  We consider a quantum quench from the strongly correlated ground state of the
Kondo model to a Fermi sea. We calculate the overlap between the ground states
before and after the quench, as well as the Loschmidt echo, that is, the
transition amplitude between the initial state and the evolved state at a time
$t$ after the quench. The overlap is known to determine the dynamics of the
echo at large times. We show in addition that the overlap depends algebraically
on the emergent Kondo length with a power law exponent equal to the difference
of long and short time contributions that appear in the echo. Our result
suggests that there may in general be more information contained in the overlap
than previously recognized.
