References of "Schlagheck, Peter"
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See detailAharonov-Bohm oscillations of bosonic matter-wave beams in the presence of disorder and interaction
Chrétien, Renaud ULg; Dujardin, Julien; Petitjean, Cyril ULg et al

Poster (2016, July 27)

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 synthetic magnetic flux φ. We specifically investigate the effects both of a disorder potential and 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. We find that a correlated disorder suppress the AB oscillations leaving thereby place to Aronov-Al’tshuler-Spivak (AAS) oscillations. The competition between disorder and interaction leads to a peak inversion at Φ = π, that is a signature of a coherent backscattering (CBS) peak inversion. This is confirmed by truncated Wigner simulations. [less ▲]

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See detailMany-Body Spin Echo
Engl, Thomas; Urbina, Juan Diego; Richter, Klaus et al

E-print/Working paper (2016)

We predict a universal echo phenomenon present in the time evolution of many-body states of interacting quantum systems described by Fermi-Hubbard models. It consists of the coherent revival of transition ... [more ▼]

We predict a universal echo phenomenon present in the time evolution of many-body states of interacting quantum systems described by Fermi-Hubbard models. It consists of the coherent revival of transition probabilities echoing a sudden flip of the spins that, contrary to its single-particle (Hahn) version, is not dephased by interactions or spin-orbit coupling. The many-body spin echo signal has a universal shape independent of the interaction strength, and an amplitude and sign depending only on combinatorial relations between the number of particles and the number of applied spin flips. Our analytical predictions, based on semiclassical interfering amplitudes in Fock space associated with chaotic mean-field solutions, are tested against extensive numerical simulations confirming that the coherent origin of the echo lies in the existence of anti-unitary symmetries. [less ▲]

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See detailCoherent backscattering in the Fock space of Bose- and Fermi-Hubbard systems
Engl, Thomas; Dujardin, Julien; Tisserond, Emilie et al

Poster (2016, July)

Coherent backscattering generally refers to a significant and robust enhancement of the average backscattering probability of a wave within a disordered medium, which from a semiclassical point of view ... [more ▼]

Coherent backscattering generally refers to a significant and robust enhancement of the average backscattering probability of a wave within a disordered medium, which from a semiclassical point of view arises due to the constructive interference between backscattered trajectories and their time-reversed counterparts. We recently investigated the manifestation of this wave interference phenomenon in the Fock space of a disordered Bose-Hubbard system of finite extent [1], which can potentially be realized using ultracold bosonic atoms within optical lattices. Preparing the atoms in a well-defined Fock state of the lattice and letting the system evolve for a finite time will, for suitable parameters of the system and upon some disorder average over random on-site energies of the lattice, generally give rise to an equidistribution of the occupation probability within the energy shell of the Fock space that corresponds to the initial energy of the system, in accordance with the quantum microcanonical ensemble. We find, however, that the initial state is twice as often encountered as other Fock states with comparable total energy, which is a consequence of coherent backscattering [1]. Most recently, we showed that this phenomenon also arises in spin 1/2 Fermi-Hubbard rings that involve Rashba hopping terms (which combine inter-site hoppings with spin flips and arise from spin-orbit coupling), for which a newly developed semiclassical theory [2] correctly predicts a coherent enhancement of the occupation probabilities of the initial state and its spin-flipped counterpart. Moreover, performing a global spin flip within this Fermi-Hubbard system will give rise to significant spin echo peaks on those two Fock states, which is again a consequence of quantum many-body interference [3]. The semiclassical predictions of these enhancements and peaks are found to be in very good agreement with numerical findings obtained from the exact quantum time evolution within this Fermi-Hubbard system. [1] T. Engl, J. Dujardin, A. Argüelles, P. Schlagheck, K. Richter, and J. D. Urbina, Phys. Rev. Lett. 112, 140403 (2014). [2] T. Engl, P. Plößl, J. D. Urbina, and K. Richter, Theoretical Chemistry Accounts 133, 1563 (2014). [3] T. Engl, J. D. Urbina, and K. Richter, arXiv:1409.5684. [less ▲]

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See detailWaveguides for walking droplets
Filoux, Boris ULg; Hubert, Maxime ULg; Schlagheck, Peter ULg et al

E-print/Working paper (2016)

When gently placing a droplet onto a vertically vibrated bath, a drop can bounce without coalescing. Upon increasing the forcing acceleration, the droplet is propelled by the wave it generates and becomes ... [more ▼]

When gently placing a droplet onto a vertically vibrated bath, a drop can bounce without coalescing. Upon increasing the forcing acceleration, the droplet is propelled by the wave it generates and becomes a walker with a well defined speed. We investigate the confinement of a walker in different rectangular cavities, used as waveguides for the Faraday waves emitted by successive droplet bounces. By studying the walker velocities, we discover that 1d confinement is optimal for narrow channels of width of D≃1.5λF. We also propose an analogy with waveguide models based on the observation of the Faraday instability within the channels. [less ▲]

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See detailAharonov-Bohm oscillations of bosonic matter-wave beams in the presence of disorder and interaction
Chrétien, Renaud ULg; Dujardin, Julien; Petitjean, Cyril ULg et al

Poster (2016, May 18)

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 synthetic magnetic flux φ. We specifically investigate the effects both of a disorder potential and 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. We find that a correlated disorder suppress the AB oscillations leaving thereby place to weaker amplitude, half period oscillations on transmission, namely the Aronov-Al’tshuler-Spivak (AAS) oscillations. The competition between disorder and interaction leads to a flip of the transmission at the AB flux φ = π. This flip could be a possible preliminary signature of an inversion of the coherent backscattering (CBS) peak. Our study paves the way to an analytical description of the inversion of that peak. [less ▲]

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See detailScattering theory of walking droplets in the presence of obstacles
Dubertrand, Rémy ULg; Hubert, Maxime ULg; Schlagheck, Peter ULg et al

E-print/Working paper (2016)

We aim to describe a droplet bouncing on a vibrating bath. Due to Faraday instability a surface wave is created at each bounce and serves as a pilot wave of the droplet. This leads to so called walking ... [more ▼]

We aim to describe a droplet bouncing on a vibrating bath. Due to Faraday instability a surface wave is created at each bounce and serves as a pilot wave of the droplet. This leads to so called walking droplets or walkers. Since the seminal experiment by {\it Couder et al} [Phys. Rev. Lett. {\bf 97}, 154101 (2006)] there have been many attempts to accurately reproduce the experimental results. Here we present a simple and highly versatile model inspired from quantum mechanics. We propose to describe the trajectories of a walker using a Green function approach. The Green function is related to Helmholtz equation with Neumann boundary conditions on the obstacle(s) and outgoing conditions at infinity. For a single slit geometry our model is exactly solvable and reproduces some general features observed experimentally. It stands for a promising candidate to account for the presence of any boundaries in the walkers'dynamics. [less ▲]

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See detailCoherent backscattering in the Fock space of Bose- and Fermi-Hubbard systems
Engl, Thomas; Dujardin, Julien; Tisserond, Emilie et al

Poster (2016, May)

Coherent backscattering generally refers to a significant and robust enhancement of the average backscattering probability of a wave within a disordered medium, which from a semiclassical point of view ... [more ▼]

Coherent backscattering generally refers to a significant and robust enhancement of the average backscattering probability of a wave within a disordered medium, which from a semiclassical point of view arises due to the constructive interference between backscattered trajectories and their time-reversed counterparts. We recently investigated the manifestation of this wave interference phenomenon in the Fock space of a disordered Bose-Hubbard system of finite extent [1], which can potentially be realized using ultracold bosonic atoms within optical lattices. Preparing the atoms in a well-defined Fock state of the lattice and letting the system evolve for a finite time will, for suitable parameters of the system and upon some disorder average over random on-site energies of the lattice, generally give rise to an equidistribution of the occupation probability within the energy shell of the Fock space that corresponds to the initial energy of the system, in accordance with the quantum microcanonical ensemble. We find, however, that the initial state is twice as often encountered as other Fock states with comparable total energy, which is a consequence of coherent backscattering [1]. Most recently, we showed that this phenomenon also arises in spin 1/2 Fermi-Hubbard rings that involve Rashba hopping terms (which combine inter-site hoppings with spin flips and arise from spin-orbit coupling), for which a newly developed semiclassical theory [2] correctly predicts a coherent enhancement of the occupation probabilities of the initial state and its spin-flipped counterpart. Moreover, performing a global spin flip within this Fermi-Hubbard system will give rise to significant spin echo peaks on those two Fock states, which is again a consequence of quantum many-body interference [3]. The semiclassical predictions of these enhancements and peaks are found to be in very good agreement with numerical findings obtained from the exact quantum time evolution within this Fermi-Hubbard system. References [1] T. Engl, J. Dujardin, A. Argüelles, P. Schlagheck, K. Richter, and J. D. Urbina, Phys. Rev. Lett. 112, 140403 (2014). [2] T. Engl, P. Plößl, J. D. Urbina, and K. Richter, Theoretical Chemistry Accounts 133, 1563 (2014). [3] T. Engl, J. D. Urbina, and K. Richter, arXiv:1409.5684. [less ▲]

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See detailDynamical thermalization in Bose-Hubbard systems
Schlagheck, Peter ULg; Shepelyansky, Dima L.

Conference (2016, March)

A bosonic many-body system can exhibit the Bose-Einstein distribution in its single-particle eigenstates not only if it is coupled to a heat and particle reservoir, but also if it is subject to a two-body ... [more ▼]

A bosonic many-body system can exhibit the Bose-Einstein distribution in its single-particle eigenstates not only if it is coupled to a heat and particle reservoir, but also if it is subject to a two-body interaction of moderately low strength which couples the single-particle eigenstates with each other. We numerically verify this dynamical thermalization conjecture within disordered Bose-Hubbard rings of finite size whose parameters are chosen such that the dynamics of the system can be expected to be ergodic [1]. This allows one to associate with each many-body eigenstate of the Bose-Hubbard system well-defined (positive or negative) values for the effective temperature and the effective chemical potential which depend on the energy per particle of the eigenstate under consideration [1]. With this information one can then predict the populations of single-particle eigenmodes within each many-body eigenstate of the system according to the Bose-Einstein distribution, without knowing more details about the quantum dynamics of the many-body system. [less ▲]

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See detailBreakdown of Anderson localization in the transport of Bose-Einstein condensates through one-dimensional disordered potentials
Dujardin, Julien ULg; Engl, Thomas; Schlagheck, Peter ULg

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 ▲]

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See detailDynamical thermalization in Bose-Hubbard systems
Schlagheck, Peter ULg; Shepelyansky, Dima L.

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 ▲]

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See detailNonlinear dynamical tunneling of optical whispering gallery modes in the presence of a Kerr nonlinearity
Shim, Jeong -Bo ULg; Schlagheck, Peter ULg; Hentschel, Martina et al

E-print/Working paper (2015)

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See detailQuantum manifestations of classical nonlinear resonances
Wisniacki, Diego A.; Schlagheck, Peter ULg

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 ▲]

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See detailDescribing many-body bosonic waveguide scattering with the truncated Wigner method
Dujardin, Julien ULg; Engl, Thomas; Urbina, Juan Diego 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 ▲]

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See detailObserving the emergence of chaos in a many-particle quantum system
Tomkovic, Jiri; Muessel, Wolfgang; Strobel, Helmut et al

E-print/Working paper (2015)

Accessing the connection between classical chaos and quantum many-body systems has been a long-standing experimental challenge. Here, we investigate the onset of chaos in periodically driven two-component ... [more ▼]

Accessing the connection between classical chaos and quantum many-body systems has been a long-standing experimental challenge. Here, we investigate the onset of chaos in periodically driven two-component Bose-Einstein condensates, whose small quantum uncertainties allow for exploring the phase space with high resolution. By analyzing the uncertainties of time-evolved many-body states, we find signatures of elliptic and hyperbolic periodic orbits generated according to the Poincar\'e-Birkhoff theorem, and the formation of a chaotic region at increasing driving strengths. The employed fluctuation analysis allows for probing the phase-space structure by use of only short-time quantum dynamics. [less ▲]

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See detailCoherent backscattering in the Fock space of a disordered Bose-Hubbard system
Engl, Thomas; Dujardin, Julien; Tisserond, Emilie et al

Poster (2015, June)

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 [1]. 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 [1]. 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 which 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. We furthermore propose a specific experimental setup in order to detect this many-body coherent backscattering phenomenon with ultracold bosonic atoms. [1] T. Engl, J. Dujardin, A. Argüelles, P. Schlagheck, K. Richter, and J. D. Urbina, Phys. Rev. Lett. 112, 140403 (2014). [less ▲]

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See detailTransport of Bose-Einstein Condensates through Aharonov-Bohm rings
Chrétien, Renaud ULg; Dujardin, Julien ULg; Petitjean, Cyril ULg 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 ▲]

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See detailElastic and inelastic transmission in guided atom lasers: A truncated Wigner approach
Dujardin, Julien ULg; Argüelles, Arturo; Schlagheck, Peter ULg

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 ▲]

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See detailA study of one-dimensional transport of Bose-Einstein condensates using exterior complex scaling
Dujardin, Julien ULg; Saenz, Alejandro; Schlagheck, Peter ULg

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 ▲]

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See detailOn the analogy of quantum wave-particle duality with bouncing droplets
Richardson, Chris D.; Schlagheck, Peter ULg; Martin, John ULg et al

E-print/Working paper (2014)

We explore the hydrodynamic analogues of quantum wave-particle duality in the context of a bouncing droplet system which we model in such a way as to promote comparisons to the de Broglie-Bohm ... [more ▼]

We explore the hydrodynamic analogues of quantum wave-particle duality in the context of a bouncing droplet system which we model in such a way as to promote comparisons to the de Broglie-Bohm interpretation of quantum mechanics. Through numerical means we obtain single-slit diffraction and double-slit interference patterns that strongly resemble those reported in experiment and that reflect a striking resemblance to quantum diffraction and interference on a phenomenological level. We, however, identify evident differences from quantum mechanics which arise from the governing equations at the fundamental level. [less ▲]

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