Zhaopin Chen, Jingfeng Liu, Shenhe Fu, Yongyao Li, Boris A. Malomed

We introduce a 2D network built of PT-symmetric dimers with on-site cubic nonlinearity, the gain and loss elements of the dimers being linked by parallel square-shaped lattices. The system may be realized as a set of PT-symmetric dual-core waveguides embedded into a photonic crystal. The system supports PT-symmetric and antisymmetric fundamental solitons (FSs) and on-site-centered solitary vortices (OnVs). Stability of these discrete solitons is the central topic of the consideration. Their stability regions in the underlying parameter space are identified through the computation of stability eigenvalues, and verified by direct simulations. Symmetric FSs represent the system’s ground state, being stable at lowest values of the power, while anti-symmetric FSs and OnVs are stable at higher powers. Symmetric OnVs, which are also stable at lower powers, are remarkably robust modes: on the contrary to other PT-symmetric states, unstable OnVs do not blow up, but spontaneously rebuild themselves into stable FSs.

http://arxiv.org/abs/1411.3943

Optics (physics.optics); Pattern Formation and Solitons (nlin.PS)

Yongyao Li, Jingfeng Liu, Wei Pang, Boris A. Malomed

We study effects of the spontaneous symmetry-breaking (SSB) in solitons built of the dipolar Bose-Einstein condensate (BEC), trapped in a dual-core system with the dipole-dipole interactions (DDIs) and hopping between the cores. Two realizations of such a matter-wave coupler are introduced, weakly- and strongly-coupled. The former one in based on two parallel pipe-shaped traps, while the latter one is represented by a single pipe sliced by an external field into parallel layers. The dipoles are oriented along axes of the pipes. In these systems, the dual-core solitons feature the SSB of the supercritical type and subcritical types, respectively. Stability regions are identified for symmetric and asymmetric solitons, and, in addition, for non-bifurcating antisymmetric ones, as well as for symmetric flat states, which may also be stable in the strongly-coupled system, due to competition between the attractive and repulsive intra- and inter-core DDIs. Effects of the contact interactions are considered too. Collisions between moving asymmetric solitons in the weakly-symmetric system feature elastic rebound, merger into a single breather, and passage accompanied by excitation of intrinsic vibrations of the solitons, for small, intermediate, and large collision velocities, respectively. A PT-symmetric version of the weakly-coupled system is briefly considered too, which may be relevant for matter-wave lasers. Stability boundaries for PT-symmetric and antisymmetric solitons are identified.

http://arxiv.org/abs/1212.5568

Quantum Gases (cond-mat.quant-gas); Pattern Formation and Solitons (nlin.PS)