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Regular-to-Chaotic Tunneling Rates: From the Quantum to the Semiclassical Regime ; ; et al in Physical Review Letters (2010), 104(11), 114101 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 ... [more ▼] 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 h regime. For systems with one or multiple dominant resonances we find excellent agreement to numerics. [less ▲] Detailed reference viewed: 39 (5 ULg)Transport and interaction blockade of cold bosonic atoms in a triple-well potential Schlagheck, Peter ; ; et al in New Journal of Physics (2010), 12 We theoretically investigate the transport properties of cold bosonic atoms in a quasi-one-dimensional (1D) triple-well potential that consists of two large outer wells, which act as microscopic source ... [more ▼] We theoretically investigate the transport properties of cold bosonic atoms in a quasi-one-dimensional (1D) triple-well potential that consists of two large outer wells, which act as microscopic source and drain reservoirs, and a small inner well, which represents a quantum-dot-like scattering region. Bias and gate 'voltages' introduce a time-dependent tilt of the triple-well configuration, and are used to shift the energetic level of the inner well with respect to the outer ones. By means of exact diagonalization considering a total number of six atoms in the triple-well potential, we find diamond-like structures for the occurrence of single-atom transport in the parameter space spanned by the bias and gate voltages. We discuss the analogy with Coulomb blockade in electronic quantum dots, and point out how one can infer the interaction energy in the central well from the distance between the diamonds. [less ▲] Detailed reference viewed: 53 (9 ULg)Anderson localization of a weakly interacting one-dimensional Bose gas ; ; Schlagheck, Peter et al in Physical Review. A (2009), 80(3), 033615 We consider the phase coherent transport of a quasi-one-dimensional beam of Bose-Einstein condensed particles through a disordered potential of length L. Among the possible different types of flow we ... [more ▼] We consider the phase coherent transport of a quasi-one-dimensional beam of Bose-Einstein condensed particles through a disordered potential of length L. Among the possible different types of flow we identified [T. Paul, P. Schlagheck, P. Leboeuf, and N. Pavloff, Phys. Rev. Lett. 98, 210602 (2007)], we focus here on the supersonic stationary regime where Anderson localization exists. We generalize the diffusion formalism of Dorokhov-Mello-Pereyra-Kumar to include interaction effects. It is shown that interactions modify the localization length and also introduce a length scale L* for the disordered region, above which most of the realizations of the random potential lead to time-dependent flows. A Fokker-Planck equation for the probability density of the transmission coefficient that takes this effect into account is introduced and solved. The theoretical predictions are verified numerically for different types of disordered potentials. Experimental scenarios for observing our predictions are discussed. [less ▲] Detailed reference viewed: 28 (4 ULg)Coherent backscattering of Bose-Einstein condensates in two-dimensional disorder potentials ; ; et al in Physical Review Letters (2008), 101(2), 020603 We study quantum transport of an interacting Bose-Einstein condensate in a two-dimensional disorder potential. In the limit of a vanishing atom-atom interaction, a sharp cone in the angle-resolved density ... [more ▼] We study quantum transport of an interacting Bose-Einstein condensate in a two-dimensional disorder potential. In the limit of a 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 the presence of nonlinearity. [less ▲] Detailed reference viewed: 21 (3 ULg)In Unordnung erstarrt Schlagheck, Peter ; Article for general public (2008) Experimente mit kalten Atomen zeigen erstmals direkt die Anderson-Lokalisierung von Materiewellen. Detailed reference viewed: 9 (1 ULg)Nonexponential decay of Bose-Einstein condensates: a numerical study based on the complex scaling method Schlagheck, Peter ; in Applied Physics B : Lasers & Optics (2007), 86(3), 385-390 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 ... [more ▼] 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 behavior, which would generally be expected in the absence of the atom-atom interaction. [less ▲] Detailed reference viewed: 17 (0 ULg)Superfluidity versus Anderson localization in a dilute Bose gas ; Schlagheck, Peter ; et al in Physical Review Letters (2007), 98(21), We consider the motion of a quasi-one-dimensional beam of Bose-Einstein condensed particles in a disordered region of finite extent. Interaction effects lead to the appearance of two distinct regions of ... [more ▼] We consider the motion of a quasi-one-dimensional beam of Bose-Einstein condensed particles in a disordered region of finite extent. Interaction effects lead to the appearance of two distinct regions of stationary flow. One is subsonic and corresponds to superfluid motion. The other one is supersonic and dissipative and shows Anderson localization. We compute analytically the interaction-dependent localization length. We also explain the disappearance of the supersonic stationary flow for large disordered samples. [less ▲] Detailed reference viewed: 16 (2 ULg)Nonlinear transport of Bose-Einstein condensates through mesoscopic waveguides ; ; et al in Physical Review. A (2007), 76(6), 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 ... [more ▼] 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 quasibound states of the quantum dot. [less ▲] Detailed reference viewed: 36 (3 ULg)Effects of short-range interactions on transport through quantum point contacts: A numerical approach ; Schlagheck, Peter ; in Physical Review. B : Condensed Matter (2007), 75(4), 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 nonequilibrium ... [more ▼] 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 nonequilibrium Green-function technique which is evaluated at the 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. [less ▲] Detailed reference viewed: 21 (2 ULg)Tunneling in Presence of Chaos and Interactions Schlagheck, Peter Post doctoral thesis (2006) Detailed reference viewed: 47 (9 ULg)Tunnelling rates for the nonlinear Wannier-Stark problem ; Schlagheck, Peter ; in Journal of Physics : B Atomic Molecular & Optical Physics (2006), 39(3), 729-740 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 ... [more ▼] 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 an analytic perturbation theory. [less ▲] Detailed reference viewed: 11 (1 ULg)Resonance- and Chaos-Assisted Tunneling Schlagheck, Peter ; ; in Yamanouchi, K.; Chin, S. L.; Agostini, P. (Eds.) et al Progress in Ultrafast Intense Laser Science I (2006) 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 28 (1 ULg)Resonance-assisted decay of nondispersive wave packets ; Schlagheck, Peter ; et al in Physical Review Letters (2006), 97(4), 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 21 (0 ULg)Quantum chaos, transport, and control - In quantum optics ; ; et al in Advances in Atomic and Molecular Physics (2006), 53 Chaos implies unpredictability, fluctuations, and the need for statistical modelling. Quantum optics has developed into one of the most advanced subdisciplines of modern physics in terms of the control of ... [more ▼] Chaos implies unpredictability, fluctuations, and the need for statistical modelling. Quantum optics has developed into one of the most advanced subdisciplines of modern physics in terms of the control of matter on a microscopic scale, and, in particular, of isolated, single quantum objects. Prima facie, both fields therefore appear rather distant in philosophy and outset. However, as we shall discuss in the present review, chaos, and, more specifically, quantum chaos opens up novel perspectives for our understanding of the dynamics of increasingly complex quantum systems, and of ultimate quantum control by tailoring complexity. [less ▲] Detailed reference viewed: 27 (2 ULg)Complex-scaling approach to the decay of Bose-Einstein condensates Schlagheck, Peter ; in Physical Review. A (2006), 73(2), The mean-field dynamics of a Bose-Einstein condensate is studied in the presence of a microscopic trapping potential from which the condensate can escape via tunneling through finite barriers. We show ... [more ▼] The mean-field dynamics of a Bose-Einstein condensate is studied in the 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. [less ▲] Detailed reference viewed: 14 (0 ULg)Influence of classical resonances on chaotic tunneling ; ; Schlagheck, Peter in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2006), 74(2), Dynamical tunneling between symmetry-related stable modes is studied in the periodically driven pendulum. We present strong evidence that the tunneling process is governed by nonlinear resonances that ... [more ▼] Dynamical tunneling between symmetry-related stable modes is studied in the periodically driven pendulum. We present strong evidence that the tunneling 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 tunneling yields good overall agreement with the quantum-tunneling rates, and indicates that partial barriers within the chaos might play a prominent role. [less ▲] Detailed reference viewed: 17 (1 ULg)Decay rates of planar helium ; Schlagheck, Peter ; et al in Europhysics Letters [=EPL] (2005), 70(2), 183-189 We compare the autoionization rates of characteristic configurations of the doubly excited helium atom, in one, two and three dimensions. We find that the decay rates of the two-dimensional restriction ... [more ▼] We compare the autoionization rates of characteristic configurations of the doubly excited helium atom, in one, two and three dimensions. We find that the decay rates of the two-dimensional restriction are in quantitative agreement with those of the real physical system, whilst the one-dimensional model can underestimate the actual decay rates by orders of magnitude. [less ▲] Detailed reference viewed: 10 (1 ULg)Nonlinear transport of Bose-Einstein condensates through waveguides with disorder ; ; et al in Physical Review. A (2005), 72(6), 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 ... [more ▼] 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 increasing L. For strong interaction (or large L), the system displays a transition toward a time-dependent flow with an algebraic decay of the time-averaged transmission. [less ▲] Detailed reference viewed: 37 (0 ULg)Resonance- and chaos-assisted tunneling in mixed regular-chaotic systems ; Schlagheck, Peter in Physical Review Letters (2005), 94(1), 014101 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 28 (1 ULg)Nonlinear resonant transport of Bose-Einstein condensates ; ; Schlagheck, Peter in Physical Review Letters (2005), 94(2), 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 the presence of a ... [more ▼] 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 the 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. [less ▲] Detailed reference viewed: 34 (1 ULg) |
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