  Metastability is a quintessential feature of first order quantum phase
transitions, which is lost either by dynamical instability or by nucleating
bubbles of true vacuum through quantum tunneling. By considering a drive across
the first order quantum phase transition in the quantum Ising chain in 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.
