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We demonstrate rapid imaging based on four-wave mixing (FWM) by assessing the quality of advanced materials through measurement of their nonlinear response, exciton dephasing, and exciton lifetimes. We use a WSe$_2$ monolayer grown by chemical vapor deposition as a canonical example to demonstrate these capabilities. By comparison, we show that extracting material parameters such as FWM intensity, dephasing times, excited state lifetimes, and distribution of dark/localized states allows for a more accurate assessment of the quality of a sample than current prevalent techniques, including white light microscopy and linear micro-reflectance spectroscopy. We further discuss future improvements of the ultrafast FWM techniques by modeling the robustness of exponential decay fits to different spacing of the sampling points. Employing ultrafast nonlinear imaging in real-time at room temperature bears the potential for rapid in-situ sample characterization of advanced materials and beyond.

Transition metal dichalcogenides (TMDs) are regarded as a possible materials platform for quantum information science and related device applications. In TMD monolayers, the dephasing time and inhomogeneity are crucial parameters for any quantum information application. In TMD heterostructures, coupling strength and interlayer exciton lifetimes are also parameters of interest. However, many demonstrations in TMDs can only be realized at specific spots on the sample, presenting a challenge to the scalability of these applications. Here, using multi-dimensional coherent imaging spectroscopy (MDCIS), we shed light on the underlying physics - including dephasing, inhomogeneity, and strain - for a MoSe$_2$ monolayer and identify both promising and unfavorable areas for quantum information applications. We furthermore apply the same technique to a MoSe$_2$/WSe$_2$ heterostructure. Despite the notable presence of strain and dielectric environment changes, coherent and incoherent coupling, as well as interlayer exciton lifetimes are mostly robust across the sample. This uniformity is despite a significantly inhomogeneous interlayer exciton photoluminescence distribution that suggests a bad sample for device applications. This robustness strengthens the case for TMDs as a next-generation materials platform in quantum information science and beyond.

Coherent coupling between excitons is at the heart of many-body interactions with transition metal dichalcogenide (TMD) heterostructures as an emergent platform for the investigation of these interactions. We employ multi-dimensional coherent spectroscopy on monolayer MoSe\textsubscript{2}/WSe\textsubscript{2} heterostructures and observe coherent coupling between excitons spatially localized in monolayer MoSe$_2$ and WSe$_2$. Through many-body spectroscopy, we further observe the absorption state arising from free interlayer electron-hole pairs. This observation yields a spectroscopic measurement of the interlayer exciton binding energy of about 250 meV.

Optical absorption is one of fundamental light-matter interactions. In most materials, optical absorption is a weak perturbation to the light. In this regime, absorption and emission are irreversible, incoherent processes due to strong damping. Excitons in monolayer transition metal dichalcogenides, however, interact strongly with light, leading to optical absorption in the non-perturbative regime where coherent re-emission of the light has to be considered. Between the incoherent and coherent limits, we show that a robust critical coupling condition exists, leading to perfect optical absorption. Up to 99.6% absorption is measured in a sub-nanometer thick MoSe2 monolayer placed in front of a mirror. The perfect absorption is controlled by tuning the exciton-phonon, exciton-exciton, and exciton-photon interactions by temperature, pulsed laser excitation, and a movable mirror, respectively. Our work suggests unprecedented opportunities for engineering exciton-light interactions using two-dimensional atomically thin crystals, enabling novel photonic applications including ultrafast light modulators and sensitive optical sensing.

The excitonic homogeneous linewidth of an exfoliated monolayer MoSe$_2$ encapsulated in hexagonal boron nitride is directly measured using multidimensional coherent spectroscopy with micron spatial resolution. The linewidth is 0.26 $\pm$ 0.02 meV, corresponding to a dephasing time $T_2 \approx$ 2.5 ps, which is almost half the narrowest reported values for non-encapsulated MoSe$_2$ flakes. We attribute the narrowed linewidth to Coulomb screening by the encapsulated material and suppression of non-radiative processes. Through direct measurements of encapsulated and non-encapsulated monolayers, we confirm that encapsulation reduces the sample inhomogeneity. However, linewidths measured using photoluminescence and linear absorption remain dominated by inhomogeneity, and these linewidths are roughly 5 times larger than the homogeneous linewidth in even the highest-quality encapsulated materials. The homogeneous linewidth of non-encapsulated monolayers is very sensitive to temperature cycling, whereas encapsulated samples are not modified by temperature cycling. The nonlinear signal intensity of non-encapsulated monolayers is degraded by high-power optical excitation, whereas encapsulated samples are very resilient to optical excitation with optical powers up to the point of completely bleaching the exciton.

We measure many-body interactions in isolated quantum dot states using double-quantum multidimensional coherent spectroscopy. Few states are probed in a diffraction limited spot, which is enabled by a novel collinear scheme in which radiated four-wave-mixing signals are measured with phase resolution. Many-body interactions are enhanced by an additional prepulse tuned to the delocalized quasi-continuum states. We propose this effect as a method for controlling coupling between quantum states.