  In quantum field theory, the decay of an extended metastable state into the
real ground state is known as ``false vacuum decay'' and it takes place via the
nucleation of spatially localized bubbles. Despite the large theoretical effort
to estimate the nucleation rate, experimental observations were still missing.
Here, we observe bubble nucleation in isolated and highly controllable
superfluid atomic systems, and we find good agreement between our results,
numerical simulations and instanton theory opening the way to the emulation of
out-of-equilibrium quantum field phenomena in atomic systems.
