  The false vacuum decay has been a central theme in physics for half a century
with applications to cosmology and to the theory of fundamental interactions.
This fascinating phenomenon is even more intriguing when combined with the
confinement of elementary particles. Due to the astronomical time scales
involved, the research has so far focused on theoretical aspects of this decay.
The purpose of this Letter is to show that the false vacuum decay is accessible
to current optical experiments as quantum analog simulators of spin chains with
confinement of the elementary excitations, which mimic the high energy
phenomenology but in one spatial dimension. We study the non-equilibrium
dynamics of the false vacuum in a quantum Ising chain and in an XXZ ladder. The
false vacuum is the metastable state that arises in the ferromagnetic phase of
the model when the symmetry is explicitly broken by a longitudinal field. This
state decays through the formation of "bubbles" of true vacuum. Using iTEBD
simulations, we are able to study the real-time evolution in the thermodynamic
limit and measure the decay rate of local observables. We find that the
numerical results agree with the theoretical prediction that the decay rate is
exponentially small in the inverse of the longitudinal field.
