109 research outputs found
Anderson Localization of Bogolyubov Quasiparticles in Interacting Bose-Einstein Condensates
We study the Anderson localization of Bogolyubov quasiparticles in an
interacting Bose-Einstein condensate (with healing length \xi) subjected to a
random potential (with finite correlation length \sigma_R). We derive
analytically the Lyapunov exponent as a function of the quasiparticle momentum
k and we study the localization maximum k_{max}. For 1D speckle potentials, we
find that k_{max} is proportional to 1/\xi when \xi is much larger than
\sigma_R while k_{max} is proportional to 1/\sigma_R when \xi is much smaller
than \sigma_R, and that the localization is strongest when \xi is of the order
of \sigma_R. Numerical calculations support our analysis and our estimates
indicate that the localization of the Bogolyubov quasiparticles is accessible
in current experiments with ultracold atoms.Comment: published version (no significant changes compared to last version
Localization of a matter wave packet in a disordered potential
We theoretically study the Anderson localization of a matter wave packet in a
one-dimensional disordered potential. We develop an analytical model which
includes the initial phase-space density of the matter wave and the spectral
broadening induced by the disorder. Our approach predicts a behavior of the
localized density profile significantly more complex than a simple exponential
decay. These results are confirmed by large-scale and long-time numerical
calculations. They shed new light on recent experiments with ultracold atoms
and may impact their analysis
Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder
We study the Anderson localization of Bogoliubov quasiparticles (elementary
many-body excitations) in a weakly interacting Bose gas of chemical potential
subjected to a disordered potential . We introduce a general mapping
(valid for weak inhomogeneous potentials in any dimension) of the Bogoliubov-de
Gennes equations onto a single-particle Schr\"odinger-like equation with an
effective potential. For disordered potentials, the Schr\"odinger-like equation
accounts for the scattering and localization properties of the Bogoliubov
quasiparticles. We derive analytically the localization lengths for correlated
disordered potentials in the one-dimensional geometry. Our approach relies on a
perturbative expansion in , which we develop up to third order, and we
discuss the impact of the various perturbation orders. Our predictions are
shown to be in very good agreement with direct numerical calculations. We
identify different localization regimes: For low energy, the effective
disordered potential exhibits a strong screening by the quasicondensate density
background, and localization is suppressed. For high-energy excitations, the
effective disordered potential reduces to the bare disordered potential, and
the localization properties of quasiparticles are the same as for free
particles. The maximum of localization is found at intermediate energy when the
quasicondensate healing length is of the order of the disorder correlation
length. Possible extensions of our work to higher dimensions are also
discussed.Comment: Published versio
Engineering the spatial confinement of exciton-polaritons in semiconductors
We demonstrate the spatial confinement of electronic excitations in a solid
state system, within novel artificial structures that can be designed having
arbitrary dimensionality and shape. The excitations under study are
exciton-polaritons in a planar semiconductor microcavity. They are confined
within a micron-sized region through lateral trapping of their photon
component. Striking signatures of confined states of lower and upper polaritons
are found in angle-resolved light emission spectra, where a discrete energy
spectrum and broad angular patterns are present. A theoretical model supports
unambiguously our observations
Direct observation of Anderson localization of matter-waves in a controlled disorder
We report the observation of exponential localization of a Bose-Einstein
condensate (BEC) released into a one-dimensional waveguide in the presence of a
controlled disorder created by laser speckle . We operate in a regime allowing
AL: i) weak disorder such that localization results from many quantum
reflections of small amplitude; ii) atomic density small enough that
interactions are negligible. We image directly the atomic density profiles vs
time, and find that weak disorder can lead to the stopping of the expansion and
to the formation of a stationary exponentially localized wave function, a
direct signature of AL. Fitting the exponential wings, we extract the
localization length, and compare it to theoretical calculations. Moreover we
show that, in our one-dimensional speckle potentials whose noise spectrum has a
high spatial frequency cut-off, exponential localization occurs only when the
de Broglie wavelengths of the atoms in the expanding BEC are larger than an
effective mobility edge corresponding to that cut-off. In the opposite case, we
find that the density profiles decay algebraically, as predicted in [Phys. Rev.
Lett. 98, 210401 (2007)]. The method presented here can be extended to
localization of atomic quantum gases in higher dimensions, and with controlled
interactions
Diffusion and Localization of Cold Atoms in 3D Optical Speckle
In this work we re-formulate and solve the self-consistent theory for
localization to a Bose-Einstein condensate expanding in a 3D optical speckle.
The long-range nature of the fluctuations in the potential energy, treated in
the self-consistent Born approximation, make the scattering strongly velocity
dependent, and its consequences for mobility edge and fraction of localized
atoms have been investigated numerically.Comment: 8 pages, 11 figure
Persistent currents in a Bose-Einstein condensate in the presence of disorder
We examine bosonic atoms that are confined in a toroidal,
quasi-one-dimensional trap, subjected to a random potential. The resulting
inhomogeneous atomic density is smoothened for sufficiently strong, repulsive
interatomic interactions. Statistical analysis of our simulations show that the
gas supports persistent currents, which become more fragile due to the
disorder.Comment: 5 pages, RevTex, 3 figures, revised version, to appear in JLT
Finite temperature phase transition for disordered weakly interacting bosons in one dimension
It is commonly accepted that there are no phase transitions in
one-dimensional (1D) systems at a finite temperature, because long-range
correlations are destroyed by thermal fluctuations. Here we demonstrate that
the 1D gas of short-range interacting bosons in the presence of disorder can
undergo a finite temperature phase transition between two distinct states:
fluid and insulator. None of these states has long-range spatial correlations,
but this is a true albeit non-conventional phase transition because transport
properties are singular at the transition point. In the fluid phase the mass
transport is possible, whereas in the insulator phase it is completely blocked
even at finite temperatures. We thus reveal how the interaction between
disordered bosons influences their Anderson localization. This key question,
first raised for electrons in solids, is now crucial for the studies of atomic
bosons where recent experiments have demonstrated Anderson localization in
expanding very dilute quasi-1D clouds.Comment: 8 pages, 5 figure
Localization of solitons: linear response of the mean-field ground state to weak external potentials
Two aspects of bright matter-wave solitons in weak external potentials are
discussed. First, we briefly review recent results on the Anderson localization
of an entire soliton in disordered potentials [Sacha et al. PRL 103, 210402
(2009)], as a paradigmatic showcase of genuine quantum dynamics beyond simple
perturbation theory. Second, we calculate the linear response of the mean-field
soliton shape to a weak, but otherwise arbitrary external potential, with a
detailed application to lattice potentials.Comment: Selected paper presented at the 2010 Spring Meeting of the Quantum
Optics and Photonics Section of the German Physical Society. V2: minor
changes, published versio
Localization from quantum interference in one-dimensional disordered potentials
We show that the tails of the asymptotic density distribution of a quantum
wave packet that localizes in the the presence of random or quasiperiodic
disorder can be described by the diagonal term of the projection over the
eingenstates of the disordered potential. This is equivalent of assuming a
phase randomization of the off-diagonal/interference terms. We demonstrate
these results through numerical calculations of the dynamics of ultracold atoms
in the one-dimensional speckle and quasiperiodic potentials used in the recent
experiments that lead to the observation of Anderson localization for matter
waves [Billy et al., Nature 453, 891 (2008); Roati et al., Nature 453, 895
(2008)]. For the quasiperiodic case, we also discuss the implications of using
continuos or discrete models.Comment: 5 pages, 3 figures; minor changes, references update
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