Nonlinear Dynamics

1. Nonlinear Dynamics of Bose-Einstein Condensates

Bose-Einstein Condensates loaded into optical lattices open a new arena for the experimental investigation of quantum transport phenomena in spatially periodic potentials. Possibly amended by particle-particle interactions (in the mean-field limit described by the nonlinear Gross-Pitaevskii equation) and decoherence, external perturbations (such as static and/or time-dependent fields) modify the dynamics of ultracold quantum matter. We try to understand the underlying phenomena in detail, and to use our understanding for the controlling and engineering of complex quantum dynamics in ultracold matter. Our research in this field is inspired and partially guided by experiments at Auckland (New Zealand), Kaiserslautern (Germany), Pisa (Italy), Stillwater (USA), Tokyo (Japan).

Scaling function 1 Phase space portrait (inset) and energy increase as a function of the scaled interaction time of kicked cold atoms in the semiclassical limit (left).
















2. Quantum cosmology

Next to the standard Gross-Pitaevskii equation for describing weakly interacting quantum gases, we investigate also the Schrödinger-Poisson equation as an example of highly nonlinear quantum dynamics. The latter models a scalar self-graviting quantum field in the non-relativistic limit, and possibily represents a quantum version of cold dark matter, see e.g.

T. Zimmermann, N. Schwersenz, M. Pietroni, and S. Wimberger,
One-Dimensional Fuzzy Dark Matter Models: Structure Growth and Asymptotic Dynamics, Phys. Rev. D 103, 083018 (2021)
















Publications

  • T. Zimmermann, N. Schwersenz, M. Pietroni, and S. Wimberger,
    One-Dimensional Fuzzy Dark Matter Models: Structure Growth and Asymptotic Dynamics, Phys. Rev. D 103, 083018 (2021)

  • T. Zimmermann, M. Pietroni, J. Madronero, L. Amendola, and S. Wimberger,
    A Quantum Model for the Dynamics of Cold Dark Matter, Condens. Mat. 4(4), 89 (2019)

  • S. Dadras, A. Gresch, C. Groiseau, S. Wimberger, and G. S. Summy
    Quantum walk in momentum space with a Bose-Einstein condensate, Phys. Rev. Lett. 121, 070402 (2018)

  • S. Mailoud Sekkouri and S. Wimberger
    Mean-field transport of a Bose-Einstein condensate, in Emergent Complexity from Nonlinearity, in Physics, Engineering and the Life Sciences, G. Mantica et al. (editors), Springer Proceedings in Physics 191 (Springer, 2017)

  • R. K. Shrestha, J. Ni, W. K. Lam, G. S. Summy, and S. Wimberger
    Dynamical tunneling of a Bose-Einstein condensate in periodically driven systems, Phys. Rev. E 88, 034901 (2013)

  • M. Sadgrove, T. Schell, K. Nakagawa, and S. Wimberger
    Engineering quantum correlations to enhance transport in cold atoms, Phys. Rev. A 87, 013631 (2013)

  • R. Dubertrand, I. Guarneri, and S. Wimberger
    Fidelity for kicked atoms with gravity near a quantum resonance, Phys. Rev. E 85, 036205 (2012)

  • M. Sadgrove and S. Wimberger
    A pseudo-classical method for the atom-optics kicked rotor: from theory to experiment and back, Adv. At. Mol. Opt. Phys. 60, 315-369 (2011, Elsevier, Amsterdam)

  • M. Abb, I. Guarneri, and S. Wimberger
    Pseudoclassical theory for fidelity of nearly resonant quantum rotors, Phys. Rev. E 80, 035206(R) (2009)

  • M. Sadgrove and S. Wimberger
    Pseudo-classical theory for directed transport at quantum resonance, New J. Phys. 11, 083027 (2009)

  • R. Khomeriki, S. Ruffo, and S. Wimberger
    Driven Collective Quantum Tunneling of Ultracold Atoms in Engineered Optical Lattices , Europhys. Lett. 77, 40005 (2007)

  • D. Witthaut, E. M. Graefe, S. Wimberger, and H. J. Korsch
    Bose-Einstein condensates in accelerated double-periodic optical lattices: Coupling and Crossing of resonances, Phys. Rev. A 75, 013617 (2007)

  • P. Schlagheck and S. Wimberger
    Nonexponential decay of Bose-Einstein condensates: a numerical study based on the complex scaling method, Appl. Phys. B 86, 385-390 (2007)

  • E. Persson, S. Fuhrthauer, S. Wimberger, and J. Burgdörfer
    Transient localization in the kicked Rydberg atom , Phys. Rev. A 74, 053417 (2006)

  • G. Carlo, G. Benenti, G. Casati, S. Wimberger, O. Morsch, R. Mannella, and E. Arimondo
    Chaotic ratchet dynamics with cold atoms in a pair of pulsed optical lattices, Phys. Rev. A 74, 033617 (2006)

  • S. Wimberger, P. Schlagheck, Ch. Eltschka, and A. Buchleitner
    Resonance-Assisted Decay of Nondispersive Wave Packets, Phys. Rev. Lett. 97, 043001 (2006)

  • S. Wimberger and M. Sadgrove
    The role of quasi-momentum in the resonant dynamics of the atom-optics kicked rotor, J. Phys. A: Math. Gen. 38, 10549 (2005)

  • S. Wimberger, P. Schlagheck, and R. Mannella
    Tunnelling rates for the nonlinear Wannier-Stark problem, J. Phys. B: At. Mol. Opt. Phys. 39, 729 (2006)

  • S. Wimberger, R. Mannella, O. Morsch, E. Arimondo, A.R. Kolovsky, and A. Buchleitner
    Nonlinearity induced destruction of resonant tunneling in the Wannier-Stark problem, Phys. Rev. A 72, 063610 (2005)

  • M. Sadgrove, S. Wimberger, S. Parkins, and R. Leonhardt
    Ballistic and localized transport for the atom optics kicked rotor in the limit of vanishing kicking period,
    Phys. Rev. Lett. 94, 174103 (2005)

  • S. Wimberger, M. Sadgrove, S. Parkins, and R. Leonhardt
    Experimental verification of a one-parameter scaling law for the quantum and "classical" resonances of the atom-optics kicked rotor, Phys. Rev. A 71, 053404 (2005)

  • S. Wimberger, I. Guarneri, and S. Fishman
    Classical scaling theory of quantum resonances, Phys. Rev. Lett. 92, 084102 (2004)


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