  We study the problem of quantum quench across a critical point in a strongly
coupled field theory using AdS/CFT techniques. The model involves a probe
neutral scalar field with mass-squared $m^2$ in the range $-9/4 < m^2 < -3/2$
in a $AdS_4$ charged black brane background. For a given brane background there
is a critical mass-squared, $m_c^2$ such that for $m^2 < m_c^2$ the scalar
field condenses. The theory is critical when $m^2 = m_c^2$ and the source for
the dual operator vanishes. At the critical point, the radial operator for the
bulk linearized problem has a zero mode. We study the dynamics of the order
parameter with a time dependent source $J(t)$, or a null-time dependent bulk
mass $m(u)$ across the critical point. We show that in the critical region the
dynamics for an initially slow variation is dominated by the zero mode : this
leads to an effective description in terms of a Landau-Ginsburg type dynamics
with a {\em linear} time derivative. Starting with an adiabatic initial
condition in the ordered phase, we find that the order parameter drops to zero
at a time $t_\star$ which is later than the time when $(m_c^2-m^2)$ or $J$ hits
zero. In the critical region, $t_\star$, and the departure of the order
parameter from its adiabatic value, scale with the rate of change, with
exponents determined by static critical behavior. Numerical results for the
order parameter are consistent with these expectations.
