Simulating Charged Particles in a Magnetic Field with Ultra-cold Atoms Using Light-induced Effective Gauge Fields

We experimentally study light-induced gauge potentials in a $^{87}$Rb Bose-Einstein condensate. Instead of rotating the trap, we prepare the atoms in a spatially-varying optically dressed state. The atomic spin state is dressed by a spatially varying two-photon Raman coupling between the three $F=1$ hyperfine ground states. The resulting effective magnetic field is equivalent to rotating the condensate (and transforming to the rotating frame), and thus generates vortices. The inter-vortex distance is given by $\sqrt{2\pi} l_B$. Using the technique, the minimum possible $l_B \approx\sqrt{R_{\rm TF} \lambda/8 \pi}$ is the magnetic length for a uniform field, $R_{\rm TF}$ is the condensate diameter, and $\lambda\approx805\ {\rm nm}$ is the optical wavelength. We prepare the condensate in the dressed state, whose projection onto internal states of various state-dependent Bragg momenta are well understood.