  We experimentally reconstruct Wigner's current of quantum phase space
dynamics for the first time. We reveal the ``push-and-pull" associated with
damping and diffusion due to the coupling of a squeezed vacuum state to its
environment. In contrast to classical dynamics, where (at zero temperature)
dissipation only ``pulls" the system toward the origin of phase space, we also
observe an outward ``push" because our system has to obey Heisenberg's
uncertainty relations. With squeezed vacuum states generated by an optical
parametric oscillator at variable pumping levels, we identify the pure
squeezing dynamics and its central stagnation point with a topological charge
of `$-1$'. We experimentally verify that this charge is protected for weakly as
well as strongly decohering conditions. This work demonstrates high resolving
power and establishes an experimental paradigm for measuring quantumness and
non-classicality of the dynamics of open quantum systems.
