  We demonstrate synthetic azimuthal gauge potentials for Bose-Einstein
condensates from engineering atom-light couplings. The gauge potential is
created by adiabatically loading the condensate into the lowest energy
Raman-dressed state, achieving a coreless vortex state. The azimuthal gauge
potentials act as effective rotations and are tunable by the Raman coupling and
detuning. We characterize the spin textures of the dressed states, in
agreements with the theory. The lowest energy dressed state is stable with a
4.5-s half-atom-number-fraction lifetime. In addition, we exploit the azimuthal
gauge potential to demonstrate the Hess-Fairbank effect, the analogue of
Meissner effect in superconductors. The atoms in the absolute ground state has
a zero quasi-angular momentum and transits into a polar-core vortex when the
synthetic magnetic flux is tuned to exceed a critical value. Our demonstration
serves as a paradigm to create topological excitations by tailoring atom-light
interactions where both types of SO(3) vortices in the $|\langle
\vec{F}\rangle|=1$ manifold, coreless vortices and polar-core vortices, are
created in our experiment. The gauge field in the stationary Hamiltonian opens
a path to investigating rotation properties of atomic superfluids under thermal
equilibrium.
