Topology of a two-dimensional spin-orbit coupled Bose gas

Spin-orbit coupling is a necessary ingredient in phenomena such as the quantum spin-Hall effect and topological insulators. We explore a new cold atom realization of two-dimensional spin- orbit coupling using far-detuned Raman transitions and a strong radio-frequency magnetic field, all within the ground state hyperfine manifold. We characterize the spin and momentum resolved dispersion relation using Fourier transform spectroscopy and observe a robust Dirac point that can be moved by changing the Raman power balance or detuning. Furthermore, using three arm “Ramsey” interferometer we detect a momentum dependent phase winding around the Dirac point and use it to calculate topological invariants.