the films low-frequency surface plasmon polariton. Our results also serve as reference for current near-field experiments which search for deviations from the macroscopic approach.