arXiv subjects

Peter Schlagheck

Publications and source records attributed to Peter Schlagheck.

At least 55 records · Page 3Linked to original sources

arXiv2012

Delocalization of ultracold atoms in a disordered potential due to light scattering

We numerically study the expansion dynamics of ultracold atoms in a one-dimensional disordered potential in the presence of a weak position measurement of the atoms. We specifically consider this position measurement to be realized by a combination of an external laser and a periodic array of optical microcavities along a waveguide. The position information is acquired through the scattering of a near-resonant laser photon into a specific eigenmode of one of the cavities. The time evolution of the atomic density in the presence of this light scattering mechanism is described within a Lindblad master equation approach, which is numerically implemented using the Monte Carlo wave function technique. We find that an arbitrarily weak rate of photon emission leads to a breakdown of Anderson localization of the atoms.

cond-mat.quant-gas↗

arXiv2012

Intensity distribution of non-linear scattering states

We investigate the interplay between coherent effects characteristic of the propagation of linear waves, the non-linear effects due to interactions, and the quantum manifestations of classical chaos due to geometrical confinement, as they arise in the context of the transport of Bose-Einstein condensates. We specifically show that, extending standard methods for non-interacting systems, the body of the statistical distribution of intensities for scattering states solving the Gross-Pitaevskii equation is very well described by a local Gaussian ansatz with a position-dependent variance. We propose a semiclassical approach based on interfering classical paths to fix the single parameter describing the universal deviations from a global Gaussian distribution. Being tail effects, rare events like rogue waves characteristic of non-linear field equations do not affect our results.

nlin.CD↗

arXiv2011

Resonance-assisted tunneling in mixed regular-chaotic systems

We present a comprehensive theory of resonance-assisted tunneling in quantum systems that exhibit a mixed regular-chaotic classical phase space structure. After general considerations, we specifically focus on quantum systems with one degree of freedom that are subject to a periodic sequence of kicks or to a periodic driving. Tunneling takes place between energetically degenerate quasimodes that are localized on symmetric regular islands within the stroboscopic Poincare surface of section. In contrast to previous theoretical descriptions of resonance-assisted tunneling, we derive a more precise expression for the effective coupling matrix elements that induce the resonance-assisted tunneling process, and we take into account the influence of partial barriers within the chaotic part of the phase space. Comparison with numerically computed level splittings of eigenphases within the quantum kicked rotor shows very good agreement.

nlin.CD↗

arXiv2010

Effective spin model for interband transport in a Wannier-Stark lattice system

We show that the interband dynamics in a tilted two-band Bose-Hubbard model can be reduced to an analytically accessible spin model in the case of resonant interband oscillations. This allows us to predict the revival time of these oscillations which decay and revive due to inter-particle interactions. The presented mapping onto the spin model and the so achieved reduction of complexity has interesting perspectives for future studies of many-body systems.

quant-ph↗

arXiv2010

Regular-to-Chaotic Tunneling Rates: From the Quantum to the Semiclassical Regime

We derive a prediction of dynamical tunneling rates from regular to chaotic phase-space regions combining the direct regular-to-chaotic tunneling mechanism in the quantum regime with an improved resonance-assisted tunneling theory in the semiclassical regime. We give a qualitative recipe for identifying the relevance of nonlinear resonances in a given $\hbar$-regime. For systems with one or multiple dominant resonances we find excellent agreement to numerics.

nlin.CD↗

arXiv2009

Transport of ultracold Bose gases beyond the Gross-Pitaevskii description

We explore atom-laser-like transport processes of ultracold Bose-condensed atomic vapors in mesoscopic waveguide structures beyond the Gross-Pitaevskii mean-field theory. Based on a microscopic description of the transport process in the presence of a coherent source which models the outcoupling from a reservoir of perfectly Bose-Einstein condensed atoms, we derive a system of coupled quantum evolution equations that describe the dynamics of a dilute condensed Bose gas in the framework of the Hartree-Fock-Bogoliubov approximation. We apply this method to study the transport of dilute Bose gases through an atomic quantum dot and through waveguides with disorder. Our numerical simulations reveal that the onset of an explictly time-dependent flow corresponds to the appearance of strong depletion of the condensate on the microscopic level and leads to a loss of global phase coherence.

cond-mat.quant-gas↗

arXiv2008

Coherent backscattering of Bose-Einstein condensates in two-dimensional disorder potentials

We study quantum transport of an interacting Bose-Einstein condensate in a two-dimensional disorder potential. In the limit of vanishing atom-atom interaction, a sharp cone in the angle-resolved density of the scattered matter wave is observed, arising from constructive interference between amplitudes propagating along reversed scattering paths. Weak interaction transforms this coherent backscattering peak into a pronounced dip, indicating destructive instead of constructive interference. We reproduce this result, obtained from the numerical integration of the Gross-Pitaevskii equation, by a diagrammatic theory of weak localization in presence of a nonlinearity.

cond-mat.other↗

arXiv2007

Nonlinear transport of Bose-Einstein condensates through mesoscopic waveguides

We study the coherent flow of interacting Bose-condensed atoms in mesoscopic waveguide geometries. Analytical and numerical methods, based on the mean-field description of the condensate, are developed to study both stationary as well as time-dependent propagation processes. We apply these methods to the propagation of a condensate through an atomic quantum dot in a waveguide, discuss the nonlinear transmission spectrum and show that resonant transport is generally suppressed due to an interaction-induced bistability phenomenon. Finally, we establish a link between the nonlinear features of the transmission spectrum and the self-consistent quasi-bound states of the quantum dot.

cond-mat.other↗

arXiv2006

Effects of short-range interactions on transport through quantum point contacts: A numerical approach

We study electronic transport through a quantum point contact, where the interaction between the electrons is approximated by a contact potential. Our numerical approach is based on the non-equilibrium Green function technique which is evaluated at Hartree-Fock level. We show that this approach allows us to reproduce relevant features of the so-called "0.7 anomaly" observed in the conductance at low temperatures, including the characteristic features in recent shot noise measurements. This is consistent with a spin-splitting interpretation of the process, and indicates that the "0.7 anomaly" should also be observable in transport experiments with ultracold fermionic atoms.

cond-mat.mes-hall↗

arXiv2006

Nonexponential decay of Bose-Einstein condensates: a numerical study based on the complex scaling method

We study the decay dynamics of an interacting Bose-Einstein condensate in the presence of a metastable trapping potential from which the condensate can escape via tunneling through finite barriers. The time-dependent decay process is reproduced by means of the instantaneous decay rates of the condensate at a given population of the quasi-bound state, which are calculated with the method of complex scaling. Both for the case of a double barrier potential as well as for the case of a tilted periodic potential, we find pronounced deviations from a monoexponential decay behaviour which would generally be expected in the absence of the atom-atom interaction.

cond-mat.other↗

arXiv2006

Influence of classical resonances on chaotic tunnelling

Dynamical tunnelling between symmetry-related stable modes is studied in the periodically driven pendulum. We present strong evidence that the tunnelling process is governed by nonlinear resonances that manifest within the regular phase-space islands on which the stable modes are localized. By means of a quantitative numerical study of the corresponding Floquet problem, we identify the trace of such resonances not only in the level splittings between near-degenerate quantum states, where they lead to prominent plateau structures, but also in overlap matrix elements of the Floquet eigenstates, which reveal characteristic sequences of avoided crossings in the Floquet spectrum. The semiclassical theory of resonance-assisted tunnelling yields good overall agreement with the quantum-tunnelling rates, and indicates that partial barriers within the chaos might play a prominent role.

quant-ph↗

arXiv2006

Resonance-assisted decay of nondispersive wave packets

We present a quantitative semiclassical theory for the decay of nondispersive electronic wave packets in driven, ionizing Rydberg systems. Statistically robust quantities are extracted combining resonance assisted tunneling with subsequent transport across chaotic phase space and a final ionization step.

nlin.CD↗

arXiv2006

Complex scaling approach to the decay of Bose-Einstein condensates

The mean-field dynamics of a Bose-Einstein condensate is studied in presence of a microscopic trapping potential from which the condensate can escape via tunneling through finite barriers. We show that the method of complex scaling can be used to obtain a quantitative description of this decay process. A real-time propagation approach that is applied to the complex-scaled Gross-Pitaevskii equation allows us to calculate the chemical potentials and lifetimes of the metastably trapped Bose-Einstein condensate. The method is applied to a one-dimensional harmonic confinement potential combined with a Gaussian envelope, for which we compute the lowest symmetric and antisymmetric quasibound states of the condensate. A comparison with alternative approaches using absorbing boundary conditions as well as complex absorbing potentials shows good agreement.

cond-mat.soft↗

arXiv2005

Tunnelling rates for the nonlinear Wannier-Stark problem

We present a method to numerically compute accurate tunnelling rates for a Bose-Einstein condensate which is described by the nonlinear Gross-Pitaevskii equation. Our method is based on a sophisticated real-time integration of the complex-scaled Gross-Pitaevskii equation, and it is capable of finding the stationary eigenvalues for the Wannier-Stark problem. We show that even weak nonlinearities have significant effects in the vicinity of very sensitive resonant tunnelling peaks, which occur in the rates as a function of the Stark field amplitude. The mean-field interaction induces a broadening and a shift of the peaks, and the latter is explained by analytic perturbation theory.

cond-mat.other↗

arXiv2005

Nonlinear Transport of Bose-Einstein Condensates Through Waveguides with Disorder

We study the coherent flow of a guided Bose-Einstein condensate incident over a disordered region of length L. We introduce a model of disordered potential that originates from magnetic fluctuations inherent to microfabricated guides. This model allows for analytical and numerical studies of realistic transport experiments. The repulsive interaction among the condensate atoms in the beam induces different transport regimes. Below some critical interaction (or for sufficiently small L) a stationary flow is observed. In this regime, the transmission decreases exponentially with L. For strong interaction (or large L), the system displays a transition towards a time dependent flow with an algebraic decay of the time averaged transmission.

cond-mat.other↗

arXiv2005

Resonance- and Chaos-Assisted Tunneling

We consider dynamical tunneling between two symmetry-related regular islands that are separated in phase space by a chaotic sea. Such tunneling processes are dominantly governed by nonlinear resonances, which induce a coupling mechanism between ``regular'' quantum states within and ``chaotic'' states outside the islands. By means of a random matrix ansatz for the chaotic part of the Hamiltonian, one can show that the corresponding coupling matrix element directly determines the level splitting between the symmetric and the antisymmetric eigenstates of the pair of islands. We show in detail how this matrix element can be expressed in terms of elementary classical quantities that are associated with the resonance. The validity of this theory is demonstrated with the kicked Harper model.

nlin.CD↗

arXiv2004

Resonance- and chaos-assisted tunneling in mixed regular-chaotic systems

We present evidence that nonlinear resonances govern the tunneling process between symmetry-related islands of regular motion in mixed regular-chaotic systems.In a similar way as for near-integrable tunneling, such resonances induce couplings between regular states within the islands and states that are supported by the chaotic sea. On the basis of this mechanism, we derive a semiclassical expression for the average tunneling rate, which yields good agreement in comparison with the exact quantum tunneling rates calculated for the kicked rotor and the kicked Harper.

nlin.CD↗

arXiv2004

Nonlinear Resonant Transport of Bose Einstein Condensates

The coherent flow of a Bose-Einstein condensate through a quantum dot in a magnetic waveguide is studied. By the numerical integration of the time-dependent Gross-Pitaevskii equation in presence of a source term, we simulate the propagation process of the condensate through a double barrier potential in the waveguide. We find that resonant transport is suppressed in interaction-induced regimes of bistability, where multiple scattering states exist at the same chemical potential and the same incident current. We demonstrate, however, that a temporal control of the external potential can be used to circumvent this limitation and to obtain enhanced transmission near the resonance on experimentally realistic time scales.

cond-mat.other↗