Chaotic Quantum Decay in Driven Biased Optical Lattices

Quantum decay in an ac driven biased periodic potential modeling cold atoms in optical lattices is studied for a symmetry broken driving. For the case of fully chaotic classical dynamics the classical exponential decay is quantum mechanically suppressed for a driving frequency \omega in resonance with the Bloch frequency \omega_B, q\omega=r\omega_B with integers q and r. Asymptotically an algebraic decay ~t^{-\gamma} is observed. For r=1 the exponent \gamma agrees with $q$ as predicted by non-Hermitian random matrix theory for q decay channels. The time dependence of the survival probability can be well described by random matrix theory. The frequency dependence of the survival probability shows pronounced resonance peaks with sub-Fourier character.Comment: 7 pages, 5 figure

Resonance solutions of the nonlinear Schr\"odinger equation in an open double-well potential

The resonance states and the decay dynamics of the nonlinear Schr\"odinger (or Gross-Pitaevskii) equation are studied for a simple, however flexible model system, the double delta-shell potential. This model allows analytical solutions and provides insight into the influence of the nonlinearity on the decay dynamics. The bifurcation scenario of the resonance states is discussed, as well as their dynamical stability properties. A discrete approximation using a biorthogonal basis is suggested which allows an accurate description even for only two basis states in terms of a nonlinear, nonhermitian matrix problem.Comment: 21 pages, 14 figure

Development of a Support Group Curriculum: Building Self-Esteem with Adolescent Girls

In the past few decades educators, social workers and psychologists have been examining the role self esteem plays in young people\u27s development and have explored why adolescent girls as a group show lower self esteem than adolescent boys. The purpose of this project is two fold: 1) to research those factors that influence the development of self esteem for young girls during the time they move into adolescence and 2) to develop a support group curriculum that addresses those factors that put young girls at risk. The curriculum is designed for girls age 12-14 and is to be facilitated by a female social worker. It is to be used in a group setting in the school environment. By using the group process, the curriculum provides opportunities for discussions, collaboration, and building connections with other young girls

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

A Sensitive Faraday Rotation Setup Using Triple Modulation

The utilization of polarized targets in scattering experiments has become a common practice in many major accelerator laboratories. Noble gases are especially suitable for such applications, since they can be easily hyper-polarized using spin exchange or metastable pumping techniques. Polarized helium-3 is a very popular target because it often serves as an effective polarized neutron due to its simple nuclear structure. A favorite cell material to generate and store polarized helium-3 is GE-180, a relatively dense aluminosilicate glass. In this paper, we present a Faraday rotation method, using a new triple modulation technique, where the measurement of the Verdet constants of SF57 flint glass, pyrex glass, and air were tested. The sensitivity obtained shows that this technique may be implemented in future cell wall characterization and thickness measurements. We also discuss the first ever extraction of the Verdet constant of GE-180 glass for four wavelength values of 632 nm, 773 nm, 1500 nm, and 1547 nm, whereupon the expected 1/{\lambda}^{2} dependence was observed.Comment: 4 pages, 2 figures Updated version for RSI submissio

Bloch oscillations of cold atoms in optical lattices

This work is devoted to Bloch oscillations (BO) of cold neutral atoms in optical lattices. After a general introduction to the phenomenon of BO and its realization in optical lattices, we study different extentions of this problem, which account for recent developments in this field. These are two-dimensional BO, decoherence of BO, and BO in correlated systems. Although these problems are discussed in relation to the system of cold atoms in optical lattices, many of the results are of general validity and can be well applied to other systems showing the phenomenon of BO.Comment: submitted to the review section of IJMPB, few misprints are correcte

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

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

An algebraic solution of driven single band tight binding dynamics

The dynamics of the driven tight binding model for Wannier-Stark systems is formulated and solved using a dynamical algebra. This Lie algebraic approach is very convenient for evaluating matrix elements and expectation values. It is also shown that a dynamical invariant can be constructed. A classicalization of the tight binding model is discussed as well as some illustrating examples of Bloch oscillations and dynamical localization effects.Comment: 13 pages; revised version (changed title and sections 6,7, added references

Addendum to "Nonlinear quantum evolution with maximal entropy production"

The author calls attention to previous work with related results, which has escaped scrutiny before the publication of the article "Nonlinear quantum evolution with maximal entropy production", Phys.Rev.A63, 022105 (2001).Comment: RevTex-latex2e, 2pgs., no figs.; brief report to appear in the May 2001 issue of Phys.Rev.