Researchers map light-driven quantum transitions in graphene

Researchers have mapped how a strong light field accelerates electrons in graphene while driving them between energy bands. In a study published in Nature on 28 October 2026, the team describes the result as the first direct observation of Landau–Zener–Majorana transitions in momentum space—a map of electrons' states of motion rather than their positions.

Earlier experiments could resolve changes within a single light-wave cycle but covered only a limited, one-dimensional slice of momentum space. The new platform records both momentum directions across graphene’s entire first Brillouin zone, the basic repeating region of its momentum map. That wider view reveals changes in the shape of the electron distribution that a narrow slice could miss.

The collaboration brings together the University of Regensburg, Philipps-Universität Marburg and Forschungszentrum Jülich. Vincent Eggers is the study’s first author. The team posted a preprint on 13 February 2026, before the October journal publication.

How the electron maps were made

The experiment used a single layer of graphene grown on silicon carbide. Intense mid-infrared pulses, centred at 30 THz, drove the electrons. The pulses were phase-stable, meaning the oscillating electric field followed a repeatable pattern. After an adjustable delay, extreme-ultraviolet pulses with a central photon energy of 21.7 electronvolts ejected electrons from the sample.

A time-of-flight photoemission momentum microscope measured the ejected electrons' kinetic energies and both components of momentum parallel to the graphene sheet. Measurements at successive delays formed a sequence of electron-distribution maps. These are reconstructed snapshots of populations and motion states, not ordinary video following individual electrons through space.

The paper reports temporal resolution below 10 femtoseconds—a femtosecond is one millionth of a billionth of a second. The probe’s high photon energy and the microscope’s wide acceptance angle let it capture the entire first Brillouin zone, including its six corners. Relative to earlier momentum-microscopy and subcycle-photoemission capabilities, the researchers report more than a hundredfold increase in accessible momentum area and a tenfold increase in available driving-field strengths.

What makes this a quantum transition

Electrons in a solid occupy allowed energy ranges called bands. A Landau–Zener–Majorana transition can occur when a system is driven rapidly through an avoided crossing, where two energy levels approach closely without crossing. Instead of remaining in the lower-energy state, an electron can enter the upper one through quantum tunnelling.

In this experiment, the light field accelerated electrons within graphene’s bands while also allowing transitions from the lower, valence band into the upper, conduction band. Graphene’s band energies vary nearly linearly near special momentum points called K points, closely matching the model underlying these transitions. Its resistance to intense light also makes it a useful experimental material.

Forschungszentrum Jülich produced the high-purity carbon layers. In the collaboration’s 28 October announcement, co-author Professor Rupert Huber said the team had worked on the experiment for years. His collaborator, Professor Ulrich Höfer, said the samples helped make the observation possible during the first measurement campaign. The collaboration said sample purity prevented impurities from obscuring the electron dynamics.

Why the team identifies tunnelling

The electron distribution moved back and forth with the driving field, but it also stretched along the field direction, changing from a circle into an ellipse. Its width in that direction oscillated at twice the driving frequency. Meanwhile, the conduction-band population rose during the strongest half-cycles. The researchers interpret these combined changes as evidence of acceleration within bands coupled to tunnelling between them.

Quantum-mechanical simulations tested that interpretation. When the researchers switched off transitions between bands in the model, the distribution moved but stayed circular. Including coupling between bands reproduced the elongation. The calculations also indicated that ordinary optical excitation was suppressed by orders of magnitude under the experimental conditions; that process would favour a distribution perpendicular to the field, unlike the observed stretching along it.

Analysis

What limits control—and what comes next

The researchers corrected for a measurement effect: the infrared field also changed electrons' momenta after they had left the sample. Removing that shift isolated the dynamics inside graphene. Scattering and limited momentum resolution also affected how closely the measured transition region matched the ideal tunnelling model.

The electron current lagged behind the driving field by 4.9 ± 0.2 femtoseconds. The paper’s attosecond-precision claim concerns the extraction of this delay by analysing the waveforms' frequency components; it does not mean the distribution snapshots have attosecond resolution. Simulations reproduced the delay with a mean scattering time of 9.0 ± 0.7 femtoseconds, showing how quickly scattering constrains the orderly, coherent motion needed for lightwave control.

The paper presents quantum control, sensing and computing as prospective applications of lightwave electronics, not device-performance results from this experiment. Co-author Giacomo Inzani of the University of Regensburg proposes extending the method to other quantum materials to investigate—and potentially control—their electronic properties with light.