Enhancement of Localization in One-Dimensional Random Potentials with Long-Range Correlations Page: 1
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PRL 100, 126402 (2008)
PHYSICAL REVIEW LETTERS
28 MARCH 2008
Enhancement of Localization in One-Dimensional Random Potentials
with Long-Range Correlations
U. Kuhl,' F. M. Izrailev,2 and A. A. Krokhin2'3
1Fachbereich Physik, Philipps-Universitit Marburg, Renthof 5, D-35032 Marburg, Germany
2lnstituto de Fisica, Universidad Autdnoma de Puebla, Apartado Postal J-48, Puebla, Puebla, 72570, Mexico
3Department of Physics, University of North Texas, P.O. Box 311427, Denton, Texas 76203, USA
(Received 7 September 2007; revised manuscript received 9 November 2007; published 28 March 2008)
We experimentally study the effect of enhancement of localization in weak one-dimensional random
potentials. Our experimental setup is a single-mode waveguide with 100 tunable scatterers periodically
inserted into the waveguide. By measuring the amplitudes of transmitted and reflected waves in the
spacing between each pair of scatterers, we observe a strong decrease of the localization length when
white-noise scatterers are replaced by a correlated arrangement of scatterers.
Processes of destructive interference at backscattering
do not vanish after averaging over disorder, unlike inter-
ference at scattering over other directions. In a random
potential this property of backscattering may lead to
Anderson localization . Experimentally it is difficult to
find Anderson localization for electrons due to Coulomb
and electron-phonon interaction, but it was found for pho-
tons in optically diffusive media [2-4] (for a review see
Ref. ). In case of white-noise one-dimensional poten-
tials U(x), where backscattering leads to localization at any
energy E independently of the strength of the potential, the
localization length 1(E) is determined by spectral compo-
sition of the correlation function [6,7],
A(E) 1 -'(E)= (o2/8k2)W(2k). (1)
Here k2 = E is the energy of an eigenstate, W(2k) is the
Fourier harmonic of the correlator (U(x) U(x')), and o2 =
(U2(x)) - (U(x))2 is the variance of disorder. Equation (1)
is obtained in the first (Born) approximation over weak
disorder, i.e., o.2 <<1.
A common opinion is that the shortest localization
length is reached for the most disordered (uncorrelated)
potentials with white-noise spectrum W(k) 1. This opin-
ion is based on the fact that correlations, reducing the
degree of disorder, typically give rise to extended states.
In the dimer model, short-range correlations result in two
resonant extended states [8,9], that was observed in a
semiconductor superlattice . A continuum of extended
states for potentials with long-range correlations was pre-
dicted in Refs. [11,12] and was experimentally verified in a
microwave waveguide with intentionally introduced corre-
lated disorder . Thus, there is a strong evidence that
correlations may destroy localization .
In this Letter we address the opposite situation and show
that correlations in weakly disordered potentials can en-
hance localization for a continuum of states, resulting in
the localization length much shorter than that in a white-
noise potential with the same o-. The effect of localization
PACS numbers: 71.23.An, 03.65.Nk, 42.25.Bs
enhancement is important for random lasers [15,16], where
extremely localized states provide higher efficiency. Our
results clearly demonstrate that the long-range correlations
may either suppress or enhance localization. This conclu-
sion probably has to change a common point of view that
correlations, being a manifestation of some kind of order,
may only suppress localization.
The setup is a single-mode waveguide with transverse
dimensions a = 20 mm, b = 10 mm, and with 100 cylin-
drical scatterers of radius r = 2.5 mm, periodically in-
serted with spacing of d = 20.5 mm, see Fig. 1. In the
experiment, we have exploited the transmission and reflec-
tion of the lowest waveguide mode in the frequency range
between rmin = c/2a - 7.5 GHz and rmax = c/a
c/2b - 15 GHz. The dispersion relation in an empty rect-
angular microwave waveguide is given by k = (2w/c) X
V Vm2 2n where c is the speed of light. Thus the nor-
malized wave vector kd/7 ranges from 0 to 1.8. The setup
was already used to show the "Hofstadter butterfly" 
and mobility edges emerging from correlated disorder .
The arrangement allows to assemble a random potential
with prescribed correlation function.
100 microme tersc rews
-- i i II
1 20,5 2Q5 20
FIG. 1. Schematic view of the waveguide with 100 scatterers.
The waveguide is closed by microwave absorbers at both ends.
The lower antenna can be placed anywhere within the scattering
2008 The American Physical Society
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Kuhl, Ulrich; Izrailev, Felix M. & Krokhin, Arkadii A. Enhancement of Localization in One-Dimensional Random Potentials with Long-Range Correlations, article, March 28, 2008; [College Park, Maryland]. (digital.library.unt.edu/ark:/67531/metadc103275/m1/1/: accessed May 27, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.