  We present a unified theory for pump-probe spectra in highly excited
semiconductors, which 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 the 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 which 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
