Hummel, Q., & Schlagheck, P. (23 September 2022). Symmetry-induced many-body quantum interference in chaotic bosonic systems: An augmented truncated Wigner method. *Journal of Physics. A, Mathematical and Theoretical, 55* (38), 384009. doi:10.1088/1751-8121/ac8085

Although highly successful, the truncated Wigner approximation (TWA) does not account for genuine many-body (MB) quantum interference between different solutions of the mean-field equations of a bosonic MB system. This renders the TWA essentially classical, where a large number of particles formally takes the role of the inverse of Planck's constant ., . The failure to describe genuine interference phenomena, such as localization and scarring in Fock space, can be seen as a virtue of this qua...

Coisne, A., Montaigne, D., Aghezzaf, S., Ridon, H., Mouton, S., Richardson, M., Polge, A.-S., LANCELLOTTI, P., Bauters, C., VALVENOR, I., Abramovici, L. (Other coll.), Aisenfarb, J.-C. (Other coll.), Alaoui, M. (Other coll.), Amiar, A. (Other coll.), Arabidze, M. (Other coll.), Aumegeat, V. (Other coll.), Avez-Lemaire, L. (Other coll.), Bardet, H. (Other coll.), Bauley, K. (Other coll.), & Tricot, O. (Other coll.). (01 December 2021). Association of Mortality With Aortic Stenosis Severity in Outpatients: Results From the VALVENOR Study. *JAMA Cardiology, 6* (12), 1424-1431. doi:10.1001/jamacardio.2021.3718

IMPORTANCE: Modern data regarding incidence and modes of death of patients with aortic stenosis (AS) are restricted to tertiary centers or studies of aortic valve replacement (AVR). OBJECTIVE: To provide new insights into the natural history of outpatients with native AS based on a large regionwide population study with inclusion by all cardiologists regardless of their mode of practice. DESIGN, SETTING, AND PARTICIPANTS: Between May 2016 and December 2017, consecutive outpatients with mild ...

Chrétien, R., & Schlagheck, P. (24 August 2021). *Inversion of coherent backscattering with interacting Bose–Einstein condensates in two–dimensional disorder*. Paper presented at 17èmes journées de la matière condensée.

We theoretically study the propagation of an interacting Bose-Einstein condensate in a two-
dimensional disorder potential, following the principle of an atom laser. The constructive
interference between time–reversed scattering paths gives rise to coherent backscattering,
which may be observed under the form of a sharp cone in the disorder–averaged angular
backscattered current. As is found by the numerical integration of the Gross-Pitaevskii equation, ...

Chrétien, R., & Schlagheck, P. (22 March 2021). Inversion of coherent backscattering with interacting Bose-Einstein condensates in two-dimensional disorder: A truncated Wigner approach. *Physical Review. A, 103*, 033319. doi:10.1103/PhysRevA.103.033319

We theoretically study the propagation of an interacting Bose-Einstein condensate in a two-dimensional disorder potential, following the principle of an atom laser. The constructive interference between time-reversed scattering paths gives rise to coherent backscattering, which may be observed under the form of a sharp cone in the disorder-averaged angular backscattered current. As is found by the numerical integration of the Gross-Pitaevskii equation, this coherent backscattering cone is inv...

Wanzenböck, R., Donsa, S., Hofstätter, H., Koch, O., Schlagheck, P., & Březinová, I. (2021). Chaos-induced loss of coherence of a Bose-Einstein condensate. *Physical Review. A, 103*, 023336. doi:10.1103/PhysRevA.103.023336

The mean-field limit of a bosonic quantum many-body system is described by (mostly) nonlinear equations of motion which may exhibit chaos very much in the spirit of classical particle chaos, i.e., by an exponential separation of trajectories in Hilbert space with a rate given by a positive Lyapunov exponent λ. The question now is whether λ imprints itself onto measurable observables of the underlying quantum many-body system even at finite particle numbers. Using a Bose-Einstein condensate ex...

Arnal, M., Chatelain, G., Cabrera-Gutiérrez, C., Fortun, A., Michon, E., Billy, J., Schlagheck, P., & Guéry-Odelin, D. (2020). Beyond effective Hamiltonians: Micromotion of Bose-Einstein condensates in periodically driven optical lattices. *Physical Review A, 101*, 013619. doi:10.1103/PhysRevA.101.013619

We investigate by statistical means a Bose-Einstein condensate held in a one-dimensional optical lattice whose phase undergoes a fast oscillation. The averaged potential experienced by the atoms yields a periodic potential having the same spatial period but with a renormalized depth. However, the atomic dynamics also contains a micromotion whose main features are revealed by a Kolmorogov-Smirnov analysis of the experimental momentum distributions. Furthermore, we discuss the impact of the mic...

Chatelain, G., Dupont, N., Arnal, M., Brunaud, V., Billy, J., Peaudecerf, B., Schlagheck, P., & Guéry-Odelin, D. (2020). Observation and control of quantized scattering halos. *New Journal of Physics, 22*, 123032. doi:10.1088/1367-2630/abcf6a

We investigate the production of s-wave scattering halos from collisions between the momentum components of a Bose–Einstein condensate released from an optical lattice. The lattice periodicity translates in a momentum comb responsible for the quantization of the halos' radii. We report on the engineering of those halos through the precise control of the atom dynamics in the lattice: we are able to specifically enhance collision processes with given center-of-mass and relative momenta. In part...

Chrétien, R., Rammensee, J., Dujardin, J., Petitjean, C., & Schlagheck, P. (05 September 2019). Al’tshuler-Aronov-Spivak oscillations of bosonic matter-wave beams in the presence of interaction. *Physical Review. A, 100*, 033606. doi:10.1103/PhysRevA.100.033606

We theoretically study the propagation of a guided atom laser across an Aharonov-Bohm ring

which is exposed to a synthetic gauge field. The presence of disorder within the ring gives rise to

Al’tshuler-Aronov-Spivak oscillations, seen in the disorder average of the transmission as a function of the effective gauge flux that is contained within the ring. Those oscillations are induced by coherent backscattering and represent a manifestation of weak localisation. Through analytical ...

which is exposed to a synthetic gauge field. The presence of disorder within the ring gives rise to

Al’tshuler-Aronov-Spivak oscillations, seen in the disorder average of the transmission as a function of the effective gauge flux that is contained within the ring. Those oscillations are induced by coherent backscattering and represent a manifestation of weak localisation. Through analytical ...

Schlagheck, P., Ullmo, D., Urbina, J. D., Richter, K., & Tomsovic, S. (2019). Enhancement of Many-Body Quantum Interference in Chaotic Bosonic Systems: The Role of Symmetry and Dynamics. *Physical Review Letters, 123*, 215302. doi:10.1103/PhysRevLett.123.215302

Although highly successful, the truncated Wigner approximation (TWA) leaves out many-body quantum interference between mean-field Gross-Pitaevskii solutions as well as other quantum effects, and is therefore essentially classical. Turned around, if a system’s quantum properties deviate from TWA, they must be exhibiting some quantum phenomenon, such as localization, diffraction, or tunneling. Here, we examine a particular interference effect arising from discrete symmetries, which can signific...

Chrétien, R., Rammensee, J., Dujardin, J., Petitjean, C., & Schlagheck, P. (17 May 2018). *Altshuler-Aronov-Spivak oscillations of coherent bosonic matter-wave beams in the presence of interaction*. Paper presented at Meeting of the Belgian Quantum Physics Initiative (BQPi), Brussels, Belgium.

We theoretically study the propagation of a guided atom laser across an Aharonov-Bohm ring
which is exposed to a synthetic gauge field. The presence of disorder within the ring gives rise to
Al’tshuler-Aronov-Spivak oscillations [1], seen in the disorder-averaged of the transmission as a function of the effective gauge flux that is contained within the ring. Those oscillations are induced by coherent backscattering and represent a manifestation of weak localisation. Through analytical and num...

Chrétien, R., Rammensee, J., Dujardin, J., Petitjean, C., & Schlagheck, P. (07 March 2018). *Altshuler-Aronov-Spivak oscillations of coherent bosonic matter-wave beams in the presence of interaction*. Paper presented at 82. Jahrestagung der DPG und DPG-Frühjahrstagung, Erlangen, Germany.

We theoretically study the propagation of a guided atom laser across an Aharonov-Bohm ring
which is exposed to a synthetic gauge field. The presence of disorder within the ring gives rise to
Al’tshuler-Aronov-Spivak oscillations [1], seen in the disorder-averaged of the transmission as a function of the effective gauge flux that is contained within the ring. Those oscillations are induced by coherent backscattering and represent a manifestation of weak localisation. Through analytical and num...

Engl, T., Urbina, J. D., Richter, K., & Schlagheck, P. (2018). Many-body spin echo. *Physical Review. A, 98*, 013630. doi:10.1103/PhysRevA.98.013630

We show that quantum coherence produces an observable many-body signature in the dynamics of few-fermion Hubbard systems (describing cold atoms in optical lattices, coupled quantum dots, or small molecules) in the form of a revival in the transition probabilities echoing a flip of the system's itinerant spins. Contrary to its single-particle (Hahn) version, this many-body spin echo is not dephased by strong interactions or spin-orbit coupling, and constitutes a benchmark of genuine many-body ...

Michon, E., Cabrera-Gutiérrez, C., Fortun, A., Berger, M., Arnal, M., Brunaud, V., Billy, J., Petitjean, C., Schlagheck, P., & Guéry-Odelin, D. (2018). Phase transition kinetics for a Bose Einstein condensate in a periodically driven band system. *New Journal of Physics, 20*, 053035. doi:10.1088/1367-2630/aabc3f

The dynamical transition of an atomic Bose–Einstein condensate from a spatially periodic state to a staggered state with alternating sign in its wavefunction is experimentally studied using a one-dimensional phase modulated optical lattice. We observe the crossover from quantum to thermal fluctuations as the triggering mechanism for the nucleation of staggered states. In good quantitative agreement with numerical simulations based on the truncated Wigner method, we experimentally investigate ...

Tadrist, L., Shim, J.-B., Gilet, T., & Schlagheck, P. (2018). Faraday instability and subthreshold Faraday waves: surface waves emitted by walkers. *Journal of Fluid Mechanics, 848*, 906. doi:10.1017/jfm.2018.358

A walker is a fluid entity comprising a bouncing droplet coupled to the waves that it generates at the surface of a vibrated bath. Thanks to this coupling, walkers exhibit a series of wave–particle features formerly thought to be exclusive to the quantum realm. In this paper, we derive a model of the Faraday surface waves generated by an impact upon a vertically vibrated liquid surface. We then particularise this theoretical framework to the case of forcing slightly below the Faraday instabil...

Tomsovic, S., Schlagheck, P., Ullmo, D., Urbina, J.-D., & Richter, K. (2018). Post-Ehrenfest many-body quantum interferences in ultracold atoms far out of equilibrium. *Physical Review. A, 97*, 061606. doi:10.1103/PhysRevA.97.061606

Far out-of-equilibrium many-body quantum dynamics in isolated systems necessarily generates interferences beyond an Ehrenfest timescale, where quantum and classical expectation values diverge. Of great recent interest is the role these interferences play in the spreading of quantum information across the many degrees of freedom, i.e., scrambling. Ultracold atomic gases provide a promising setting to explore these phenomena. Theoretically speaking, the heavily-relied-upon truncated Wigner appr...

Chrétien, R., Dujardin, J., Petitjean, C., & Schlagheck, P. (09 June 2017). *Coherent backscattering of bosonic matter-wave in the presence of disorder and interaction*. Poster session presented at CESAM day, Liège, Belgium.

Coherent backscattering, which is an enhancement of the backscattered intensity of a light going
through a medium made of point-like scatterers, is known as one of the most robust interference
effects. It has been shown, although it is nowadays not fully understood yet, that in the presence of
non-linearities, this enhancement turns to an inhibition. We propose to study that effect by means of a system in which we study the transport of a Bose-Einstein condensate through Aharonov-Bohm rings i...

Chrétien, R., Dujardin, J., Petitjean, C., & Schlagheck, P. (17 May 2017). *Aharonov-Bohm oscillations of bosonic matter-wave beams in the presence of disorder and interaction*. Poster session presented at Annual meeting of the belgian physical society, Mons, Belgium.

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...

Filoux, B., Hubert, M., Schlagheck, P., & Vandewalle, N. (2017). Walking droplets in linear channels. *Physical Review Fluids, 2*, 013601. doi:10.1103/PhysRevFluids.2.013601

When a droplet is placed onto a vertically vibrated bath, it can bounce without coalescing. Upon an increase of 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 one-dimensional confinement is optimal for narrow c...

Schlagheck, P., & Dujardin, J. (2017). Coherent backscattering in the Fock space of ultracold bosonic atoms. *Annalen der Physik, 529*, 1600311. doi:10.1002/andp.201600311

We present numerical evidence for the occurrence of coherent backscattering in the Fock space of a small disordered Bose-Hubbard system consisting of four sites and containing five particles. This many-body interference phenomenon can most conveniently be seen in time evolution processes that start from a Fock state of the Bose-Hubbard system. It manifests itself in an enhanced detection probability of this initial state as compared to other Fock states with comparable total energy. We argue...

Shim, J.-B., Schlagheck, P., Hentschel, M., & Wiersig, J. (November 2016). Nonlinear dynamical tunneling of optical whispering gallery modes in the presence of a Kerr nonlinearity. *Physical Review. A, 94*, 053849. doi:10.1103/PhysRevA.94.053849

The effect of a Kerr nonlinearity on dynamical tunneling is studied, using coupled whispering gallery modes in an optical microcavity. The model system that we have chosen is the “add-drop filter,” which is comprised of an optical microcavity and two waveguides coupled to the cavity. Due to the evanescent fields scattering on the waveguide, the whispering gallery modes in the microcavity form doublets, which manifest themselves as splittings in the spectrum. As these doublets can be regarded ...

Filoux, B., Hubert, M., Schlagheck, P., & Vandewalle, N. (12 October 2016). *Walking droplets in confined geometries*. Poster session presented at Mécamolle, Liège, Belgium.

When gently placing a droplet onto a vertically vibrated bath, under specific conditions, coalescence may be avoided. The drop bounces permanently. Upon increasing the forcing acceleration, the drop interacts with the wave it generates, and becomes a walker [1,2]. Recently, some 2D confining systems for walking droplets have been developed: cylindrical cavity, harmonic potential or the use of Coriolis force [3,4]. In addition, the interactions between two identical walkers have been studied i...

Chrétien, R., Dujardin, J., Petitjean, C., & Schlagheck, P. (27 July 2016). *Aharonov-Bohm oscillations of bosonic matter-wave beams in the presence of disorder and interaction*. Poster session presented at XVIII Giambiagi winter school : quantum chaos & control, Buenos Aires, Argentina.

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...

Engl, T., Urbina, J. D., Richter, K., & Schlagheck, P. (2016). *Many-Body Spin Echo*. Eprint/Working paper retrieved from https://orbi.uliege.be/2268/199795.

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 onl...

Engl, T., Dujardin, J., Tisserond, E., Argüelles, A., Richter, K., Urbina, J. D., & Schlagheck, P. (July 2016). *Coherent backscattering in the Fock space of Bose- and Fermi-Hubbard systems*. Poster session presented at Disorder, Interactions and Coherence: Warps and Delights, Dresden, Germany.

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 ...

Filoux, B., Hubert, M., Schlagheck, P., & Vandewalle, N. (2016). *Waveguides for walking droplets*. Eprint/Working paper retrieved from https://orbi.uliege.be/2268/199803.

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 ...

Chrétien, R., Dujardin, J., Petitjean, C., & Schlagheck, P. (18 May 2016). *Aharonov-Bohm oscillations of bosonic matter-wave beams in the presence of disorder and interaction*. Poster session presented at Annual Scientific Meeting of the Belgian Physical Society, Ghent, Belgium.

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...

Dubertrand, R., Hubert, M., Schlagheck, P., Vandewalle, N., Bastin, T., & Martin, J. (08 May 2016). Scattering theory of walking droplets in the presence of obstacles. *New Journal of Physics, 18*, 113037. doi:10.1088/1367-2630/18/11/113037

We aim to describe a droplet bouncing on a vibrating bath using a simple and highly versatile model inspired from quantum mechanics. Close to the Faraday instability, a long-lived surface wave is created at each bounce, which serves as a pilot wave for 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. We ...

Engl, T., Dujardin, J., Tisserond, E., Argüelles, A., Richter, K., Urbina, J. D., & Schlagheck, P. (May 2016). *Coherent backscattering in the Fock space of Bose- and Fermi-Hubbard systems*. Poster session presented at Ultracold Quantum Gases - Current Trends and Future Perspectives, Bad Honnef, Germany.

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 ...

Schlagheck, P., & Shepelyansky, D. L. (March 2016). *Dynamical thermalization in Bose-Hubbard systems*. Paper presented at DPG-Frühjahrstagung (spring meeting), Regensburg, Germany.

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 exp...

Dujardin, J., Engl, T., & Schlagheck, P. (January 2016). Breakdown of Anderson localization in the transport of Bose-Einstein condensates through one-dimensional disordered potentials. *Physical Review. A, 93*, 013612. doi:10.1103/PhysRevA.93.013612

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 metho...

Schlagheck, P., & Shepelyansky, D. L. (January 2016). Dynamical thermalization in Bose-Hubbard systems. *Physical Review. E ,Statistical, Nonlinear, and Soft Matter Physics, 93*, 012126. doi:10.1103/PhysRevE.93.012126

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 consid...

Wisniacki, D. A., & Schlagheck, P. (December 2015). Quantum manifestations of classical nonlinear resonances. *Physical Review. E ,Statistical, Nonlinear, and Soft Matter Physics, 92*, 062923. doi:10.1103/PhysRevE.92.062923

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 express...

Dujardin, J. (2015). *Coherence and many-body effects in the transport of Bose–Einstein condensates*. Unpublished doctoral thesis, ULiège - Université de Liège.

Jury: Schlagheck, P. (Promotor), Silhanek, A., Richter, K., Saenz, A., Bastin, T., & Martin, J.

Jury: Schlagheck, P. (Promotor), Silhanek, A., Richter, K., Saenz, A., Bastin, T., & Martin, J.

This thesis presents investigations on the interplay of coherence and many-body effects in the quasi one-dimensional transport of Bose-Einstein condensates (BEC) through scattering potentials. Such configurations can be realized with guided atom lasers that provide a coherent atomic beam. An exact theoretical description of the dynamics is out of reach due to the presence atom-atom interactions. Different levels of approximations are nevertheless possible with their strengths and weaknesses. ...

Dujardin, J., Engl, T., Urbina, J. D., & Schlagheck, P. (October 2015). Describing many-body bosonic waveguide scattering with the truncated Wigner method. *Annalen der Physik, 527*, 629. doi:10.1002/andp.201500113

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 pro...

Tomkovic, J., Muessel, W., Strobel, H., Löck, S., Schlagheck, P., Ketzmerick, R., & Oberthaler, M. (2015). *Observing the emergence of chaos in a many-particle quantum system*. Eprint/Working paper retrieved from https://orbi.uliege.be/2268/199805.

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...

Engl, T., Dujardin, J., Tisserond, E., Argüelles, A., Richter, K., Urbina, J. D., & Schlagheck, P. (June 2015). *Coherent backscattering in the Fock space of a disordered Bose-Hubbard system*. Poster session presented at Quantum Correlated Matter and Chaos: A workshop in Honor of the Life and Work of Richard Prange, Dresden, Germany.

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 int...

Chrétien, R., Dujardin, J., Petitjean, C., & Schlagheck, P. (13 May 2015). *Transport of Bose-Einstein Condensates through Aharonov-Bohm rings*. Poster session presented at Annual Scientific Meeting of the Belgian Physical Society, Liege, Belgium.

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 tha...

Dujardin, J., Argüelles, A., & Schlagheck, P. (11 March 2015). Elastic and inelastic transmission in guided atom lasers: A truncated Wigner approach. *Physical Review. A, 91*, 033614. doi:10.1103/PhysRevA.91.033614

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-sta...

Dujardin, J., Saenz, A., & Schlagheck, P. (December 2014). A study of one-dimensional transport of Bose-Einstein condensates using exterior complex scaling. *Applied Physics. B, Lasers and Optics, 117* (3), 765. doi:10.1007/s00340-014-5804-3

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 ...

Richardson, C. D., Schlagheck, P., Martin, J., Vandewalle, N., & Bastin, T. (2014). *On the analogy of quantum wave-particle duality with bouncing droplets*. Eprint/Working paper retrieved from https://orbi.uliege.be/2268/199797.

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, howeve...

Schlagheck, P. (June 2014). *Coherent backscattering in the Fock space of a disordered Bose-Hubbard system*. Paper presented at Quantum Disordered Systems: What’s Next?, Toulouse, France.

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 int...

Engl, T., Dujardin, J., Argüelles, A., Schlagheck, P., Richter, K., & Urbina, J. D. (2014). Coherent Backscattering in Fock Space: A Signature of Quantum Many-Body Interference in Interacting Bosonic Systems. *Physical Review Letters, 112*, 140403. doi:10.1103/PhysRevLett.112.140403

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 interfer...

Richardson, C., Schlagheck, P., Martin, J., Vandewalle, N., & Bastin, T. (2014). Nonlinear Schrödinger wave equation with linear quantum behavior. *Physical Review. A, 89*, 032118. doi:10.1103/PhysRevA.89.032118

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 n...

Kristinsdóttir, L. H., Karlström, O., Cremon, J. C., Schlagheck, P., Wacker, A., & Reimann, S. M. (2013). Total Current Blockade in an Ultracold Dipolar Quantum Wire. *Physical Review Letters, 110*, 085303. doi:10.1103/PhysRevLett.110.085303

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 dipola...

Le Deunff, J., Mouchet, A., & Schlagheck, P. (2013). Semiclassical description of resonance-assisted tunneling in one-dimensional integrable models. *Physical Review. E ,Statistical, Nonlinear, and Soft Matter Physics, 88*, 042927. doi:10.1103/PhysRevE.88.042927

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 ...

Nowak, B., Kinnunen, J. J., Holland, M. J., & Schlagheck, P. (October 2012). Delocalization of ultracold atoms in a disordered potential due to light scattering. *Physical Review. A, 86*, 043610. doi:10.1103/PhysRevA.86.043610

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 o...

Hartmann, T., Hartung, M., Michl, J., Petitjean, C., Urbina, J. D., Wellen, T., Müller, C. A., Richter, K., & Schlagheck, P. (June 2012). *Weak localization with interacting Bose-Einstein condensates*. Poster session presented at Theory of Quantum Gases and Quantum Coherence, Lyon, France.

We study the quasi-stationary propagation of Bose-Einstein condensates through two-dimensional mesoscopic scattering geometries that correspond to disorder potentials [1] or to ballistic billiard con nements with chaotic classical dynamics [2]. Our theoretical approach is based on the two-dimensional Gross-Pitaevskii equation, which is numerically integrated in order to determine reflection and transmission probabilities associated with self-consistent stationary scattering states, and which ...

Dujardin, J., Argüelles Parra, A., & Schlagheck, P. (29 March 2012). *1D many-body quantum transport of Bose-Einstein condensates : a truncated Wigner approach*. Poster session presented at DPG Spring Meeting 2012, Berlin, Germany.

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 boundar...

Hartmann, T., Michl, J., Petitjean, C., Wellens, T., Urbina, J.-D., Richter, K., & Schlagheck, P. (2012). Weak localization with nonlinear bosonic matter waves. *Annals of Physics, 327*, 1998-2049. doi:10.1016/j.aop.2012.04.002

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...

Hartmann, T., Urbina, J.-D., Richter, K., & Schlagheck, P. (2012). Intensity distribution of non-linear scattering states. In M. Robnik & V. G. Romanovski (Eds.), *LET'S FACE CHAOS THROUGH NONLINEAR DYNAMICS* (pp. 193). AIP.

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 ...

Klein, C., Petitjean, C., & Waintal, X. (2012). Interplay between Nonequilibrium and Equilibrium Spin Torque Using Synthetic Ferrimagnets. *Physical Review Letters, 108* (8), 086601-5. doi:10.1103/PhysRevLett.108.086601

We discuss the current induced magnetization dynamics of spin valves F-0 vertical bar N vertical bar SyF where the free layer is a synthetic ferrimagnet SyF made of two ferromagnetic layers F-1 and F-2 coupled by RKKY exchange coupling. When the magnetic moment of the outer layer F-2 dominates the magnetization of the SyF, the sign of the effective spin torque exerted on the layer F-1 is controlled by the coupling's strength: for weak coupling the spin torque tends to antialign F-1's magnetiz...

Petitjean, C., Luc, D., & Waintal, X. (2012). Unified Drift-Diffusion Theory for Transverse Spin Currents in Spin Valves, Domain Walls, and Other Textured Magnets. *Physical Review Letters, 109* (11), 117204-5. doi:10.1103/PhysRevLett.109.117204

Spins transverse to the magnetization of a ferromagnet only survive over a short distance. We develop a drift-diffusion approach that captures the main features of transverse spin effects in systems with arbitrary spin textures (e.g., vortices and domain walls) and generalizes the Valet-Fert theory. In addition to the standard characteristic lengths (mean free path for majority and minority electrons, and spin diffusion length), the theory introduces two length scales, the transverse spin coh...

Shevtsov, O., Carmier, P., Petitjean, C., Groth, C., Carpentier, D., & Waintal, X. (2012). Graphene-Based Heterojunction between Two Topological Insulators. *Physical Review X, 2* (3), 031004-10. doi:10.1103/PhysRevX.2.031004

Quantum Hall (QH) and quantum spin Hall (QSH) phases have very different edge states and, when going from one phase to the other, the direction of one edge state must be reversed. We study this phenomenon in graphene in the presence of a strong perpendicular magnetic field on top of a spin-orbit (SO)-induced QSH phase. We show that, below the SO gap, the QSH phase is virtually unaffected by the presence of the magnetic field. Above the SO gap, the QH phase is restored. An electrostatic gate p...

Borlenghi, S., Rychkov, V., Petitjean, C., & Waintal, X. (2011). Multiscale approach to spin transport in magnetic multilayers. *Physical Review. B, Condensed Matter and Materials Physics, 84* (3), 035412-16. doi:10.1103/PhysRevB.84.035412

This paper discusses two dual approaches to spin transport in magnetic multilayers: a direct, purely quantum, approach based on a tight-binding (TB) model and a semiclassical approach [continuous random matrix theory CRMT]. The combination of both approaches provides a systematic way to perform multiscale simulations of systems that contain relevant physics at scales larger (spin accumulation, spin diffusion) and smaller (specular reflexions, tunneling) than the elastic mean free paths of the...

Kuipers, J., Engl, T., Berkolaiko, G., Petitjean, C., Waltner, D., & Richter, K. (2011). Density of states of chaotic Andreev billiards. *Physical Review. B, Condensed Matter and Materials Physics, 83* (19), 195316-21. doi:10.1103/PhysRevB.83.195316

Quantum cavities or dots have markedly different properties depending on whether their classical counterparts are chaotic or not. Connecting a superconductor to such a cavity leads to notable proximity effects, particularly the appearance, predicted by random matrix theory, of a hard gap in the excitation spectrum of quantum chaotic systems. Andreev billiards are interesting examples of such structures built with superconductors connected to a ballistic normal metal billiard since each time a...

Plötz, P., Schlagheck, P., & Wimberger, S. (2011). Effective spin model for interband transport in a Wannier-Stark lattice system. *European Physical Journal D -- Atoms, Molecules, Clusters and Optical Physics, 63*, 47. doi:10.1140/epjd/e2010-10554-7

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.

Schlagheck, P., Malet, F., Cremon, J. C., & Reimann, S. M. (August 2010). *Transport and interaction blockade of cold bosonic atoms in a triple-well potential*. Poster session presented at Quo vadis Bose-Einstein condensation?, Dresden, Germany.

We investigate the transport properties of cold bosonic atoms in a 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. Such configurations can be realized by optical triple-well lattices generalizing the setup realized in the interaction blockade experiment by Cheinet et al. [Phys. Rev. Lett. 101, 090404 (2008)]. Bias and gate "voltages" are introduced...

Schlagheck, P., Malet, F., Cremon, J. C., & Reimann, S. M. (May 2010). *Transport and interaction blockade of cold bosonic atoms in a triple-well potential*. Poster session presented at Time-dependent dynamics and non-equilibrium quantum systems, Budapest, Hungary.

We investigate the transport properties of cold bosonic atoms in a 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. Such configurations can be realized by optical triple-well lattices generalizing the setup realized in the interaction blockade experiment by Cheinet et al. [Phys. Rev. Lett. 101, 090404 (2008)]. Bias and gate "voltages" are introduced...

Briquet, C., Renders, P., & Petitjean, E. (2010). A Virtualization-Based Retrieval and Update API for XML-Encoded Corpora. In *Proceedings of Balisage: The Markup Conference 2010*. doi:10.4242/BalisageVol5.Briquet01

Providing support for flexible automated tagging of text-oriented XML documents (i.e. text with intersparsed markup) is a challenging issue. This requires support for tag-aware full text search (i.e. the capability to skip some tags or make invisible whole sections of the document), match points, and transparent updates. An API addressing this issue is described. Based on the virtualization of selected sections of the XML document, the API produces a tag-aware representation, backed by the do...

Engl, T., Kuipers, J., Berkolaiko, G., Petitjean, C., Waltner, D., & Richter, K. (2010). Semiclassics of Andreev billiards. In vanTiggelen, B Stockmann, HJ (Ed.), *MESOSCOPIC PHYSICS IN COMPLEX MEDIA* (pp. 03009-2). E D P Sciences. doi:10.1051/iesc/2010mpcm03009

By coupling a superconductor to a quantum cavity or dot one may decide whether its classical counterpart has integrable or chaotic dynamics by looking at the density of states. Random matrix theory (RMT) predicts a true gap of the order of the Thoules energy E(T) if the classical motion is chaotic and an exponential damping in the case of integrable motion. We use semiclassical techniques developed in the recent years to reproduce the RMT predictions. Using the same techniques we show that th...

Ernst, T., Paul, T., & Schlagheck, P. (2010). Transport of ultracold Bose gases beyond the Gross-Pitaevskii description. *Physical Review. A, General Physics, 81* (1), 013631. doi:10.1103/PhysRevA.81.013631

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 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 ...

Kuipers, J., Waltner, D., Petitjean, C., Berkolaiko, G., & Richter, K. (2010). Semiclassical Gaps in the Density of States of Chaotic Andreev Billiards. *Physical Review Letters, 104* (2), 027001-4. doi:10.1103/PhysRevLett.104.027001

The connection of a superconductor to a chaotic ballistic quantum dot leads to interesting phenomena, most notably the appearance of a hard gap in its excitation spectrum. Here we treat such an Andreev billiard semiclassically where the density of states is expressed in terms of the classical trajectories of electrons (and holes) that leave and return to the superconductor. We show how classical orbit correlations lead to the formation of the hard gap, as predicted by random matrix theory in ...

Loeck, S., Baecker, A., Ketzmerick, R., & Schlagheck, P. (2010). Regular-to-Chaotic Tunneling Rates: From the Quantum to the Semiclassical Regime. *Physical Review Letters, 104* (11), 114101. doi:10.1103/PhysRevLett.104.114101

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-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.

Schlagheck, P., Malet, F., Cremon, J. C., & Reimann, S. M. (2010). Transport and interaction blockade of cold bosonic atoms in a triple-well potential. *New Journal of Physics, 12*, 065020. doi:10.1088/1367-2630/12/6/065020

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...

Jacquod, P., & Petitjean, C. (2009). Decoherence, entanglement and irreversibility in quantum dynamical systems with few degrees of freedom. *Advances in Physics, 58* (2), 67-196. doi:10.1080/00018730902831009

In this review we summarize and amplify recent investigations of coupled quantum dynamical systems with few degrees of freedom in the short-wavelength, semiclassical limit. Focusing on the correspondence between quantum and classical physics, we mathematically formulate and attempt to answer three fundamental questions. (i) How can one drive a small dynamical quantum system to behave classically? (ii) What determines the rate at which two single-particle quantum-mechanical subsystems become e...

Paul, T., Albert, M., Schlagheck, P., Leboeuf, P., & Pavloff, N. (2009). Anderson localization of a weakly interacting one-dimensional Bose gas. *Physical Review. A, 80* (3), 033615. doi:10.1103/PhysRevA.80.033615

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 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 sh...

Petitjean, C., Waltner, D., Kuipers, J., Adagideli, I., & Richter, K. (2009). Semiclassical approach to the ac conductance of chaotic cavities. *Physical Review. B, Condensed Matter and Materials Physics, 80* (11), 115310-12. doi:10.1103/PhysRevB.80.115310

We address frequency-dependent quantum transport through mesoscopic conductors in the semiclassical limit. By generalizing the trajectory-based semiclassical theory of dc quantum transport to the ac case, we derive the average screened conductance as well as ac weak-localization corrections for chaotic conductors. Thereby we confirm respective random matrix results and generalize them by accounting for Ehrenfest time effects. We consider the case of a cavity connected through many leads to a ...

Hartung, M., Wellens, T., Mueller, C. A., Richter, K., & Schlagheck, P. (2008). Coherent backscattering of Bose-Einstein condensates in two-dimensional disorder potentials. *Physical Review Letters, 101* (2), 020603. doi:10.1103/PhysRevLett.101.020603

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 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. W...

Whitney, R. S., Jacquod, P., & Petitjean, C. (2008). Dephasing in quantum chaotic transport: A semiclassical approach. *Physical Review. B, Condensed Matter and Materials Physics, 77* (4), 045315-22. doi:10.1103/PhysRevB.77.045315

We investigate the effect of dephasing (decoherence) on quantum transport through open chaotic ballistic conductors in the semiclassical limit of small Fermi wavelength to system size ratio, lambda(F)/L < 1. We use the trajectory-based semiclassical theory to study a two-terminal chaotic dot with decoherence originating from (i) an external closed quantum chaotic environment, (ii) a classical source of noise, and (iii) a voltage probe, i.e., an additional current-conserving terminal. We focus...

Lassl, A., Schlagheck, P., & Richter, K. (2007). Effects of short-range interactions on transport through quantum point contacts: A numerical approach. *Physical Review. B, Condensed Matter, 75* (4). doi:10.1103/PhysRevB.75.045346

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...

Paul, T., Hartung, M., Richter, K., & Schlagheck, P. (2007). Nonlinear transport of Bose-Einstein condensates through mesoscopic waveguides. *Physical Review. A, 76* (6). doi:10.1103/PhysRevA.76.063605

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 intera...

Paul, T., Schlagheck, P., Leboeuf, P., & Pavloff, N. (2007). Superfluidity versus Anderson localization in a dilute Bose gas. *Physical Review Letters, 98* (21). doi:10.1103/PhysRevLett.98.210602

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 lar...

Petitjean, C., Bevilaqua, D. V., Heller, E. J., & Jacquod, P. (2007). Displacement echoes: Classical decay and quantum freeze. *Physical Review Letters, 98* (16), 164101-4. doi:10.1103/PhysRevLett.98.164101

Motivated by neutron scattering experiments, we investigate the decay of the fidelity with which a wave packet is reconstructed by a perfect time-reversal operation performed after a phase-space displacement. In the semiclassical limit, we show that the decay rate is generically given by the Lyapunov exponent of the classical dynamics. For small displacements, we additionally show that, following a short-time Lyapunov decay, the decay freezes well above the ergodic value because of quantum ef...

Petitjean, C., Jacquod, P., & Whitney, R. S. (2007). Dephasing in the semiclassical limit is system-dependent. *JETP Letters, 86* (10), 647-651. doi:10.1134/S0021364007220079

Dephasing in open quantum chaotic systems has been investigated in the limit of large system sizes to the Fermi wavelength ratio, L/lambda F >> 1. The weak localization correction g(wl) to the conductance for a quantum dot coupled to (i) an external closed dot and (ii) a dephasing voltage probe is calculated in the semiclassical approximation. In addition to the universal algebraic suppression g wl proportional to (1 + tau(D)/tau(phi))(-1) with the dwell time tau(D) through the cavity and the...

Schlagheck, P., & Wimberger, S. (2007). Nonexponential decay of Bose-Einstein condensates: a numerical study based on the complex scaling method. *Applied Physics. B, Lasers and Optics, 86* (3), 385-390. doi:10.1007/s00340-006-2511-8

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 per...

Madronero, J., Ponomarev, A., Carvalho, A. R. R., Wimberger, S., Viviescas, C., Kolovsky, A., Hornberger, K., Schlagheck, P., Krug, A., & Buchleitner, A. (2006). Quantum chaos, transport, and control - In quantum optics. *Advances in Atomic and Molecular Physics, 53*, 33-73. doi:10.1016/S1049-250X(06)53002-2

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 perspecti...

Mouchet, A., Eltschka, C., & Schlagheck, P. (2006). Influence of classical resonances on chaotic tunneling. *Physical Review. E ,Statistical, Nonlinear, and Soft Matter Physics, 74* (2). doi:10.1103/PhysRevE.74.026211

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 l...

Petitjean, C., & Jacquod, P. (2006). Lyapunov generation of entanglement and the correspondence principle. *Physical Review Letters, 97* (19), 194103-4. doi:10.1103/PhysRevLett.97.194103

We show how a classically vanishing interaction generates entanglement between two initially nonentangled particles, without affecting their classical dynamics. For chaotic dynamics, the rate of entanglement is shown to saturate at the Lyapunov exponent of the classical dynamics as the interaction strength increases. In the saturation regime, the one-particle Wigner function follows classical dynamics better and better as one goes deeper and deeper in the semiclassical limit. This demonstrate...

Petitjean, C., & Jacquod, P. (2006). Quantum reversibility and echoes in interacting systems. *Physical Review Letters, 97* (12), 124103-4. doi:10.1103/PhysRevLett.97.124103

In echo experiments, imperfect time-reversal operations are performed on a subset of the total number of degrees of freedom. To capture the physics of these experiments, we introduce a partial fidelity M(B)(t), the Boltzmann echo, where only part of the system's degrees of freedom can be time reversed. We present a semiclassical calculation of M(B)(t). We show that, as the time-reversal operation is performed more and more accurately, the decay rate of M(B)(t) saturates at a value given by th...

Schlagheck, P., Eltschka, C., & Ullmo, D. (2006). Resonance- and Chaos-Assisted Tunneling. In K. Yamanouchi, S. L. Chin, P. Agostini, & G. Agostini (Eds.), *Progress in Ultrafast Intense Laser Science I* (pp. 107-131). Berlin, Germany: Springer.

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 be...

Schlagheck, P., & Paul, T. (2006). Complex-scaling approach to the decay of Bose-Einstein condensates. *Physical Review. A, 73* (2). doi:10.1103/PhysRevA.73.023619

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-...

Wimberger, S., Schlagheck, P., Eltschka, C., & Buchleitner, A. (2006). Resonance-assisted decay of nondispersive wave packets. *Physical Review Letters, 97* (4). doi:10.1103/PhysRevLett.97.043001

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.

Wimberger, S., Schlagheck, P., & Mannella, R. (2006). Tunnelling rates for the nonlinear Wannier-Stark problem. *Journal of Physics : B Atomic Molecular and Optical Physics, 39* (3), 729-740. doi:10.1088/0953-4075/39/3/024

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 i...

Eltschka, C., & Schlagheck, P. (2005). Resonance- and chaos-assisted tunneling in mixed regular-chaotic systems. *Physical Review Letters, 94* (1), 014101. doi:10.1103/PhysRevLett.94.014101

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 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 qua...

Madronero, J., Schlagheck, P., Hilico, L., Gremaud, B., Delande, D., & Buchleitner, A. (2005). Decay rates of planar helium. *Europhysics Letters, 70* (2), 183-189. doi:10.1209/epl/i2004-10474-0

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.

Paul, T., Leboeuf, P., Pavloff, N., Richter, K., & Schlagheck, P. (2005). Nonlinear transport of Bose-Einstein condensates through waveguides with disorder. *Physical Review. A, 72* (6). doi:10.1103/PhysRevA.72.063621

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 stati...

Paul, T., Richter, K., & Schlagheck, P. (2005). Nonlinear resonant transport of Bose-Einstein condensates. *Physical Review Letters, 94* (2). doi:10.1103/PhysRevLett.94.020404

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 sa...

Petitjean, C., & Jacquod, P. (2005). Mesoscopic fluctuations of the Loschmidt echo. *Physical Review. E ,Statistical, Nonlinear, and Soft Matter Physics, 71* (3), 036223-6. doi:10.1103/PhysRevE.71.036223

We investigate the time-dependent variance of the fidelity with which an initial narrow wave packet is reconstructed after its dynamics is time reversed with a perturbed Hamiltonian. In the semiclassical regime of perturbation, we show that the variance first rises algebraically up to a critical time t(c), after which it decays. To leading order in the effective Planck's constant h(eff), this decay is given by the sum of a classical term similar or equal to exp[-2 lambda t], a quantum term si...

Schlagheck, P., & Buchleitner, A. (2003). Nondispersive two-electron wave packets in driven helium. *European Physical Journal D -- Atoms, Molecules, Clusters and Optical Physics, 22* (3), 401-415. doi:10.1140/epjd/e2003-00017-9

We provide a detailed quantum treatment of the spectral characteristics and of the dynamics of nondispersive two-electron wave packets along the periodically driven, collinear frozen planet configuration of helium. These highly correlated, long-lived wave packets arise as a quantum manifestation of regular islands in a mixed classical phase space, which are induced by nonlinear resonances between the external driving and the unperturbed dynamics of the frozen-planet configuration. Particular ...

Schlagheck, P., Pingel, D., & Schmelcher, P. (2003). Collinear helium under periodic driving: Stabilization of the asymmetric stretch orbit. *Physical Review. A, 68* (5), 053410. doi:10.1103/PhysRevA.68.053410

The collinear eZe configuration of helium, with the electrons on opposite sides of the nucleus, is studied in the presence of an external electromagnetic (laser or microwave) field. We show that the classically unstable "asymmetric stretch" orbit, on which doubly excited intrashell states of helium with maximum interelectronic angle are anchored, can be stabilized by means of a resonant driving where the frequency of the electromagnetic field equals the frequency of Kepler-like oscillations a...

Brodier, O., Schlagheck, P., & Ullmo, D. (2002). Resonance-assisted tunneling. *Annals of Physics, 300* (1), 88-136. doi:10.1006/aphy.2002.6281

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 an underlying picture, we obtain that the quantum state is coupled, via a succession of classically forbidden transitions across n...

Brodier, O., Schlagheck, P., & Ullmo, D. (2001). Resonance-assisted tunneling in near-integrable systems. *Physical Review Letters, 87* (6), 064101. doi:10.1103/PhysRevLett.87.064101

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/(h) over bar obtained for ...

Schlagheck, P., & Buchleitner, A. (2001). Algebraic decay of the survival probability in chaotic helium. *Physical Review. A, 63* (2), 024701. doi:10.1103/PhysRevA.63.024701

We demonstrate that the classical helium atom exhibits algebraic decay of the survival probability in the autoionizing eZe configuration. Excitation towards asymptotic orbits of marginal stability is identified as the cause of the nonexponential decay. Since one electron travels along a bound Kepler trajectory of infinite excitation in these orbits, we argue that the classical decay law will prevail in the quantum dynamics of a wave packet launched along the eZe configuration.

Madsen, L. B., Schlagheck, P., & Lambropoulos, P. (2000). Laser-induced transitions between triply excited hollow states. *Physical Review. A, 62* (6), 062719. doi:10.1103/PhysRevA.62.062719

Using complex scaling and a correlated basis constructed in terms of B splines, we calculate the Li+ photoion yield in the presence of a laser-induced coupling between the triply excited 2s(2)2p(P-2(0)) and 2s2p(2)(D-2(e)) resonances in lithium, the first of which is assumed to be excited by synchrotron radiation from the ground state. The laser coupling between the triply excited states is shown to lead to a significant and readily measurable modification of the line profile which provides a...

Madsen, L. B., Schlagheck, P., & Lambropoulos, P. (2000). Laser-induced transitions between triply excited hollow states. *Physical Review Letters, 85* (1), 42-45. doi:10.1103/PhysRevLett.85.42

We present an ab initio calculation of the Li+ photoion yield in the presence of laser coupling between the triply; excited 2s(2)2p(2)P(o) and 2s2p(2) D-2(e) resonances in lithium, the first of which is assumed excited by synchrotron radiation from the ground state. The laser coupling between the triply excited states is shown to lead to a significant and readily measurable modification of the line profile which provides a unique probe of the dipole strength between highly correlated triply e...

Schlagheck, P., & Buchleitner, A. (1999). Nondispersive two-electron wave packets in the collinear driven helium atom. *Europhysics Letters, 46* (1), 24-30. doi:10.1209/epl/i1999-00557-x

Nondispersive two-electron wave packets are found in the Floquet spectrum of the driven, one-dimensional helium atom. In classical phase space, they are anchored to the principal nonlinear resonance between the collinear frozen planet orbit and the driving field linearly polarized along the orbit. These novel, highly correlated eigenstates of the driven three-body Coulomb problem, exhibit lifetimes of the order of 10(3)...10(7) periods of the driving field, with strong fluctuations reminiscen...

Schlagheck, P., & Buchleitner, A. (1999). Stable classical configurations in strongly driven helium. *Physica D. Nonlinear Phenomena, 131* (1-4), 110-124. doi:10.1016/S0167-2789(98)00223-1

We present a detailed analysis of the classical dynamics of the frozen-planet configuration of helium in an external, linearly polarized electromagnetic field. It is shown that the phase space of the collinear frozen planet in the held is mixed regular-chaotic and exhibits regular islands corresponding to nonlinear resonances between the periodic external force and the frozen-planet dynamics. An analysis of the transverse stability properties of the configuration shows that - except for regul...

Bachau, H., Gayet, R., Lambropoulos, P., Schlagheck, P., & Wolf, A. (1998). Laser-assisted dielectronic recombination in C4+ ions. *Journal of Physics : B Atomic Molecular and Optical Physics, 31* (14), 3263-3280. doi:10.1088/0953-4075/31/14/021

We study the effect of laser-driven transitions between autoionizing resonances on the dielectronic recombination rates observed after the formation of such resonances in electron-ion collisions. The autoionizing states of S-1(e) and P-1(0) symmetry belonging to the 2l2l' and 2l3l' configurations of C4+ are considered. The resonance parameters are calculated in the Feshbach formalism and compared with other accurate calculations, and transition dipole moments between the autoionizing states a...

Schlagheck, P., & Buchleitner, A. (1998). Classical support for non-dispersive two electron wave packets in the driven helium atom [letter to the editor]. *Journal of Physics : B Atomic Molecular and Optical Physics, 31* (11), 489-L495. doi:10.1088/0953-4075/31/11/003

We present numerical evidence for the existence of a classically non-ionizing, highly correlated two-electron configuration which emerges from the frozen planet configuration of helium exposed to an electromagnetic field of linear polarization. A static electric field parallel to the polarization axis prevents this configuration from transverse ionization. We argue that the corresponding nonlinear resonance island in 12D phase space supports nondispersive wave packets of the helium atom in co...

Schlagheck, P., & Lambropoulos, P. (1997). A theoretical description of laser induced dielectronic recombination. *Hyperfine Interactions, 108* (1-3), 267-271. doi:10.1023/A:1012619014627

We present the theoretical description of a dielectronic recombination process in which the autoionizing state is coupled to a bound state by a laser field, The system is described by density matrix equations in which the continuum components of the density matrix have been eliminated. Model calculations with these density matrix equations have been performed in order to compare the spectra of laser induced dielectronic recombination with the corresponding autoionization spectra.

Schlagheck, P., & Lambropoulos, P. (1997). Theory of laser-induced dielectronic recombination: A case study in Helium. *Zeitschrift für Physik. D, Atoms, Molecules, and Clusters, 39* (3), 173-180. doi:10.1007/s004600050125

We present the theoretical description of laser-induced dielectronic recombination in the density matrix formalism and show how the continuum components can be eliminated. The resulting equations are applied to the calculation of specific recombination processes in Helium from the point of view of resolving the involved autoionizing states in the recombination spectrum. We examine how the shape of the spectrum depends on the laser pulse duration in processes in which the autoionizing state to...

Schlagheck, P., Maragakis, P., & Lambropoulos, P. (1996). Theory of laser-induced two-step electron-ion recombination. *Zeitschrift für Physik. D, Atoms, Molecules, and Clusters, 37* (1), 19-27. doi:10.1007/s004600050004

A theoretical framework for the quantitative interpretation of laser-induced electron-ion recombination is presented in terms of the density matrix taking into account stochastic bandwidth and pulse duration of the laser. The theory deals with recombination induced from the continuum into one group of states by one laser and further stabilized into a lower group of states by a second laser. Rate equations are then derived from the complete density matrix, and the conditions for their validity...