Quantum transport and localization in biased periodic structures under bi- and polychromatic driving

We consider the dynamics of a quantum particle in a one-dimensional periodic potential (lattice) under the action of a static and time-periodic field. The analysis is based on a nearest-neighbor tight-binding model which allows a convenient closed form description of the transport properties in terms of generalized Bessel functions. The case of bichromatic driving is analyzed in detail and the intricate transport and localization phenomena depending on the communicability of the two excitation frequencies and the Bloch frequency are discussed. The case of polychromatic driving is also discussed, in particular for flipped static fields, i.e. rectangular pulses, which can support an almost dispersionless transport with a velocity independent of the field amplitude.Comment: 18 pages, 11 figur

Beyond mean-field dynamics of small Bose-Hubbard systems based on the number-conserving phase space approach

The number-conserving quantum phase space description of the Bose-Hubbard model is discussed for the illustrative case of two and three modes, as well as the generalization of the two-mode case to an open quantum system. The phase-space description based on generalized SU(M) coherent states yields a Liouvillian flow in the macroscopic limit, which can be efficiently simulated using Monte Carlo methods even for large systems. We show that this description clearly goes beyond the common mean-field limit. In particular it resolves well-known problems where the common mean-field approach fails, like the description of dynamical instabilities and chaotic dynamics. Moreover, it provides a valuable tool for a semi-classical approximation of many interesting quantities, which depend on higher moments of the quantum state and are therefore not accessible within the common approach. As a prominent example, we analyse the depletion and heating of the condensate. A comparison to methods ignoring the fixed particle number shows that in this case artificial number fluctuations lead to ambiguities and large deviations even for quite simple examples.Comment: Significantly enhanced and revised version (20 pages, 20 figures

Bloch oscillations of Bose-Einstein condensates: Breakdown and revival

We investigate the dynamics of Bose-Einstein condensates (BEC) in a tilted one-dimensional periodic lattice within the mean-field (Gross-Pitaevskii) description. Unlike in the linear case the Bloch oscillations decay because of nonlinear dephasing. Pronounced revival phenomena are observed. These are analyzed in detail in terms of a simple integrable model constructed by an expansion in Wannier-Stark resonance states. We also briefly discuss the pulsed output of such systems for stronger static fields.Comment: RevTeX4, 9 pages, 14 figure

Global Phase Space of Coherence and Entanglement in a double-well BEC

Ultracold atoms provide an ideal system for the realization of quantum technologies, but also for the study of fundamental physical questions such as the emergence of decoherence and classicality in quantum many-body systems. Here, we study the global structure of the quantum dynamics of bosonic atoms in a double-well trap and analyze the conditions for the generation of many-particle entanglement and spin squeezing which have important applications in quantum metrology. We show how the quantum dynamics is determined by the phase space structure of the associated mean-field system and where true quantum features arise beyond this `classical' approximation

Bose-Einstein condensates in accelerated double-periodic optical lattices: Coupling and Crossing of resonances

We study the properties of coupled linear and nonlinear resonances. The fundamental phenomena and the level crossing scenarios are introduced for a nonlinear two-level system with one decaying state, describing the dynamics of a Bose-Einstein condensate in a mean-field approximation (Gross-Pitaevskii or nonlinear Schroedinger equation). An important application of the discussed concepts is the dynamics of a condensate in tilted optical lattices. In particular the properties of resonance eigenstates in double-periodic lattices are discussed, in the linear case as well as within mean-field theory. The decay is strongly altered, if an additional period-doubled lattice is introduced. Our analytic study is supported by numerical computations of nonlinear resonance states, and future applications of our findings for experiments with ultracold atoms are discussed.Comment: 12 pages, 17 figure

Nonlinear resonant tunneling of Bose-Einstein condensates in tilted optical lattices

We study the tunneling decay of a Bose-Einstein condensate out of tilted optical lattices within the mean-field approximation. We introduce a novel method to calculate also excited resonance eigenstates of the Gross-Pitaevskii equation, based on a grid relaxation procedure with complex absorbing potentials. This algorithm works efficiently in a wide range of parameters where established methods fail. It allows us to study the effects of the nonlinearity in detail in the regime of resonant tunneling, where the decay rate is enhanced by resonant coupling to excited unstable states.Comment: Revised and enlarged version, including 1 additional figur

Exact number conserving phase-space dynamics of the M-site Bose-Hubbard model

The dynamics of M-site, N-particle Bose-Hubbard systems is described in quantum phase space constructed in terms of generalized SU(M) coherent states. These states have a special significance for these systems as they describe fully condensed states. Based on the differential algebra developed by Gilmore, we derive an explicit evolution equation for the (generalized) Husimi-(Q)- and Glauber-Sudarshan-(P)-distributions. Most remarkably, these evolution equations turn out to be second order differential equations where the second order terms scale as 1/N with the particle number. For large N the evolution reduces to a (classical) Liouvillian dynamics. The phase space approach thus provides a distinguished instrument to explore the mean-field many-particle crossover. In addition, the thermodynamic Bloch equation is analyzed using similar techniques.Comment: 11 pages, Revtex

Mütterliche posttraumatische Belastungsreaktion nach der Geburt eines sehr kleinen Frühgeborenen

Als bisher einzige prospektive Längsschnittuntersuchung wurde in dieser Studie das traumatische Erleben einer Frühgeburt seitens der Mutter erforscht. Zu drei Messzeitpunkten innerhalb der ersten drei Tage, vierzehn Tage und sechs Monate nach der Geburt wurde jeweils eine Gruppe von Müttern Frühgeborener und termingerecht geborener Kinder untersucht. Als Messinstrumente wurden die IESR und der PDEQ für posttraumatische Symptome, der BDI und die MADRS für Depression, das STAI und die HAMA für Angst, der F-SOZU für soziale Unterstützung, sowie das SKID für psychiatrische Diagnostik verwendet. Die Frühgeborenengruppe zeigte zu allen drei Messzeitpunkten erhöhte Werte bezüglich traumatischen Erlebens und Depression. Vierzehn Tage nach der Geburt fand man vermehrt Angstsymptome. Im Gegensatz zur Kontrollgruppe fand sich bei den Müttern der Frühgeborenen im Verlauf keine Reduktion der Werte posttraumatischer Symptome