  Cold atoms with laser-induced spin-orbit (SO) interactions provide intriguing
new platforms to explore novel quantum physics beyond natural conditions of
solids. Recent experiments demonstrated the one-dimensional (1D) SO coupling
for boson and fermion gases. However, realization of 2D SO interaction, a much
more important task, remains very challenging. Here we propose and
experimentally realize, for the first time, 2D SO coupling and topological band
with $^{87}$Rb degenerate gas through a minimal optical Raman lattice scheme,
without relying on phase locking or fine tuning of optical potentials. A
controllable crossover between 2D and 1D SO couplings is studied, and the SO
effects and nontrivial band topology are observed by measuring the atomic cloud
distribution and spin texture in the momentum space. Our realization of 2D SO
coupling with advantages of small heating and topological stability opens a
broad avenue in cold atoms to study exotic quantum phases, including the
highly-sought-after topological superfluid phases.
