  We study quantum quench in a holographic model of a zero temperature
insulator-superfluid transition. The model is a modification of that of
arXiv:0911.0962 and involves a self-coupled complex scalar field, Einstein
gravity with a negative cosmological constant, and Maxwell field with one of
the spatial directions compact. In a suitable regime of parameters, the scalar
field can be treated as a probe field whose backreaction to both the metric and
the gauge field can be ignored. We show that when the chemical potential of the
dual field theory lies between two critical values, the equilibrium background
geometry is a AdS soliton with a constant gauge field, while the complex scalar
condenses leading to broken symmetry. We then turn on a time dependent source
for the order parameter which interpolates between constant values and crosses
the order-disorder critical point. In the critical region adiabaticity breaks
down, but for a small rate of change of the source $v$ there is a new small-$v$
expansion in fractional powers of $v$. The resulting critical dynamics is
dominated by a zero mode of the bulk field. To lowest order in this small-$v$
expansion, the order parameter satisfies a time dependent Landau-Ginsburg
equation which has $z=2$, but non-dissipative. These predictions are verified
by explicit numerical solutions of the bulk equations of motion.
