In ultrafast spectroscopy, we typically excite a quantum system, such as a molecule, with a short “pump” light pulse and then observe its dynamics with a time-delayed “probe” pulse. This well-known scheme of “femtochemistry” is broadly applied to investigate mechanisms of photochemical reactions or energy and charge transfer in various natural and artificial functional materials.

However, because light absorption is a statistical process, a quantum system might interact with more than one photon of the pump pulse. These multiple excitations typically cannot be distinguished spectroscopically and therefore lead to errors in interpretation, such as wrong kinetic time constants. Thus, the credo in ultrafast science has been: “Decrease the pump laser power as much as possible to reduce the influence of multiple excitations!” Often it is difficult to estimate the degree of contamination, and thus artifacts remain. At the same time, removing the signature of multiple excitations also deletes meaningful information that could provide additional insights.

We have developed a novel approach to time-resolved spectroscopy that separates nonlinear orders systematically and solves this decades-old artifact problem.[1,4] The experiment is simple to carry out and works in any laser lab, for any sample and arbitrary observables. We have already demonstrated the concept for transient absorption,[1-5] coherently detected two-dimensional electronic spectroscopy,[6,7] fluorescence-detected spectroscopy, photoemission electron spectroscopy, and coherent control scenarios. Examples for studied systems are squaraine polymers,[1] a squaraine dimer,[7] a squaraine oligomer,[3] the laser dye cresyl violet,[1] Si nanocrystals,[1] the light-harvesting complex LHCII,[1] a merocyanine dimer in an RNA template[2], zinc phthalocyanine molecules coupled to a plasmonic gold surface[5], CdSe/CdxZn1-xS core-alloyed shell nanoplatelets, and more.

From the analysis we can quantify properties of higher excited states that are not accessible with established methods.[7] We also measure exciton diffusion that is relevant for the efficiency of organic electronic devices.[1,5] Theoretically, the perturbative expansion of light–matter interaction is known since 100 years, i.e., since Fermi’s Golden Rule and its higher-order analogs. With our scheme, it is now finally possible to obtain the individual terms of the perturbative series also in experiment, rather than just their combined sum.

Acknowledgements: This work has been supported by the European Research Council (ERC) in Advanced Grant “IMPACTS”.

[1] P. Malý, J. Lüttig, P. A. Rose, A. Turkin, C. Lambert, J. J. Krich, T. Brixner, Nature, 2023, 616, 280–287. https://doi.org/10.1038/s41586-023-05846-7

[2] J. Dietzsch, A. Jayachandran, S. Mueller, C. Höbartner, T. Brixner, Chem. Commun., 2023, 59, 7395–7398. https://doi.org/10.1039/d3cc02024j

[3] J. Lüttig, P. A. Rose, P. Malý, A. Turkin, M. Bühler, C. Lambert, J. J. Krich, T. Brixner, J. Chem. Phys., 2023, 158, 234201. https://doi.org/10.1063/5.0139090

[4] J. Lüttig, S. Mueller, P. Malý, J. J. Krich, T. Brixner, J. Phys. Chem. Lett., 2023, 14, 7556–7573. https://doi.org/10.1021/acs.jpclett.3c01694

[5] S. Büttner, L.N. Philipp, J. Lüttig, M. Rödel; M. Hensen, J. Pflaum, R. Mitric, T. Brixner, J. Chem. Phys., 2025, 163, 044702. https://doi.org/10.48550/arXiv.2504.19615

[6] J. J. Krich, L. Brenneis, P. A. Rose, K. Mayershofer, S. Büttner, J. Lüttig, P. Malý, T. Brixner, J. Phys. Chem. Lett., 2025, 16, 5897–5905. https://doi.org/10.1021/acs.jpclett.5c01177

[7] K. Mayershofer, P. A. Rose, J. Lüttig, L. Brenneis, S. Büttner, J. J. Krich, T. Brixner. https://doi.org/10.48550/arXiv.2605.23763

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