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Dynamical thermalization in Bose-Hubbard systems Schlagheck, Peter ; in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2016), 93 We numerically study a Bose-Hubbard ring of finite size with disorder containing a finite number of bosons that are subject to an on-site two-body interaction. Our results show that moderate interactions ... [more ▼] We numerically study a Bose-Hubbard ring of finite size with disorder containing a finite number of bosons that are subject to an on-site two-body interaction. Our results show that moderate interactions induce dynamical thermalization in this isolated system. In this regime the individual many-body eigenstates are well described by the standard thermal Bose-Einstein distribution for well-defined values of the temperature and the chemical potential, which depend on the eigenstate under consideration. We show that the dynamical thermalization conjecture works well at both positive and negative temperatures. The relations to quantum chaos, quantum ergodicity, and the Åberg criterion are also discussed. [less ▲] Detailed reference viewed: 7 (0 ULg)Breakdown of Anderson localization in the transport of Bose-Einstein condensates through one-dimensional disordered potentials Dujardin, Julien ; ; Schlagheck, Peter in Physical Review A (2016), 93 We study the transport of an interacting Bose–Einstein condensate through a 1D correlated disorder potential. We use for this purpose the truncated Wigner method, which is, as we show, corresponding to ... [more ▼] We study the transport of an interacting Bose–Einstein condensate through a 1D correlated disorder potential. We use for this purpose the truncated Wigner method, which is, as we show, corresponding to the diagonal approximation of a semiclassical van Vleck–Gutzwiller representation of this many-body transport process. We also argue that semiclassical corrections beyond this diagonal approximation are vanishing under disorder average, thus confirming the validity of the truncated Wigner method in this context. Numerical calculations show that, while for weak atom-atom interaction strengths Anderson localization is preserved with a slight modification of the localization length, for larger interaction strengths a crossover to a delocalized regime exists due to inelastic scattering. In this case, the transport is fully incoherent. [less ▲] Detailed reference viewed: 18 (4 ULg)Quantum manifestations of classical nonlinear resonances ; Schlagheck, Peter in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2015), 92 When an integrable classical system is perturbed, nonlinear resonances are born, grow, and eventually disappear due to chaos. In this paper the quantum manifestations of such a transition are studied in ... [more ▼] When an integrable classical system is perturbed, nonlinear resonances are born, grow, and eventually disappear due to chaos. In this paper the quantum manifestations of such a transition are studied in the standard map. We show that nonlinear resonances act as a perturbation that break eigenphase degeneracies for unperturbed states with quantum numbers that differ in a multiple of the order of the resonance. We show that the eigenphase splittings are well described by a semiclassical expression based on an integrable approximation of the Hamiltonian in the vicinity of the resonance. The morphology in phase space of these states is also studied. We show that the nonlinear resonance imprints a systematic influence in their localization properties [less ▲] Detailed reference viewed: 12 (0 ULg)Describing many-body bosonic waveguide scattering with the truncated Wigner method Dujardin, Julien ; ; et al in Annalen der Physik (2015), 527 We consider quasi-stationary scattering of interacting bosonic matter waves in one-dimensional waveguides, as they arise in guided atom lasers. We show how the truncated Wigner (tW) method, which ... [more ▼] We consider quasi-stationary scattering of interacting bosonic matter waves in one-dimensional waveguides, as they arise in guided atom lasers. We show how the truncated Wigner (tW) method, which corresponds to the semiclassical description of the bosonic many-body system on the level of the diagonal approximation, can be utilized in order to describe such many-body bosonic scattering processes. Special emphasis is put on the discretization of space at the exact quantum level, in order to properly implement the semiclassical approximation and the tW method, as well as on the discussion of the results to be obtained in the continuous limit. [less ▲] Detailed reference viewed: 11 (3 ULg)Transport of Bose-Einstein Condensates through Aharonov-Bohm rings Chrétien, Renaud ; Dujardin, Julien ; Petitjean, Cyril et al Poster (2015, May 13) We study the one-dimensional (1D) transport properties of an ultracold gas of Bose-Einstein condensed atoms through Aharonov-Bohm (AB) rings. Our system consists of a Bose-Einstein condensate (BEC) that ... [more ▼] We study the one-dimensional (1D) transport properties of an ultracold gas of Bose-Einstein condensed atoms through Aharonov-Bohm (AB) rings. Our system consists of a Bose-Einstein condensate (BEC) that is outcoupled from a magnetic trap into a 1D waveguide which is made of two semi-infinite leads that join a ring geometry exposed to a magnetic flux φ. We specifically investigate the effects of a small atom-atom contact interaction strength on the AB oscillations. The main numerical tools that we use for this purpose are a mean-field Gross-Pitaevskii (GP) description and the truncated Wigner (tW) method. The latter allows for the description of incoherent transport and corresponds to a classical sampling of the evolution of the quantum bosonic many-body state through effective GP trajectories. We find that resonant transmission peaks move with an increasing interaction strength and can be suppressed for sufficiently strong interaction. We also observe that the coherent transmission blockade due to destructive interference at the AB flux φ = π is very robust with respect to the interaction strength. [less ▲] Detailed reference viewed: 97 (21 ULg)Elastic and inelastic transmission in guided atom lasers: A truncated Wigner approach Dujardin, Julien ; ; Schlagheck, Peter in Physical Review A (2015), 91 We study the transport properties of a Bose-Einstein condensate formed by an ultracold gas of bosonic atoms that is coupled from a magnetic trap into a one-dimensional waveguide. Our theoretical approach ... [more ▼] We study the transport properties of a Bose-Einstein condensate formed by an ultracold gas of bosonic atoms that is coupled from a magnetic trap into a one-dimensional waveguide. Our theoretical approach to tackling this problem is based on the truncated Wigner method for which we assume the system to consist of two semi-infinite noninteracting leads and a finite interacting scattering region with two constrictions modeling an atomic quantum dot. The transmission is computed in the steady-state regime and we find a good agreement between truncated Wigner and matrix-product state calculations. We also identify clear signatures of inelastic resonant scattering by analyzing the distribution of energy in the transmitted atomic-matter wave beam. [less ▲] Detailed reference viewed: 47 (4 ULg)A study of one-dimensional transport of Bose-Einstein condensates using exterior complex scaling Dujardin, Julien ; ; Schlagheck, Peter in Applied Physics B : Lasers & Optics (2014), 117(3), 765 We numerically investigate the one-dimensional transport of Bose-Einstein condensates in the context of guided atom lasers using a mean-field description of the condensate in terms of a spatially ... [more ▼] We numerically investigate the one-dimensional transport of Bose-Einstein condensates in the context of guided atom lasers using a mean-field description of the condensate in terms of a spatially discretized Gross-Pitaevskii equation. We specifically consider a waveguide configuration in which spatial inhomogeneities and nonvanishing atom-atom interactions are restricted to a spatially localized scattering region of finite extent. We show how the method of smooth exterior complex scaling can be implemented for this particular onfiguration in order to efficiently absorb the outgoing flux within the waveguide. A numerical comparison with the introduction of a complex absorbing potential as well as with the analytically exact elimination of the dynamics of the free non-interacting motion outside the scattering region, giving rise to transparent boundary conditions, clearly confirms the accuracy and efficiency of the smooth exterior complex scaling method. [less ▲] Detailed reference viewed: 84 (32 ULg)Nonlinear Schrödinger wave equation with linear quantum behavior Richardson, Christopher ; Schlagheck, Peter ; Martin, John et al in Physical Review A (2014), 89 We show that a nonlinear Schroedinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition ... [more ▼] We show that a nonlinear Schroedinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory governed by a nonlinear classical wave equation to quantum theory. The classical wave equation includes a nonlinear classicality enforcing potential which when eliminated transforms the wave equation into the linear Schro ̈dinger equation. We show that it is not necessary to completely cancel this nonlinearity to recover the linear behavior of quantum mechanics. Scaling the classicality enforcing potential is sufficient to have quantumlike features appear and is equivalent to scaling Planck’s constant. [less ▲] Detailed reference viewed: 29 (7 ULg)Coherent Backscattering in Fock Space: A Signature of Quantum Many-Body Interference in Interacting Bosonic Systems ; Dujardin, Julien ; et al in Physical Review Letters (2014), 112 We predict a generic signature of quantum interference in many-body bosonic systems resulting in a coherent enhancement of the average return probability in Fock space. This enhancement is robust with ... [more ▼] We predict a generic signature of quantum interference in many-body bosonic systems resulting in a coherent enhancement of the average return probability in Fock space. This enhancement is robust with respect to variations of external parameters even though it represents a dynamical manifestation of the delicate superposition principle in Fock space. It is a genuine quantum many-body effect that lies beyond the reach of any mean-field approach. Using a semiclassical approach based on interfering paths in Fock space, we calculate the magnitude of the backscattering peak and its dependence on gauge fields that break time-reversal invariance. We confirm our predictions by comparing them to exact quantum evolution probabilities in Bose-Hubbard models, and discuss their relevance in the context of many-body thermalization. [less ▲] Detailed reference viewed: 58 (4 ULg)Semiclassical description of resonance-assisted tunneling in one-dimensional integrable models ; ; Schlagheck, Peter in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2013), 88 Resonance-assisted tunneling is investigated within the framework of one-dimensional integrable systems. We present a systematic recipe, based on Hamiltonian normal forms, to construct one-dimensional ... [more ▼] Resonance-assisted tunneling is investigated within the framework of one-dimensional integrable systems. We present a systematic recipe, based on Hamiltonian normal forms, to construct one-dimensional integrable models that exhibit resonance island chain structures with accurately controlled sizes and positions of the islands. Using complex classical trajectories that evolve along suitably defined paths in the complex time domain, we construct a semiclassical theory of the resonance-assisted tunneling process. This semiclassical approach yields a compact analytical expression for tunnelling-induced level splittings which is found to be in very good agreement with the exact splittings obtained through numerical diagonalization. [less ▲] Detailed reference viewed: 24 (0 ULg)Total Current Blockade in an Ultracold Dipolar Quantum Wire ; ; et al in Physical Review Letters (2013), 110 Cold-atom systems offer a great potential for the future design of new mesoscopic quantum systems with properties that are fundamentally different from semiconductor nanostructures. Here, we investigate ... [more ▼] Cold-atom systems offer a great potential for the future design of new mesoscopic quantum systems with properties that are fundamentally different from semiconductor nanostructures. Here, we investigate the quantum-gas analogue of a quantum wire and find a new scenario for the quantum transport: Attractive interactions may lead to a complete suppression of current in the low-bias range, a total current blockade. We demonstrate this effect for the example of ultracold quantum gases with dipolar interactions. [less ▲] Detailed reference viewed: 40 (8 ULg)Delocalization of ultracold atoms in a disordered potential due to light scattering ; ; et al in Physical Review. A (2012), 86 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 33 (2 ULg)1D many-body quantum transport of Bose-Einstein condensates : a truncated Wigner approach Dujardin, Julien ; Argüelles Parra, Arturo ; Schlagheck, Peter Poster (2012, March 29) We calculate the transport properties of an ultracold gas of Bose- Einstein condensed atoms that is coupled from a magnetic trap into a one-dimensional waveguide. A central aim of such guided atom lasers ... [more ▼] We calculate the transport properties of an ultracold gas of Bose- Einstein condensed atoms that is coupled from a magnetic trap into a one-dimensional waveguide. A central aim of such guided atom lasers is to study the role of atom-atom interaction in many-body transport processes across finite scattering regions within the waveguide resembling tunnel junctions and quantum dots. Our numerical approach to solve this many-body scattering problem is based on a home-made theory where the boundaries of the system are simulating an open system enabling us to calulate observable in the steady-state regime such as density, current, transmission. The results are compared to the mean-field regime. [less ▲] Detailed reference viewed: 93 (8 ULg)Intensity distribution of non-linear scattering states ; ; et al in Robnik, M.; Romanovski, V.G. (Eds.) LET'S FACE CHAOS THROUGH NONLINEAR DYNAMICS (2012) 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 30 (4 ULg)Weak localization with nonlinear bosonic matter waves ; ; et al in Annals of Physics (2012), 327 We investigate the coherent propagation of dilute atomic Bose-Einstein condensates through irregularly shaped billiard geometries that are attached to uniform incoming and outgoing waveguides. Using the ... [more ▼] We investigate the coherent propagation of dilute atomic Bose-Einstein condensates through irregularly shaped billiard geometries that are attached to uniform incoming and outgoing waveguides. Using the mean-field description based on the nonlinear Gross–Pitaevskii equation, we develop a diagrammatic theory for the self-consistent stationary scattering state of the interacting condensate, which is combined with the semiclassical representation of the single-particle Green function in terms of chaotic classical trajectories within the billiard. This analytical approach predicts a universal dephasing of weak localization in the presence of a small interaction strength between the atoms, which is found to be in good agreement with the numerically computed reflection and transmission probabilities of the propagating condensate. The numerical simulation of this quasi-stationary scattering process indicates that this interaction-induced dephasing mechanism may give rise to a signature of weak antilocalization, which we attribute to the influence of non-universal short-path contributions. [less ▲] Detailed reference viewed: 36 (3 ULg)Resonance-assisted tunneling in mixed regular-chaotic systems Schlagheck, Peter ; ; in Keshavamurthy, Srihari; Schlagheck, Peter (Eds.) Dynamical Tunneling - Theory and Experiment (2011) Detailed reference viewed: 32 (4 ULg)Effective spin model for interband transport in a Wannier-Stark lattice system ; Schlagheck, Peter ; in European Physical Journal D -- Atoms, Molecules, Clusters & Optical Physics (2011), 63 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 22 (2 ULg)Dynamical Tunneling - Theory and Experiment ; Schlagheck, Peter Book published by CRC Press (2011) Detailed reference viewed: 62 (3 ULg)Transport of ultracold Bose gases beyond the Gross-Pitaevskii description ; ; Schlagheck, Peter in Physical Review. A : General Physics (2010), 81(1), 013631 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 ... [more ▼] 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 that 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 explicitly 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. [less ▲] Detailed reference viewed: 58 (9 ULg)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: 38 (5 ULg) |
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