Quantum Localisation Phenomena

1. Anderson Localisation

Anderson localisation, also known as strong localisation, refers to the absence of diffusion of waves in a random medium. This phenomenon is named after the American physicist Philip Warren Anderson, who first suggested the possibility of electron localisation inside a semiconductor, provided that the degree of randomness of the impurities or defects is sufficiently large. Anderson localisation is a general wave phenomenon that applies to the transport of electromagnetic waves as well as quantum mechanical waves, and should be distinguished from weak localisation, which is the precursor effect of Anderson localisation. Weak localisation originates from the wave interference between multiple-scattering paths. In strong scattering limit, the interferences can completely halt the waves inside the random sample.

2. Dynamical Localisation

Strongly driven one electron Rydberg atoms exhibit strongly chaotic classical dynamics beyond a critical value of the driving field amplitude. In a certain regime of driving field frequencies, the real (quantum) atom exhibits a vanishing ionisation yield, whereas a classical picture predicts efficient diffusive phase space transport towards the ionisation threshold, i.e., efficient chaotic ionisation. This quantum suppression of classically diffusive ionisation has been put into parallel with Anderson localisation of electronic transport in disordered solid state samples, and was baptised ``dynamical localisation'' such as to stress its dynamical (rather than disorder-induced) origin. So far, however, this analogy remained somewhat qualitative in nature, and it remained unclear whether an Anderson-like scenario was the real cause of dynamical localisation effects. With our approximation free treatment of Rydberg states of atomic hydrogen, we strive for a quantitative foundation of this analogy.

Conductance Fluctuations in Atoms
The figure shows the conductance fluctuations in the ionisation yield of a driven Rydberg atom (inset) and the exponential scaling of the conductance in function of the inverse localisation length.

3. Wannier-Stark Localisation

The solutions of the Schrödinger equation for a single-particle in a periodic potential are the famous Bloch waves. These extended waves start to localise in the presence of a linear static (socalled Stark) force, performing now temporally periodic Bloch oscillations. We extend the well-know Wannier-Stark problem to allow for atom-atom interactions and a coupling to higher lying energy bands. Both extensions, particularly if considered simultaneously, bring to light new phenomena. A transition between a Stark-localised and a completely quantum chaotic phase occurs, and the tunnelling-rate distributions of the open system are similar to the predictions of random matrix and Anderson-localisation theory, respectively. These various regimes of complex quantum transport are accessible to state-of-the-art experiments with ultracold bosons or fermions in optical lattices, and in the mean-field regime of small interactions our results have already been verfified experimentally.

Publications

  • C. Albrecht and S. Wimberger
    Induced Delocalization by Correlation and Interaction in the one-dimensional Anderson Model, Phys. Rev. B 85, 045107 (2012)
  • A. Zenesini, H. Lignier, G. Tayebirad, J. Radogostowicz, D. Ciampini, R. Mannella, S. Wimberger, O. Morsch, and E. Arimondo
    Time-resolved measurement of Landau-Zener tunneling in periodic potentials, Phys. Rev. Lett. 103, 090403 (2009)
  • A. Zenesini, C. Sias, H. Lignier, Y. Singh, D. Ciampini, O. Morsch, R. Mannella, E. Arimondo, A. Tomadin, and S. Wimberger
    Resonant tunneling of Bose-Einstein condensates in optical lattices, New J. Phys. 10, 053038 (2008)
  • P. Buonsante and S. Wimberger
    Engineering many-body quantum dynamics by disorder, Phys. Rev. A 77, 041606(R) (2008)
  • A. Tomadin, R. Mannella, and S. Wimberger
    Many-body Landau-Zener tunneling in the Bose-Hubbard model, Phys. Rev. A 77, 013606 (2008)
  • A. Tomadin, R. Mannella, and S. Wimberger
    Many-body interband tunneling as a witness for complex dynamics in the Bose-Hubbard model, Phys. Rev. Lett. 98, 130402 (2007)
  • C. Sias, A. Zenesini, H. Lignier, S. Wimberger, D. Ciampini, O. Morsch, and E. Arimondo
    Resonantly enhanced tunneling of Bose-Einstein condensates in periodic potentials, Phys. Rev. Lett. 98, 120403 (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)
  • A. Krug, S. Wimberger, and A. Buchleitner
    Decay, interference, and chaos: How simple atoms mimic disorder, Eur. Phys. J. D 26, 21 (2003)
  • S. Wimberger, A. Krug, and A. Buchleitner
    Decay rates and survival probabilities in open quantum systems, Phys. Rev. Lett. 89, 263601 (2002)
  • S. Wimberger and A. Buchleitner
    Signatures of Anderson localization in the ionization rates of periodically driven Rydberg states, J. Phys. A: Math. Gen. 34, 7181 (2001)

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