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Observation of Nonadiabatic Landau-Zener Tunneling among Floquet States

Yun Yen1,2,3, Marcel Reutzel4,5,6, Andi Li7, Zehua Wang7, Hrvoje Petek7,8,*, and Michael Schüler1,9,†

  • *Contact author: petek@pitt.edu
  • †Contact author: michael.schueler@psi.ch
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Phys. Rev. X 16, 021004 – Published 3 April, 2026

DOI: https://doi.org/10.1103/ggyn-bn4v

Abstract

Electromagnetic fields induce electronic transitions, generate currents, and fundamentally alter quantum states of matter through strong light-matter interactions. As one established route, Floquet engineering provides a powerful framework to dress electronic states with time-periodic fields, giving rise to quasistationary Floquet states. With increasing field strength, nonperturbative responses of the dressed states emerge, yet their nonlinear dynamics remain challenging to interpret. In this work, we explore the emergence of nonadiabatic Landau-Zener transitions among Floquet states in Cu(111) under intense optical fields. With increasing field strength, we reveal a transition from perturbative dressing to a regime where nonadiabatic tunneling among Floquet states dominate the electronic dynamics. These insights are obtained through interferometrically time-resolved multiphoton photoemission spectroscopy, which serves as a sensitive probe of transient Floquet state dynamics. Numerical simulations and the theory of instantaneous Floquet states allow us to directly examine real-time excitation pathways in this nonperturbative photoemission regime. Our results clarify different light-dressing regimes in materials and provide microscopic insight relevant to ultrafast light wave electronics.

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Understanding the nonlinear dynamics of quantum states under intense electromagnetic fields remains a central challenge for developing ultrafast technologies. We explore this regime by employing coherent interferometrically time-resolved multiphoton photoemission spectroscopy to observe the electronic dynamics of copper surface states coherently dressed by intense optical fields. Our work reveals a transition from perturbative Floquet dressing to a nonperturbative regime where nonadiabatic Landau-Zener tunneling among Floquet states dominates the real-time excitation pathways. These findings demonstrate that we can actively control quantum population dynamics by tuning the phase delay between pulses, and help provide a microscopic insight to interpret complex strong-field responses in solids. By clarifying how these light-dressed states evolve and interact, we provide essential insights for the advancement of lightwave electronics and high-harmonic generation in condensed matter systems.

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Phys. Rev. X 16, 021004– Published 3 April, 2026
  • Received 11 April 2025
  • Revised 2 November 2025
  • Accepted 23 January 2026
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