  Nonlinear wave-mixing in solids with ultrafast x-rays can provide new insight
into complex electronic dynamics of materials. Here, tabletop-based attosecond
noncollinear four-wave mixing (FWM) spectroscopy using one extreme ultraviolet
(XUV) pulse from high harmonic generation and two separately timed few-cycle
near-infrared (NIR) pulses characterizes the dynamics of the Na+ L2,3 edge
core-excitons in NaCl around 33.5 eV. An inhomogeneous distribution of
core-excitons underlying the well-known doublet absorption of the Na+
\Gamma-point core-exciton spectrum is deconvoluted by the resonance-enhanced
nonlinear wave-mixing spectroscopy. In addition, other dark excitonic states
that are coupled to the XUV-allowed levels by the NIR pulses are characterized
spectrally and temporally. Approximate sub-10 femtosecond coherence lifetimes
of the core-exciton states are observed. The core-excitonic properties are
discussed in the context of strong electron-hole exchange interactions,
electron-electron correlation, and electron-phonon broadening. This
investigation successfully indicates that tabletop attosecond FWM
spectroscopies represent a viable technique for time-resolved solid-state
measurements.
