Attosecond Transient-Absorption Spectroscopy in One-Dimensional Periodic Crystals

We investigate theoretically the application of attosecond transient-absorption spectroscopy to a one-dimensional periodic crystal in a regime where the dynamical Franz-Keldysh effect is presented around the energy gap. It is found that in the presence of a few-cycle dressing pulse the delay-dependent absorption spectrogram from the numerically exactly solvable model exhibits a general feature of the V-shaped fringes of subcycle oscillations. This structure represents femtosecond-resolved transient modulation of the conductivity, which is similar to recent experimental observation. We identify a regime where the higher-order even oscillation frequency becomes remarkable in the absorption spectrum for using the midinfrared pump laser. An analytical formula is also developed with the two-band approximation in order to facilitate analysis of the absorption spectrum. Our result shows that the full information on the momentum-dependent band gap across the entire Brillouin zone is encoded into the absorption spectrogram, thus suggesting an all-optical method to reconstruct the one-dimensional gap structure. The reconstruction feasibility is successfully demonstrated by a two-step algorithm even if considering the effect of noise. Moreover, we derive an analytical expression of the delay- and frequency-dependent conductivity with some additional assumptions. Some important features are successfully interpreted in terms of this analytical approach.