Aleksandra Maluckov, Goran Gligoric, Ljupco Hadzievski, Boris A. Malomed, Tilman Pfau
Density-wave patterns in (quasi-) discrete media with local interactions are
known to be unstable. We demonstrate that \emph{stable} double- and triple-
period patterns (DPPs and TPPs), with respect to the period of the underlying
lattice, exist in media with nonlocal nonlinearity. This is shown in detail for
dipolar Bose-Einstein condensates (BECs), loaded into a deep one-dimensional
(1D) optical lattice (OL), by means of analytical and numerical methods in the
tight-binding limit. The patterns featuring multiple periodicities are
generated by the modulational instability of the continuous-wave (CW) state,
whose period is identical to that of the OL. The DPP and TPP emerge via phase
transitions of the second and first kind, respectively. The emerging patterns
may be stable provided that the dipole-dipole (DD) interactions are repulsive
and sufficiently strong, in comparison with the local repulsive nonlinearity.
Within the set of the considered states, the TPPs realize a minimum of the free
energy. Accordingly, a vast stability region for the TPPs is found in the
parameter space, while the DPP\ stability region is relatively narrow. The same
mechanism may create stable density-wave patterns in other physical media
featuring nonlocal interactions, such as arrayed optical waveguides with
thermal nonlinearity.
View original:
http://arxiv.org/abs/1202.0145
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