Spin-orbit coupled weakly interacting Bose-Einstein condensates in   harmonic traps
  We investigate theoretically the phase diagram of a spin-orbit coupled Bose gas in two-dimensional harmonic traps. We show that discrete Landau levels develop at strong spin-orbit coupling. For a weakly interacting gas, quantum states with skyrmion lattice patterns emerge spontaneously and preserve either parity symmetry or combined parity-time-reversal symmetry. These phases can be readily observed by experimentally engineering spin-orbit coupling and interatomic interactions for a cloud of $^{87}$Rb atoms in a highly oblate trap. 
Hui Hu, B. Ramachandhran, Han Pu, and Xia-Ji Liu
cond-mat.quant-gas