  In this work, we investigate the real-time dynamics of quenching a state from
phase separation in a holographic model of first-order phase transition. In
addition to the typical phase-separated and high-energy final states, we have
discovered a novel dynamical process that drives the system to a
low-temperature supercooled final state within a narrow range of quench
parameters. The critical behavior is also revealed during the fully non-linear
dynamics. Following a sudden quench with critical parameters, the phase
separation can be attracted to a critical nucleus. Specifically, the critical
nucleus will subsequently shrink in size and eventually disappear for
super-critical parameters, where the system is actually supercooled with a
temperature lower than the initial one. While for sub-critical parameters, the
nucleus will grow in size and finally reform a phase separation, where the
absorbed quenching energy is reflected in the increment of the latent heat.
