David Campbell - Boston University  #
Transfer of Bose-Einstein Condensates through Intrinsic 
Localized Modes in an Optical Lattice #
Atomic Bose-Einstein condensates (BECs) trapped in optical 
lattices (OLs) have been the subject
of great recent experimental and theoretical interest, both in 
their own right and as analog models
of certain solid state systems. Recent studies of the leakage of 
a BEC trapped in an OL have
shown that highly localized nonlinear excitations known as 
"Intrinsic Localized Modes" (ILMs)
can prevent atoms from reaching the leaking boundaries, thereby 
slowing the decay of the
condensate.
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In this talk I report the results of a recent study&sup1; 
(conducted 
with Holger Hennig and
Jerome Dorignac) of this problem. To understand the mechanism by 
which these ILMs
enhance the trapping, we study the case of atom 
transport-"tunneling"-through an
ILM on a nonlinear trimer. We show that this transport is 
related to the destabilization
and subsequent motion of DB and that there exists a threshold in 
the total energy on
the trimer that controls this destabilization. We find that this 
threshold and the resultant
tunneling can be described analytically by defining a 
two-dimensional "Peierls-Nabarro"
energy landscape which restricts the dynamics of the trimer to a 
limited region of phase
space. We further establish that the value of the energy 
threshold is related to the Peierls-
Nabarro barrier of a single ILM. We then embed our nonlinear 
trimer in an extended
lattice and show numerically that the same destabilization 
mechanism applies in the
extended lattice. Our results suggest a possible means for 
controlling the transmission of
coherent atomic beams in interferometry and other processes.
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&sup1;  Phys. Rev. A 82, 053604 (2010)