  We study the non-equilibrium quench dynamics crossing a continuous phase
transition between the charge density wave (CDW) and supersolid (SS) phases of
a bosonic lattice gas with cavity-mediated interactions. When changing the
hopping amplitude in the Hamiltonian as a function of time, we investigate the
scaling behavior of the correlation length and vortex density with respect to
the quench time and find that there is a threshold of the quench rate
separating two distinct scaling regimes. When slowly varying the system below
that threshold, we find a power-law scaling as predicted by the Kibble-Zurek
mechanism (KZM). While considering fast quench above that threshold, a
deviation from the KZM prediction occurs, manifested by a saturation of the
defect density. We further show that such distinct scaling behaviors during
different dynamic procedures can be understood through comparing the relaxation
time and the quench rate.

Quantum Gases