  Interactions between particles in quantum many-body systems play a crucial
role in determining the electric, magnetic, optical, and thermal properties of
the system. The recent progress in the laser-pulse technique has enabled the
manipulations and measurements of physical properties on ultrafast timescales.
Here, we propose a method for the direct and ultrafast probing of quantum
many-body interaction through coherent two-dimensional (2D) spectroscopy. Up to
a moderate interaction strength, the inter-particle interaction manifests
itself in the emergence of off-diagonal peaks in the 2D spectrum before all the
peaks coalesce into a single diagonal peak as the system approaches the
Mott-insulating phase in the strongly interacting regime. The evolution of the
2D spectrum as a function of the time delay between the second and third laser
pulses can provide important information on the ultrafast time variation of the
interaction.
