  We consider quantum quench by a time dependent double trace coupling in a
strongly coupled large N field theory which has a gravity dual via the AdS/CFT
correspondence. The bulk theory contains a self coupled neutral scalar field
coupled to gravity with negative cosmological constant. We study the scalar
dynamics in the probe approximation in two backgrounds: AdS soliton and AdS
black brane. In either case we find that in equilibrium there is a critical
phase transition at a {\em negative} value of the double trace coupling
$\kappa$ below which the scalar condenses. For a slowly varying homogeneous
time dependent coupling crossing the critical point, we show that the dynamics
in the critical region is dominated by a single mode of the bulk field. This
mode satisfies a Landau-Ginsburg equation with a time dependent mass, and leads
to Kibble Zurek type scaling behavior. For the AdS soliton the system is
non-dissipative and has $z=1$, while for the black brane one has dissipative
$z=2$ dynamics. We also discuss the features of a holographic model which would
describe the non-equilibrium dynamics around quantum critical points with
arbitrary dynamical critical exponent $z$ and correlation length exponent
$\nu$. These analytical results are supported by direct numerical solutions.
