  We study the time evolution of a conformal field theory deformed by a
relevant operator under a smooth but fast quantum quench which brings it to the
conformal point. We argue that when the quench time scale $\delta t$ is small
compared to the scale set by the relevant coupling, the expectation value of
the quenched operator scales universally as $\delta g/ \delta t ^{2\Delta-d}$
where $\delta g$ is the quench amplitude. This growth is further enhanced by a
logarithmic factor in even dimensions. We present explicit results for free
scalar and fermionic field theories, supported by an analytic understanding of
the leading contribution for fast quenches. Results from this Letter suggest
that this scaling result, first found in holography, is in fact universal to
quantum quenches. Our considerations also show that this limit of fast smooth
quenches is quite different from an instantaneous quench from one
time-independent Hamiltonian to another, where the Schrodinger picture state at
the time of the quench simply serves as an initial condition for subsequent
evolution with the final Hamiltonian.
