Superballistic transport and anomalous diffusion in inhomogeneous lattices
seminar Quantum Dynamics
on November 6, 2013
Alexander Szameit
Universität Jena
Superballistic transport and anomalous diffusion in inhomogeneous lattices
Wave transport in time-independent potentials is formally divided into two major categories depending on how the second moment of the evolving excitation grows with 'time'. If translational symmetry is present, the eigenmodes of the system are plane waves or Floquet-Bloch modes [1], and the variance of an initially localized excitation increases quadratically in time (ballistic spreading). On the other hand, since the pioneering work of Anderson [2], it is known that disorder - at least in one-dimensional (1D) systems - tends to suppress propagation and leads to localization [3]. In this case the modes of the system are exponentially localized with an inverse rate given by the so-called localization length.
In the first part of my demonstration, I will report on our experimental demonstration of anomalous diffusion in a disordered Random Dimer Model (RDM) lattice [4, 5]. In such a system, pairs of adjacent energy levels are assigned at random, leading to two-site correlations in an otherwise random model. Below a certain disorder threshold, a number of transparent states for finite samples emerge, and their existence results in a diffusive and super-diffusive wave propagation.
In the second part of my talk I will provide experimental evidence for a faster than ballistic growth of the variance of an initially localized beam. This superballistic evolution [6] is achieved by employing arrays of evanescent coupled waveguides, where a finite number of irregularly spaced waveguides, is embedded into an otherwise periodic waveguide array having homogeneous intersite spacing.
Importantly, as our results are general, they may pave the way for developments in other fields of physics like for example quantum walk problems of single particles etc.
[1] N. W. Ashcroft and N. D. Mermin, Solid State Physics Brooks Cole (1976).
[2] P. W. Anderson, Phys. Rev. 109, 1492 (1958).
[3] T. Schwartz et al., Nature 446, 52 (2007); Y. Lahini et al., Phys. Rev. Lett. 100, 013906 (2008).
[4] P. Phillips and H. L. Wu, Science 252, 1805(1991)
[5] U. Naether, S. Stützer et al., New J. Phys. 15, 013045 (2013).
[6] L. Hufnagel et al., Phys. Rev E 64, 012301 (2001).