Dynamical tunneling between symmetry related invariant tori is studied in the near-integrable regime. Using the kicked Harper model as an illustration, we show that the exponential decay of the wave functions in the classically forbidden region is modified due to coupling processes that are mediated by classical resonances. This mechanism leads to a substantial deviation of the splitting between quasidegenerate eigenvalues from the purely exponential decrease with 1/Planck's over 2pi obtained for the integrable system. A simple semiclassical framework, which takes into account the effect of the resonance substructure on the invariant tori, allows one to quantitatively reproduce the behavior of the eigenvalue splittings.

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.PACS numbers: 03.75. Dg, 03.75.Kk, 42.65.Pc The rapid progress in the fabrication and manipulation of ultracold Bose-Einstein condensates has lead to a number of fascinating experiments probing complex condensed matter phenomena in perfectly controllable environments, such as the creation of vortex lattices [1] and the quantum phase transition from a superfluid to a Mott insulator state in optical lattices [2]. With the development of "atom chips" [3][4][5], new perspectives are opened also towards mesoscopic physics. The possibility to generate atomic waveguides of arbitrary complexity above microfabricated surfaces does not only permit highly accurate matter-wave interference experiments [6], but would also allow to study the interplay between interaction and transport with an unprecedented degree of control of the involved parameters. The connection to electronic mesoscopic physics was appreciated by Thywissen et al. [7] who proposed a generalization of Landauer's theory of conductance [8] to the transport of noninteracting atoms through point contacts. Related theoretical studies were focused on the adiabatic propagation of a Bose-Einstein condensate in presence of obstacles [9][10][11][12], the dynamics of soliton-like structures in waveguides (e.g. [13]), and the influence of optical lattices on transport (e.g. [14]), to mention just a few examples.Particularly interesting in this context is the propagation of a Bose-Einstein condensate through a double barrier potential, which can be seen as a Fabry-Perot interferometer for matter waves. In the context of atom chips, such a bosonic quantum dot could be realized by suitable geometries of microfabricated wires. An alternative implementation based on optical lattices was suggested by Carusotto and La Rocca [15,16] who pointed out that the interaction-induced nonlinearity in the meanfield dynamics would lead to a bistability behaviour of the transmitted flux in the vicinity of resonances. This phenomenon is well known from nonlinear optics [17] and arises also in electronic transport through quantum wells (e.g. [18][19][20]) due to the Coulomb interaction in the well.In this Letter, we investigate to which extent resonant transport through such a double barrier potential can be achieved for an interacting condensate in a realistic propagation p...

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 variant Planck's over 2pi regime. For systems with one or multiple dominant resonances we find excellent agreement to numerics.

We present evidence that tunneling processes in near-integrable systems are enhanced due to the manifestation of nonlinear resonances and their respective island chains in phase space. A semiclassical description of this "resonance-assisted" mechanism is given, which is based on a local perturbative description of the dynamics in the vicinity of the resonances. As underlying picture, we obtain that the quantum state is coupled, via a succession of classically forbidden transitions across nonlinear resonances, to high excitations within the well, from where tunneling occurs with a rather large rate. The connection between this description and the complex classical structure of the underlying integrable dynamics is furthermore studied, giving ground to the general coherence of the description as well as guidelines for the identification of the dominant tunneling paths. The validity of this mechanism is demonstrated within the kicked Harper model, where good agreement between quantum and semiclassical (resonance-assisted) tunneling rates is found.