  We investigate the time evolution of the Kondo resonance in response to a
quench by applying the time-dependent numerical renormalization group (TDNRG)
approach to the Anderson impurity model in the strong correlation limit. For
this purpose, we derive within TDNRG a numerically tractable expression for the
retarded two-time nonequilibrium Green function $G(t+t',t)$, and its associated
time-dependent spectral function, $A(\omega,t)$, for times $t$ both before and
after the quench. Quenches from both mixed valence and Kondo correlated initial
states to Kondo correlated final states are considered. For both cases, we find
that the Kondo resonance in the zero temperature spectral function, a preformed
version of which is evident at very short times $t\to 0^{+}$, only fully
develops at very long times $t\gtrsim 1/T_{\rm K}$, where $T_{\rm K}$ is the
Kondo temperature of the final state. In contrast, the final state satellite
peaks develop on a fast time scale $1/\Gamma$ during the time interval
$-1/\Gamma \lesssim t \lesssim +1/\Gamma$, where $\Gamma$ is the hybridization
strength. Initial and final state spectral functions are recovered in the
limits $t\rightarrow -\infty$ and $t\rightarrow +\infty$, respectively. Our
formulation of two-time nonequilibrium Green functions within TDNRG provides a
first step towards using this method as an impurity solver within
nonequilibrium dynamical mean field theory.
