Quench dynamics of neutral atoms in out-equilibrium one dimensional optical lattices

A quantum simulator is proposed for nucleation and growth dynamics using an out-of equilibrium optical lattice. We calculate the density of neutral atoms in the lattice and we establish the connection with the Kolmogorov-Mehl-Johnson-Avrami model. Here we show that a Avrami equation can describe most of the evolution in time of the population growth in the lattice, coherence between neutral atoms leads a complex growth rate.