arXiv subjects

Martin Holthaus

Publications and source records attributed to Martin Holthaus.

At least 37 records · Page 2Linked to original sources

arXiv2015

Hypergeometric analytic continuation of the strong-coupling perturbation series for the 2d Bose-Hubbard model

We develop a scheme for analytic continuation of the strong-coupling perturbation series of the pure Bose-Hubbard model beyond the Mott insulator-to-superfluid transition at zero temperature, based on hypergeometric functions and their generalizations. We then apply this scheme for computing the critical exponent of the order parameter of this quantum phase transition for the two-dimensional case, which falls into the universality class of the three-dimensional $XY$ model. This leads to anontrivial test of the universality hypothesis.

cond-mat.stat-mech↗

arXiv2015

Emergence and destruction of macroscopic wave functions

The concept of the macroscopic wave function is a key for understanding macroscopic quantum phenomena. The existence of this object reflects a certain order, as is present in a Bose-Einstein condensate when a single-particle orbital is occupied by a macroscopic number of bosons. We extend these ideas to situations in which a condensate is acted on by an explicitly time-dependent force. While one might assume that such a force would necessarily degrade any pre-existing order, we demonstrate that macroscopic wave functions can persist even under strong forcing. Our definition of the time-dependent order parameter is based on a comparison of the evolution of $N$-particle states on the one hand, and of states with $N - 1$ particles on the other. Our simulations predict the possibility of an almost instantaneous dynamical destruction of a macroscopic wave function under currently accessible experimental conditions.

cond-mat.quant-gas↗

arXiv2014

Quasiparticle tunneling in a periodically driven bosonic Josephson junction

A resonantly driven bosonic Josephson junction supports stable collective excitations, or quasiparticles, which constitute analogs of the Trojan wave packets previously explored with Rydberg atoms in strong microwave fields. We predict a quantum beating effect between such symmetryrelated many-body Trojan states taking place on time scales which are long in comparison with the driving period. Within a mean-field approximation, this quantum beating can be regarded as a manifestation of dynamical tunneling. On the full N-particle level, the beating phenomenon leads to an experimentally feasible, robust strategy for probing highly entangled mesoscopic states.

cond-mat.quant-gas↗

arXiv2014

Fluctuations of the order parameter of a mesoscopic Floquet condensate

We suggest that nonequilibrium Bose-Einstein condensates may occur in time-periodically driven interacting Bose gases. Employing the model of a periodically forced bosonic Josephson junction, we demonstrate that resonance-induced ground state-like many-particle Floquet states possess an almost perfect degree of coherence, as corresponding to a mesoscopically occupied, explicitly time-dependent single-particle orbital. In marked contrast to the customary time-independent Bose-Einstein condensates, the order parameter of such systems is destroyed by violent fluctuations when the particle number becomes too large, signaling the non-existence of a proper mean field limit.

cond-mat.quant-gas↗

arXiv2014

Trojan quasiparticles

We argue that a time-periodically driven bosonic Josephson junction supports stable, quasi-particle-like collective response modes which are $N$-particle analogs of the nonspreading Trojan wave packets known from microwave-driven Rydberg atoms. Similar to their single-particle counterparts, these collective modes, dubbed "flotons", are well described by a Floquet-Mathieu approximation, and possess a well-defined discrete set of excitations. In contrast to other, "chaotic" modes of response, the nonheating Trojan modes conform to a mean-field description, and thus may be of particular interest for the more general question under which conditions the reduction of quantum $N$-particle dynamics to a strongly simplified mean-field evolution is feasible. Our reasoning is supported by phase-space portraits which reveal the degree of correspondence beween the $N$-particle dynamics und the mean-field picture in an intuitive manner.

cond-mat.quant-gas↗

arXiv2014

Perturbative calculation of critical exponents for the Bose-Hubbard model

We develop a strategy for calculating critical exponents for the Mott insulator-to-superfluid transition shown by the Bose-Hubbard model. Our approach is based on the field-theoretic concept of the effective potential, which provides a natural extension of the Landau theory of phase transitions to quantum critical phenomena. The coefficients of the Landau expansion of that effective potential are obtained by high-order perturbation theory. We counteract the divergency of the weak-coupling perturbation series by including the seldom considered Landau coefficient $a_6$ into our analysis. Our preliminary results indicate that the critical exponents for both the condensate density and the superfluid density, as derived from the two-dimensional Bose-Hubbard model, deviate by less than $1\%$ from the best known estimates computed so far for the three-dimensional $XY$ universality class.

quant-ph↗

arXiv2014

Energy flow in periodic thermodynamics

A key quantity characterizing a time-periodically forced quantum system coupled to a heat bath is the energy flowing in the steady state through the system into the bath, where it is dissipated. We derive a general expression which allows one to compute this energy dissipation rate for a heat bath consisting of a large number of harmonic oscillators, and work out two analytically solvable model examples. In particular, we distinguish between genuine transitions effectuating a change of the systems's Floquet state, and pseudo-transitions preserving that state; the latter are shown to yield an important contribution to the total dissipation rate. Our results suggest possible driving-mediated heating and cooling schemes on the quantum level. They also indicate that a driven system does not necessarily occupy only a single Floquet state when being in contact with a zero-temperature bath.

quant-ph↗

arXiv2012

ac Stark shift and multiphoton-like resonances in low-frequency driven optical lattices

We suggest that Bose-Einstein condensates in optical lattices subjected to ac forcing with a smooth envelope may provide detailed experimental access to multiphoton-like transitions between ac-Stark-shifted Bloch bands. Such transitions correspond to resonances described theoretically by avoided quasienergy crossings. We show that the width of such anticrossings can be inferred from measurements involving asymmetric pulses. We also introduce a pulse tracking strategy for locating the particular driving amplitudes for which resonances occur. Our numerical calculations refer to a currently existing experimental set-up [Haller et al., PRL 104, 200403 (2010)].

cond-mat.quant-gas↗

arXiv2012

Kilohertz-driven Bose-Einstein condensates in optical lattices

We analyze time-of-flight absorption images obtained with dilute Bose-Einstein con-densates released from shaken optical lattices, both theoretically and experimentally. We argue that weakly interacting, ultracold quantum gases in kilohertz-driven optical potentials constitute equilibrium systems characterized by a steady-state distri-bution of Floquet-state occupation numbers. Our experimental results consistently indicate that a driven ultracold Bose gas tends to occupy a single Floquet state, just as it occupies a single energy eigenstate when there is no forcing. When the driving amplitude is sufficiently high, the Floquet state possessing the lowest mean energy does not necessarily coincide with the Floquet state connected to the ground state of the undriven system. We observe strongly driven Bose gases to condense into the former state under such conditions, thus providing nontrivial examples of dressed matter waves.

cond-mat.quant-gas↗

arXiv2011

Controlled wave-packet manipulation with driven optical lattices

Motivated by recent experimental progress achieved with ultracold atoms in kilohertz-driven optical lattices, we provide a theoretical discussion of mechanisms governing the response of a particle in a cosine lattice potential to strong forcing pulses with smooth envelope. Such pulses effectuate adiabatic motion of a wave packet's momentum distribution on quasienergy surfaces created by spatiotemporal Bloch waves. Deviations from adiabaticity can then deliberately be exploited for exerting coherent control and for reaching target states which may not be accessible by other means. As one particular example, we consider an analog of the π-pulses known from optical resonance. We also suggest adapting further techniques previously developed for controlling atomic and molecular dynamics by laser pulses to the coherent control of matter waves in shaken optical lattices.

cond-mat.quant-gas↗

arXiv2011

Generalized acceleration theorem for spatiotemporal Bloch waves

A representation is put forward for wave functions of quantum particles in periodic lattice potentials subjected to homogeneous time-periodic forcing, based on an expansion with respect to Bloch-like states which embody both the spatial and the temporal periodicity. It is shown that there exists a generalization of Bloch's famous acceleration theorem which grows out of this representation and captures the effect of a weak probe force applied in addition to a strong dressing force. Taken together, these elements point at a "dressing and probing" strategy for coherent wave-packet manipulation, which could be implemented in present experiments with optical lattices.

cond-mat.quant-gas↗

arXiv2011

Perturbation theory for plasmonic eigenvalues

We develop a perturbative approach for calculating, within the quasistatic approximation, the shift of surface resonances in response to a deformation of a dielectric volume. Our strategy is based on the conversion of the homogeneous system for the potential which determines the plasmonic eigenvalues into an inhomogeneous system for the potential's derivative with respect to the deformation strength, and on the exploitation of the corresponding compatibility condition. The resulting general expression for the first-order shift is verified for two explicitly solvable cases, and for a realistic example of a deformed nanosphere. It can be used for scanning the huge parameter space of possible shape fluctuations with only quite small computational effort.

cond-mat.mes-hall↗

arXiv2011

Shape-dependence of near-field heat transfer between a spheroidal nanoparticle and a flat surface

We study the radiative heat transfer between a spheroidal metallic nanoparticle and a planar metallic sample for near- and far-field distances. In particular, we investigate the shape dependence of the heat transfer in the near-field regime. In comparison with spherical particles, the heat transfer typically varies by factors between 1/2 and 2 when the particle is deformed such that its volume is kept constant. These estimates help to quantify the deviation of the actual heat transfer recorded by a near-field scanning thermal microscope from the value provided by a dipole model which assumes a perfectly spherical sensor.

cond-mat.mes-hall↗

arXiv2011

Dynamic Localization in Optical Lattices

We recapitulate the principle enabling the phenomenon of dynamic localization, and provide model calculations for ultracold atoms in driven optical lattices which indicate that the localization effect remains almost unaffected by interband transitions if the parameters are chosen carefully. In addition, we suggest to exploit the underlying quasienergy band collapse for coherently controlling the metal-insulator transition that occurs in the Harper model, as realized with quasiperiodic optical lattices.

cond-mat.quant-gas↗

arXiv2011

Spheroidal nanoparticles as thermal near-field sensors

We suggest to exploit the shape-dependence of the near-field heat transfer for nanoscale thermal imaging. By utilizing strongly prolate or oblate nanoparticles as sensors one can assess individual components of the correlation tensors characterizing the thermal near field close to a nanostructured surface, and thus obtain directional information beyond the local density of states. Our theoretical considerations are backed by idealized numerical model calculations.

cond-mat.mes-hall↗

arXiv2011

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

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 Green's functions. Based on these, general expressions are derived for both the system's 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 film's 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 film's low-frequency surface plasmon polariton. Our results also serve as reference for current near-field experiments which search for deviations from the macroscopic approach.

cond-mat.mes-hall↗

arXiv2011

Second-order calculation of the local density of states above a nanostructured surface

We have numerically implemented a perturbation series for the scattered electromagnetic fields above rough surfaces, due to Greffet, allowing us to evaluate the local density of states to second order in the surface profile function. We present typical results for thermal near fields of surfaces with regular nanostructures, investigating the relative magnitude of the contributions appearing in successive orders. The method is then employed for estimating the resolution limit of an idealized Near-Field Scanning Thermal Microscope (NSThM).

cond-mat.mes-hall↗

arXiv2011

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 corresponding 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.

cond-mat.mes-hall↗