  The photo-excited state associated with superconducting fluctuation above the
superconducting critical temperature $T_c$ is studied based on the
time-dependent Ginzburg-Laundau approach. The excited state is created by an
electric-field pulse and is probed by a weak secondary external field, which is
treated by the linear response theory mimicking pump-probe spectroscopy
experiments. The behavior is basically controlled by two relaxation rates: one
is $\gamma_1$ proportional to the temperature measured from the critical point
$T - T_c$ and the other is $\gamma_2$ proportional to the excitation intensity
of the pump pulse. The excited state approaches the equilibrium state
exponentially in a long time $t \gg \gamma_1^{-1}$, while in the intermediate
time domain we find a power-law or logarithmic decay with different exponents
for $t\ll \gamma_2^{-1}$ and $\gamma_2^{-1} \ll t \ll \gamma_1^{-1}$, even
though the system is located away from the critical point. This is interpreted
as the critical point in equilibrium being extended to a finite region in the
excited situation. The parameter dependences on both the pump and probe
currents are also systematically studied in all dimensions.

Superconductivity