  We propose a scheme to create coherent superpositions of annular flow of
strongly-interacting bosonic atoms in a 1D ring trap. The non-rotating ground
state is coupled to a vortex state with mesoscopic angular momentum by means of
a narrow potential barrier and an applied phase that originates from either
rotation or a synthetic magnetic field. We show that superposition states in
the Tonks-Girardeau regime are robust against single-particle loss due to the
effects of strong correlations. The coupling between the mesoscopically
distinct states scales much more favorably with particle number than in schemes
relying on weak interactions, thus making particle numbers of hundreds or
thousands feasible. Coherent oscillations induced by time variation of
parameters may serve as a 'smoking gun' signature for detecting superposition
states.
