Emerging ultrafast techniques for studying quantum materials

Ultrafast spectroscopies enable the characterization of quantum materials and of their functional properties arising from strong correlations and electronic topology. This Review discusses three emerging techniques: attosecond transient absorption spectroscopy, solid-state high-harmonic generation spectroscopy and extreme ultraviolet-second harmonic generation spectroscopy. In quantum materials, emergent functional properties resulting from strong correlations or electronic topology offer opportunities for new applications. Over the past decade, ultrafast techniques such as photoemission, scattering and optical spectroscopies have complemented traditional control knobs such as temperature, pressure, chemical substitution and external fields, adding the time coordinate as a new dimension for understanding and engineering the properties of quantum materials out of equilibrium. Despite remarkable progress, there remains a host of open questions that will require detailed understanding of the non-equilibrium response of quantum materials to enable applications in areas such as clean energy production, energy storage and quantum computation and communication. In this Review, we survey three categories of emerging ultrafast spectroscopies for investigating condensed matter systems - attosecond transient absorption spectroscopy, solid-state high-harmonic generation spectroscopy and extreme ultraviolet second-harmonic generation spectroscopy - and we discuss their potential applications to the study of quantum materials. We analyse these ultrafast tools from the standpoint of open questions in quantum materials, highlighting the unique observables and capabilities these methods can offer to address them.