  Rotation of a container holding a viscous fluid forms a vortex which grows
with increasing angular velocity. A superfluid, however, is intrinsically
different from these normal fluids because its rotation is quantized. Even if a
container of superfluid is rotating, the fluid itself remains still until a
critical velocity is reached. Beyond the critical velocity, all the particles
conspire to suddenly pick up an angular momentum of $\hbar$ each and forms a
quantized vortex. As a result, a superfluid is known to increase its rotation
by a total angular momentum of $N\hbar$. In this letter, we show that
exciton-polariton superfluid can split into an irrotational part and a
rotational part. The relative ratio between the two states can be controlled by
either pump beam's power or spot size. Consequently, angular momentum of
exciton-polariton superfluid can be tuned from zero to $N\hbar$ continuously.
This striking observation sets the stage for studying non-equilibrium
properties of a superfluid with exciton-polaritons.
