Anderson localization of weakly interacting bosons

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Anderson localization of weakly interacting bosons
Giovanni Modugno
LENS and Dipartimento di Fisica, Università di
Firenze 2 INSTANS Conference, September 11,
2008
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G. Roati, L. Fallani, G. M., C. DErrico C.
Fort, M. Inguscio, M. Fattori, M. Modugno, M.
Zaccanti
The team
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Disorder
Disorder is ubiquitous in nature
Superfluids in porous media
Superconducting thin films
Wave propagation in random media
Still under investigation, despite of several
decades of research also applicative interests
Wave propagation in engineered materials
(photonic lattices)
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Anderson localization
No transport can occurr for DgtJ, due to the
destructive interference of many possible paths
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Anderson localization
An essential feature is the absence of
interactions between particles
Light in powders and disordered photonic
crystals Van Albada Lagendijk, Phys. Rev. Lett.
55, 2692 (1985) Wiersma, et al. , Nature 390, 671
(1997) Lahini, et al., Phys. Rev. Lett. 100,
013906 (2008).
Microwaves Dalichaouch, et al, Nature 354, 53
(1991).
Ultrasounds Weaver, Wave Motion 12, 129-142
(1990).
Disordered electronic systems Akkermans
Montambaux Mesoscopic Physics of electrons and
photons (Cambridge University Press,2006). Lee
Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985)
Dynamical systems (kicked rotor) under
study Chabè et al, arXiv07094320.
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What about ultracold atoms?
Both Bose and Fermi gases available in traps
Optical standing-waves realize perfect lattices
with adjustable dimensionality
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What about ultracold atoms?
The atoms in a Bose-Einstein condensate are
naturally interacting
Mott insulator in an ordered lattice
M. Greiner et al., Nature 415, 39 (2002)
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What about ultracold atoms?
Tuning of the atom-atom interaction (s-wave
scattering length) is in some case possible
through magnetically-tunable Feshbach resonances
Moerdijk et al, Phys. Rev. A 51, 4852 (1995)
Inouye et al, Nature 392, 151 (1998).
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Our approach to Anderson localization
A binary incommensurate lattice in 1D
quasi-disorder is easier to realize than random
disorder, but shows the same phenomenology
An ultracold Bose gas of 39K atoms precise
tuning of the interaction to zero
Investigation of transport in space and of
momentum distribution direct observation of
Anderson localization for matter-waves
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Disorder models
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Realization of the Aubry-Andrè model
The first lattice sets the tunneling energy J The
second lattice controls the site energy
distribution D
S. Aubry and G. André, Ann. Israel Phys. Soc. 3,
133 (1980) G. Harper, Proc. Phys. Soc. A 68, 674
(1965). Grempel, D. R., Fishman, S. Prange, R.
E., Phys. Rev. Lett. 49, 833-836 (1982).
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Localization threshold in the A-A model
Solution of the A-A model for the experimental
parameters b 1030/860 1.1972..
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Energy spectrum
4J
2D
Localization takes place at energies well above
the disorder
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The weakly interacting Bose gas
G. Roati et al. Phys. Rev. Lett. 99, 010403
(2007).
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Experimental scheme
Roati et al., Nature 453, 895 (2008)
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Probing the transport properties
The noninteracting BEC is initially confined in a
harmonic trap and then left free to expand in the
quasiperiodic lattice
Ballistic expansion with reduced velocity
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Probing the transport properties
0 ms
time
750 ms
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Probing the transport properties
Size of the condensate after 750 ms of expansion
in the quasi-periodic lattice
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Probing the spatial distribution
No disorder wavefunction is delocalized on the
whole system size ...
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Exponential localization
Fit of the density distribution with a
generalized exponential function
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Probing the momentum distribution
Long free expansion x?k
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Probing the momentum distribution
experiment
theory
Density distribution after time-of-flight of the
initial stationary state
Width of the central peak
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Counting the localized states
one localized state
two localized states
three localized states
10 localized states
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AL of matter-waves in random disorder (no lattice)
Before expansion
After expansion
J. Billy et al., Nature 453, 891 (2008)
(Bouyer-Aspect group, Orsay)
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AL of photons in a quasi-disordered lattice
Lahini. et al., arXiv (2008). (Group of
Silberberg, Weizmann)
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Whats next?
Disorder with controllable interaction. The
disordered Bose-Hubbard model
Higher dimensionality for disorder ideal and
superfluid Fermi gases random disorder
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Delocalization due to interaction preliminary
No interaction few independent localized states
With interaction localized states get more
extendend and lock in phase
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Delocalization due to interaction preliminary
a1.7 a0 U0.15 D
a9.6 a0 U0.8 D
a23 a0 U2.0 D
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Quantum gases experiments at LENS
Three-body Efimov physics
Quantum gases with dipolar interaction
Quantum interferometry, and fundamental forces
close to surfaces