  Multi-dimensional coherent spectroscopy (MDCS)1,2 is a powerful method for
optical spectroscopy that has become an important tool for studying ultrafast
dynamics in a wide range of systems. It is an optical analog of
multidimensional nuclear magnetic resonance spectroscopy that enables the
measurement of homogeneous linewidths in inhomogeneously broadened systems,
many-body interactions, and coupling between excited resonances, all of which
are not simultaneously accessible by any other linear or non-linear method.
Current implementations of MDCS require a bulky apparatus and suffer from
resolution and acquisition speed limitations that constrain their applications
outside the laboratory3-5. Here we propose and demonstrate an approach to
nonlinear coherent spectroscopy that utilizes three frequency combs with
slightly different repetition rates. Unlike traditional nonlinear methods,
tri-comb spectroscopy uses only a single photodetector and no mechanical moving
elements to enable faster acquisition times, while also providing comb
resolution. As a proof of concept, a multidimensional coherent spectrum with
comb cross-diagonal resolution is generated using only 365 ms of data. These
improvements make multidimensional coherent spectroscopy relevant for systems
with narrow resonances (especially cold atomic and molecular systems). In
addition the method has the potential to be field deployable for chemical
sensing applications.
