Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Observation of the algebraic localization-delocalization transition in a
  1D disordered potential with a bias force   In a one-dimensional (1D) disordered potential, quantum interferences leading
to Anderson lo-calization are ubiquitous, such that all wave-functions are
exponentially localized. Moreover, no phase transition toward delocalization is
expected in 1D. This behavior is strongly modified in the presence of a bias
force. We experimentally study this case, launching a non-interacting 39 K
Bose-Einstein condensate in a 1D disordered potential induced by a
far-off-resonance laser speckle, while controlling a bias force. In agreement
with theoretical predictions, we observe a transition between algebraic
localization and delocalization as a function of our control parameter that is
the relative strength of the disorder against the bias force. We also
demonstrate that the initial velocity of the wave-packet only plays a role
through an effective disorder strength due to the correlation of the disorder.
Adding a bias force is a quite natural way to probe the transport properties of
quantum systems, a subject of broad interest that can be in particular
addressed with atomic quantum gases thanks to their high degree of control and
versatility [1]. For example, Bloch oscillations has been measured through the
addition of a constant force to atoms in periodic potential induced by an
optical lattice [2]. A force applied to a harmonic trap is equivalent to a trap
displacement. The response to such a displacement permits to reveal the fluid
or insulating behavior of atomic systems. In 1D interacting Bose gases, the
pinning transition by an optical lattice [3] or the insulating transition in
quasi-disordered optical lattice [4, 5] have been studied in this manner. More
recently, transport in quantum gases is also studied in junction-type setup
more analogous to condensed-matter systems: two reservoirs with different
chemical potentials are connected through a constriction. For example, in a gas
of fermions, the quantization of conductance through a quantum point contact
[6] and the superfluid to normal transition in a disordered thin film have been
observed [7]. In our work, we focus on the transport of non-interacting
particles in disordered media. Without a bias force, quantum interferences
between multiple paths lead to Anderson localization [8] whose signature is an
exponential decay in space of single particle wave-function [9]. This
phenomenon is ubiquitous in wave/quantum physics and it has been observed in
many physical contexts [10] including condensed-matter [11] and ultra-cold
atoms [12-14]. One-dimensional truly disordered systems are always localized
[15], contrary to the 3D case where a phase transition between localized and
extended single particle wave-functions takes place as a function of the
disorder strength [16-18]. The localization properties of 1D disordered systems
are modified in the presence of a bias force. Theoretical studies predict a
transition from algebraic localization to delocalization as a function of a
single control non-dimensional parameter $\alpha$ which is the ratio of the
force to the disorder strength [19, 20]. Physically, $\alpha$ is the relative
energy gain $\Delta$E/E of a particle of energy E when moving over a
localization length. Interestingly, in a 1D white noise disorder, this quantity
is independent of E as the localization length is proportional to E. If
$\alpha$ is small, the force does not considerably change the localization
behavior of the particle while for large $\alpha$ its dynamics is severely
affected leading to delocalization. This localization-delocalization transition
is predicted in the infinite time limit for white noise disorder [20]. In a
correlated disorder, as the one produced from a far-off-resonance laser speckle
[21], the situation is more complicated. Speckles have no Fourier component
beyond a spatial frequency 2k c. As a consequence, back-scattering and
localization are not expected in the framework of Born approximation for atoms
with wavevectors k > k c [12, 22]. Since localized wave-functions always have a
small fraction at long distance corresponding to large energies and momenta in
the presence of a bias force, we thus expect correlation-induced delocalization
at infinite time. However, signatures of the algebraic
localization-delocalization transition are predicted to be observable at
transient times [20]. In this paper, we report on the observation of the
algebraic localization-delocalization transition with cold-atoms propagating in
a one dimensional disordered potential in the presence of a controlled bias
force. We experimentally show that the non-dimensional parameter $\alpha$ is
the only relevant parameter to describe the transition. We notice that the
initial velocity of the quantum wave packet only plays a role through the
correlation of the disordered potential, showing that the transition is
in-trinsically energy independent. In the localized regime, we demonstrate an
algebraic decay of the density and measure the corresponding decay exponent as
a function of $\alpha$. At large disorder strength, a saturation of the expo

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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th