Nonlinear Spectroscopy in the Extreme Ultraviolet: Probing Ultrafast Dynamics with Attosecond Pulses

Ultrafast electronic dynamics underlie the most fundamental processes in chemical physics. Nonlinear spectroscopic techniques with extreme ultraviolet (XUV) pulses promise to probe these dynamics on their natural attosecond (10^-18 s) to few femtosecond (10^-15 s) timescales, but remain under-utilized due to the low photon flux of tabletop attosecond light sources. Recently, the coherent interaction of subfemtosecond XUV pulses and few-cycle near infrared (NIR) pulses have been shown to generate transient wave-mixing signals, extending nonlinear techniques into the XUV regime. Manipulation of the sequence, wavevector, and spectra of these pulses permits selective measurements of excited state evolution with exceptional temporal and spectral resolution. Utilizing a noncollinear geometry between subfemtosecond XUV and two angled NIR pulses, the earliest dynamics of nonlinear signal generation are probed in Rydberg and transient light-induced states in helium gas, revealing few-femtosecond delays in the emergence of higher order signals attributed to the formation of an AC Stark phase grating. This wave-mixing technique is further employed to measure the timescales of ultrafast decay processes in benchmark systems, including the (²P_1/2)nd/ns autoionizing states of krypton. Despite pronounced quantum beating due to the XUV-induced coherence, the lifetimes obtained from background-free wave-mixing signals compare favorably with linewidth measurements for the short-lived (²P_1/2)nd states. These results illustrate the potential of attosecond nonlinear spectroscopies to elucidate electronic dynamics in diverse systems with unprecedented selectivity. With the continued development of XUV wave-mixing and multidimensional techniques and applications to more complex molecular and solid-state systems, these initial results will provide the foundation for critical insights into the electronic dynamics of chemical reactions.