Dual laser frequency combs can rapidly measure high-resolution linear absorption spectra. However, one-dimensional linear techniques cannot distinguish the sources of resonances in a mixture of different analytes, nor can they separate inhomogeneous and homogeneous broadening. Here, we overcame these limitations by acquiring high-resolution multidimensional nonlinear coherent spectra with frequency combs. We experimentally differentiated and assigned the Doppler-broadened features of two naturally occurring isotopes of rubidium atoms (Rb and Rb) according to the placement of their hyperfine energy states in a two-dimensional spectrum.

Frequency-comb based multidimensional coherent spectroscopy is a novel optical method that enables high-resolution measurement in a short acquisition time. The method's resolution makes multidimensional coherent spectroscopy relevant for atomic systems that have narrow resonances. We use double-quantum multidimensional coherent spectroscopy to reveal collective hyperfine resonances in rubidium vapor at 100 °C induced by dipole-dipole interactions. We observe tilted and elongated line shapes in the double-quantum 2D spectra, which have never been reported for Doppler-broadened systems. The elongated line shapes suggest that the signal is predominately from the interacting atoms that have a near zero relative velocity.

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 laboratory 3-5 . 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.Rapid, high precision, and sensitive spectroscopic measurements of materials are desirable both in the laboratory and for field applications such as chemical sensing and atmospheric monitoring. The development of frequency comb technology led to a method known as Dual-Comb Spectroscopy (DCS) that emerged as a revolutionary approach to optical spectroscopy 6,7 .