  The transverse field in the quantum Ising chain is linearly ramped from the
para- to the ferromagnetic phase across the quantum critical point at a rate
characterized by a quench time $\tau_Q$. We calculate a connected kink-kink
correlator in the final state at zero transverse field. The correlator is a sum
of two terms: a negative (anti-bunching) Gaussian that depends on the
Kibble-Zurek (KZ) correlation length only and a positive term that depends on a
second longer scale of length. The second length is made longer by dephasing of
the state excited near the critical point during the following ramp across the
ferromagnetic phase. This interpretation is corroborated by considering a
linear ramp that is halted in the ferromagnetic phase for a finite waiting time
and then continued at the same rate as before the halt. The extra time
available for dephasing increases the second scale of length that
asymptotically grows linearly with the waiting time. The dephasing also
suppresses magnitude of the second term making it negligible for waiting times
much longer than $\tau_Q$. The same dephasing can be obtained with a smooth
ramp that slows down in the ferromagnetic phase. Assuming sufficient dephasing
we obtain also higher order kink correlators and the ferromagnetic correlation
function.
