Nature of superconducting fluctuation in photo-excited systems

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.

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