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.
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)
[back to group page]