Many-body theory of pump-probe spectra for highly excited semiconductors

We present a unified theory for pump-probe spectra in highly excited semiconductors that is applicable throughout the whole density regime including the high-density electron-hole BCS state and the low-density excitonic Bose-Einstein condensate (BEC). The analysis is based on the BCS-like pairing theory combined with the Bethe-Salpeter (BS) equation, which first enables us to incorporate the state-filling effect, the band-gap renormalization, and the strong/weak electron-hole pair correlations in a unified manner. We show that the electron-hole BCS state is distinctly stabilized by the intense pump light, and this result strongly suggests that the macroscopic quantum state can be observed under strong photoexcitation. The calculated spectra considerably deviate from results given by the BCS-like mean-field theory and the simple BS equation without electron-hole pair correlation, especially in the intermediate-density states between the electron-hole BCS state and the excitonic BEC state. In particular, we find the sharp stimulated emission and absorption lines that originate from the optical transition accompanied by the collective phase fluctuation mode in the electron-hole BCS state. From the pump-probe spectral viewpoint, we show that this fluctuation mode changes to the exciton mode with decreasing carrier density.