Sub-cycle multidimensional spectroscopy of strongly correlated materials

Strongly correlated solids are complex and fascinating quantum systems, where new electronic states continue to emerge, especially when interaction with light triggers interplay between them. In this interplay, a sub-laser-cycle electronic response is particularly attractive as a tool for the ultrafast manipulation of matter at the petahertz scale. Here we introduce a new type of nonlinear multidimensional spectroscopy, which allows us to unravel charge and energy flows in strongly correlated systems interacting with few-cycle infrared pulses and the complex interplay between different correlated states evolving on the sub-femtosecond timescale. We demonstrate that the sub-cycle spectroscopy of a single-particle electronic response is extremely sensitive to correlated many-body dynamics and provides direct access to many-body response functions. For the two-dimensional Hubbard model under the influence of ultrashort, intense electric-field transients, we resolve the sub-femtosecond pathways of charge and energy flows between localized and delocalized many-body states and the creation of a highly correlated state surviving after the end of the laser pulse. Our findings open the way towards a regime of imaging and manipulating strongly correlated materials at optical rates, beyond the multicycle approach employed in Floquet engineering, with the sub-cycle response being a key tool for accessing many-body phenomena. Nonlinear multidimensional spectroscopy that can image the sub-cycle dynamics of strongly correlated systems on the sub-femtosecond timescale is demonstrated by using the carrier-envelope-phase dependence of the correlated multielectron response to decode the complex interplay between different many-body states.