Separating single- from multi-particle dynamics in nonlinear spectroscopy

Quantum states depend on the coordinates of all their constituent particles, with essential multi-particle correlations. Time-resolved laser spectroscopy¹ is widely used to probe the energies and dynamics of excited particles and quasiparticles such as electrons and holes^2,3, excitons^4-6, plasmons⁷, polaritons⁸ or phonons⁹. However, nonlinear signals from single- and multiple-particle excitations are all present simultaneously and cannot be disentangled without a priori knowledge of the system^4,10. Here, we show that transient absorption-the most commonly used nonlinear spectroscopy-with N prescribed excitation intensities allows separation of the dynamics into N increasingly nonlinear contributions; in systems well-described by discrete excitations, these N contributions systematically report on zero to N excitations. We obtain clean single-particle dynamics even at high excitation intensities and can systematically increase the number of interacting particles, infer their interaction energies and reconstruct their dynamics, which are not measurable via conventional means. We extract single- and multiple-exciton dynamics in squaraine polymers^11,12 and, contrary to common assumption^6,13, we find that the excitons, on average, meet several times before annihilating. This surprising ability of excitons to survive encounters is important for efficient organic photovoltaics^14,15. As we demonstrate on five diverse systems, our procedure is general, independent of the measured system or type of observed (quasi)particle and straightforward to implement. We envision future applicability in the probing of (quasi)particle interactions in such diverse areas as plasmonics⁷, Auger recombination² and exciton correlations in quantum dots^5,16,17, singlet fission¹⁸, exciton interactions in two-dimensional materials¹⁹ and in molecules^20,21, carrier multiplication²², multiphonon scattering⁹ or polariton-polariton interaction⁸.