Bose-Einstein Condensates in Spin-Orbit Coupled Optical Lattices: Flat Bands and Superfluidity

Recently spin-orbit (SO) coupled superfluids in free space or harmonic traps have been extensively studied, motivated by the recent experimental realization of SO coupling for Bose-Einstein condensates (BEC). However, the rich physics of SO coupled BEC in optical lattices has been largely unexplored. In this paper, we show that in suitable parameter region the lowest Bloch state forms an isolated flat band in a one dimensional (1D) SO coupled optical lattice, which thus provides an experimentally feasible platform for exploring the recently celebrated topological flat band physics in lattice systems. We show that the flat band is preserved even with the mean field interaction in BEC. We investigate the superfluidity of the BEC in SO coupled lattices through dynamical and Landau stability analysis, and show that the BEC is stable on the whole flat band.Comment: 5 pages, 4 figures, to appear in Phys. Rev.

Control and synchronization of Julia sets of the complex dissipative standard system

The fractal behaviors of the complex dissipative standard system are discussed in this paper. By using the boundedness of the forward and backward orbits, Julia set of the system is introduced and visualization of Julia set is also given. Then a controller is designed to achieve Julia set shrinking or expanding with the changing of the control parameter. And synchronization of two different Julia sets is discussed by adding a coupling item, which makes one Julia set change to be the other. The simulations illustrate the efficacy of these methods

Patterning by dynamically unstable spin-orbit-coupled Bose-Einstein condensates

In a two-dimensional atomic Bose-Einstein condensate, we demonstrate Rashba spin-orbit coupling can always introduce dynamical instability into specific zero-quasimomentum states in all parameter regimes. During the evolution of the zero-quasimomentum states, such spin-orbit-coupling-induced instability can fragment the states and lead to a dynamically patterning process. The features of formed patterns are identified from the symmetries of the Bogoliubov-de Gennes Hamiltonian. We show that spin-orbit-coupled Bose-Einstein condensates provide an interesting platform for the investigation of pattern formations.Comment: Accepted for publication in Chao, Solitons & Fractal