Stable periodic density waves in dipolar Bose-Einstein condensates trapped in optical lattices

TL;DR

This paper demonstrates the existence of stable double- and triple-period density-wave patterns in dipolar Bose-Einstein condensates within optical lattices, driven by nonlocal interactions and phase transitions, with potential applications in other nonlocal media.

Contribution

It reveals stable multi-period density-wave patterns in dipolar BECs with nonlocal nonlinearity, supported by analytical and numerical analysis in the tight-binding limit.

Findings

Stable DPPs and TPPs exist in dipolar BECs with nonlocal interactions.

TPPs have a broad stability region in parameter space.

Patterns can be stable in other media with nonlocal interactions.

Abstract

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.