  Bacterial suspensions--a premier example of active fluids--show an unusual
response to shear stresses. Instead of increasing the viscosity of the
suspending fluid, the emergent collective motions of swimming bacteria can turn
a suspension into a "superfluid" with zero apparent viscosity. Although the
existence of active "superfluids" has been demonstrated in bulk rheological
measurements, the microscopic origin and dynamics of such an exotic phase have
not been experimentally probed. Here, using high-speed confocal rheometry, we
study the dynamics of concentrated bacterial suspensions under simple planar
shear. We find that bacterial "superfluids" under shear exhibit unusual
symmetric shear bands, defying the conventional wisdom on shear-banding of
complex fluids, where the formation of steady shear bands necessarily breaks
the symmetry of unsheared samples. We propose a simple hydrodynamic model based
on the local stress balance and the ergodic sampling of nonequilibrium shear
configurations, which quantitatively describes the observed symmetric
shear-banding structure. The model also successfully predicts various
interesting features of swarming vortices in stationary bacterial suspensions.
Our study provides new insights into the physical properties of collective
swarming in active fluids and illustrates their profound influences on
transport processes.
