  Metastability is a quintessential feature of first order quantum phase
transitions, which is lost either by dynamical instability or by nucleating
bubbles of a true vacuum through quantum tunneling. By considering a drive
across the first order quantum phase transition in the quantum Ising chain in
the presence of both transverse and longitudinal fields, we reveal multiple
regions in the parameter space where the initial metastable state loses its
metastability in successive stages. The mechanism responsible is found to be
semi-degenerate resonant tunnelings to states with specific bubble sizes. We
show that such dynamics of quantized bubble nucleations can be understood in
terms of Landau-Zener transitions, which provide quantitative predictions of
nucleation probabilities for different bubble sizes.
