Ultrafast microscopy has spent a decade learning to film energy as it moves. A short laser pulse creates excitons — bound electron-hole pairs — in a semiconductor, a second pulse probes them a controlled instant later, and the snapshots become a movie of propagation: how far the energy travels, how fast, and whether it moves diffusively or ballistically. The numbers the movies yield — diffusion coefficients, mobilities, propagation lengths — are functional metrics that contact-based transport measurements cannot provide. There has been one flaw running through all of them. The camera could not count. It could not tell whether the motion it recorded belonged to one exciton moving alone or to a crowd of excitons moving together, colliding, and annihilating one another. And that distinction is exactly the one that governs the physics the field cares most about.
A paper published in Nature Materials on November 6, 2026, closes that gap. Jakhangirkhodja A. Tulyagankhodjaev, Michelle E. Reynoso, and Milan Delor, of the Department of Chemistry at Columbia University, report spatiotemporal intensity-cycling microscopy, which separates single-particle from multi-particle transport in van der Waals semiconductors. The idea is disarmingly simple: measure the same ultrafast movie at a few different pump intensities, and combine the results so that the single-particle, pair-interaction, and higher-order parts of the signal each emerge as their own image. A companion News & Views by Pavel Malý of Charles University in Prague, who co-invented intensity cycling, lays out the scheme in a single figure.
Why counting matters
Start with what an exciton does when it is not alone. Two excitons that meet can annihilate: one gives up its energy to the other, which is kicked to a higher state and then relaxes, usually by giving the energy to the lattice as heat. The pair is gone, one exciton’s worth of energy wasted. Annihilation is a real physical process, and it is also a measurement contaminant. In a conventional ultrafast microscopy experiment, the signal at any point in space and time is a mixture: some of it records single excitons diffusing, some of it records pairs annihilating, and the two contributions scale differently with excitation density. Turn the pump intensity up for a better signal, and the annihilation contribution grows faster than the diffusion contribution, because annihilation needs two excitons and scales with the square of the density. The standard defence has been to turn the intensity down until the multi-particle contribution is negligible, accepting the weak signal and long averaging times that follow. Even then the defence is approximate: at any finite intensity, some annihilation is present, and the diffusion coefficient extracted from the movie is partly a measure of how fast excitons disappear, not how fast they move.
The contamination is not hypothetical. In monolayer transition metal dichalcogenides, annihilation is fast enough to reshape the spatial profile of the exciton cloud itself, producing the halo effects documented by Kulig and colleagues in 2018: at high fluence, the centre of the distribution is eaten away by annihilation faster than diffusion can refill it, so the cloud develops a ring. A movie of that cloud, read naively, reports motion that is partly disappearance.
The trick: let the intensity do the sorting
Intensity cycling, the spectroscopic idea behind the new microscope, was introduced by Malý and colleagues in Nature in 2023 and formalised in a tutorial by Lüttig and Malý in the Journal of Physics B earlier this year. Its logic rests on the perturbative expansion of the pump-probe signal into contributions scaling with different powers of the pump intensity I. The first term — third-order in the language of nonlinear optics — describes the dynamics of a single excitation. The next term, fifth-order, describes the dynamics of two excitations interacting: the pair channel, which is where exciton-exciton annihilation lives. Higher terms describe three or more particles. At any single intensity, all of these are superimposed in one measured number. But they scale differently, so measurements at several intensities give a system of equations that can be solved for the separate contributions.
The new paper gives that spectroscopic separation spatial resolution. The Columbia team records the pump-probe signal as a function of position and of pump-probe delay, at three pump intensities: a base intensity I₀, and 3I₀ and 4I₀. Three linear combinations then yield three separate movies. The coefficients are given in Malý’s News & Views figure: the single-particle diffusion movie is 2 times the I₀ measurement, minus two-thirds of the 3I₀ measurement, plus one-quarter of the 4I₀ measurement; the pair-interaction movie is minus two-thirds, plus five-sixths, minus one-third; and the higher-order movie is plus one-sixth, minus one-sixth, plus one-half. The arithmetic is elementary. The consequence is not: for the first time, the diffusion of a lone exciton, the interaction of a pair, and the correlated motion of still larger groups can be watched as separate films of the same sample, under the same conditions, at the same time.
That separation answers, directly, whether the method resolves exciton-exciton annihilation separately from transport. It does — that is the point of the fifth-order channel. Annihilation is a two-particle process, so it belongs to the pair-interaction movie, while single-particle diffusion belongs to the third-order movie. Previously, annihilation served as an indirect probe of diffusion: fluence-dependent measurements inferred a diffusion coefficient from how quickly the population decayed. With intensity cycling, the inference is replaced by a separation: diffusion is measured in the channel that contains no annihilation, and annihilation in the channel that contains no single-particle diffusion.
What the microscope is for
The paper’s abstract states the scope of the demonstration in general terms: the method separates single-particle and multi-particle transport in van der Waals semiconductors, “enabling imaging of charge mobility, exciton interactions, and correlated many-body states in van der Waals semiconductors, including Mott transitions.”
Charge mobility is the most immediately practical. Mobility is a single-particle property — how fast one charge moves, or how far it diffuses before scattering — but optical measurements of it have always been entangled with the many-body effects that appear at the intensities needed to see anything. A clean single-particle channel means a mobility extracted from an image rather than from a fit that must first model away the annihilation.
Exciton interactions are the second application, and here the pair channel is the measurement rather than the correction. The strength of exciton-exciton interaction sets the nonlinear optical response of a material, the density at which a condensate can form, and the losses in any device that operates at high excitation density. Imaging the pair channel as a function of position means watching where in a sample interactions are strong and where they are weak — near a defect, at a grain boundary, in a strained region — rather than averaging over all of it.
The third application, correlated many-body states including Mott transitions, is the most ambitious and the one that most directly connects to this publication’s long-running coverage of moiré and correlated excitonic phases. The exciton Mott transition is the density-driven dissociation of bound electron-hole pairs into a plasma of free carriers: below a critical density the excitations are excitons, above it they are not. Whether that transition is abrupt or gradual in a given material has been contested — a recent study of monolayer WS₂ argued from lineshape analysis that it is discontinuous, with the plasma phase appearing suddenly above a threshold density and decaying back within 0.65 picoseconds. Imaging the transition as it happens, with the channels separated, would show whether the plasma nucleates in patches or appears uniformly. That is the kind of question a spatially resolved, number-resolved measurement is built to answer.
The group and the instrument
The Columbia group is not new to filming excitons. In 2023, Tulyagankhodjaev and colleagues — with Delor as senior author — reported in Science the room-temperature wavelike transport of excitons in Re₆Se₈Cl₂, a van der Waals superatomic semiconductor assembled from rhenium-selenium-chloride clusters in the laboratory of Xavier Roy. In that material, excitons bind to slow acoustic phonons to form acoustic exciton-polarons, quasiparticles shielded from ordinary lattice scattering, which propagate quasi-ballistically for nanoseconds and across several microns at room temperature — energy propagation that, over nanosecond timescales, exceeded even silicon. The experiment was built on ultrafast stroboscopic scattering microscopy, a technique the Delor group developed to image exciton motion directly.
The new paper is, in a sense, the sequel that the 2023 result required. Wavelike transport is a single-particle claim, but it was demonstrated in a measurement that, like all ultrafast microscopy before it, mixed single- and multi-particle contributions. Intensity cycling is the correction the group’s own earlier work needed, and the fact that the same first author led both papers is not a coincidence. The materials imaged in the new study are the layered van der Waals semiconductors of the group’s programme — the published abstract frames the demonstrations in general terms, and the detailed material-by-material results sit in the full paper — but the logic of the advance does not depend on which flake was on the stage.
What it is not
Three cautions, stated plainly because the framing invites overreading. First, this is not a wavefunction image. It does not recover the internal quantum-mechanical phase of an exciton, as the Graz trPOT result we covered recently does for an organic film. Intensity-cycling microscopy resolves populations and their motion — where excitons are, how fast they spread, how often they meet — separated by how many particles are involved. The phase information that defines coherence is not part of the measurement.
Second, the separation has a limit, and the method’s own literature states it. Intensity cycling rests on the perturbative expansion: it works while the signal can still be written as a sum of terms scaling with successive powers of the intensity. Lüttig and Malý note that whenever the perturbative description is no longer suitable, intensity cycling is expected to fail with it. At very high excitation densities, where the response saturates, the expansion breaks down and the linear combinations no longer isolate clean orders.
Third, this is a methods advance demonstrated on layered semiconductors, not a device result and not yet a survey. The abstract’s three applications — charge mobility, exciton interactions, Mott transitions — are capabilities the method enables, demonstrated on the group’s van der Waals samples. Whether the same separation is as clean in a disordered organic film, a perovskite, or a moiré heterostructure is a question for the next papers, not a finding of this one. The moiré connection is the most tantalising and the least demonstrated: a Mott insulator of excitons in a moiré lattice is a system whose entire physics is the difference between one exciton per site and two. But the paper’s claim, as published, is the capability, not a moiré result.
What to watch
The most interesting follow-ups divide naturally along the three channels. In the single-particle channel: clean mobility maps — the transition metal dichalcogenides first. In the pair channel: spatial maps of interaction strength, and whether annihilation is uniform across a flake or concentrated at defects and edges. In the higher-order channel: the correlated states themselves, watched as they form — and the moiré systems, where the exciton Mott insulator and the generalised Wigner crystal are the obvious first targets.
There is also a quieter implication for theory. Models of exciton transport have traditionally been fitted to mixed data, with the annihilation rate as a free parameter absorbing whatever the diffusion model could not explain. Separated channels give theory separate targets — a diffusion coefficient for the third-order movie, an interaction strength for the fifth — with no parameter free to trade one against the other.
The deepest reason this result matters is the one the paper’s title states: ultrafast microscopy could watch energy move, but it could not say how many particles were moving. Every claim about a correlated phase — every Mott transition, every condensate — rested on a measurement that mixed the very distinction the claim depended on. The Columbia team has not discovered a new phase. They have built the instrument that can tell whether the phases already claimed are real, and how they move.
Sources and further reading
Tulyagankhodjaev, J. A.; Reynoso, M. E.; Delor, M. “Spatiotemporal intensity-cycling microscopy unveils many-body interactions and correlated transport in van der Waals semiconductors.” Nature Materials (2026), published November 6, 2026. DOI: 10.1038/s41563-026-02800-6. Dataset: Zenodo, DOI: 10.5281/zenodo.23321245.
Malý, P. “Imaging multi-particle dynamics in space and time.” Nature Materials (2026), News & Views, published November 6, 2026. DOI: 10.1038/s41563-026-02785-2.
Malý, P. et al. “Separating single- from multi-particle dynamics in nonlinear spectroscopy.” Nature 616, 280–287 (2023). Lüttig, J.; Malý, P. “A simple method to extract nonlinear signals in time-resolved spectroscopy.” J. Phys. B 59, 063001 (2026). Krich, J. J. et al. “Separating orders of response in transient absorption and coherent multidimensional spectroscopy by intensity variation.” Journal of Physical Chemistry Letters 16, 5897–5905 (2025).
Tulyagankhodjaev, J. A. et al. “Room-temperature wavelike exciton transport in a van der Waals superatomic semiconductor.” Science 382, 438–442 (2023). Kulig, M. et al. “Exciton diffusion and halo effects in monolayer semiconductors.” Physical Review Letters 120, 207401 (2018). Deng, S. et al. “Frozen non-equilibrium dynamics of exciton Mott insulators in moiré superlattices.” Nature Materials 24, 527–534 (2025).
For the wider measurement context, see this site’s explainers on how excitons are seen and on coherence, dephasing, and why room temperature is hard. This article is analysis of published research, not investment advice.