Speaker
Description
Abstract: We experimentally demonstrate free-electron spectral shearing interferometry as a universally applicable approach to measure free-electron quantum states in the time-energy domain. © 2026 The Author(s)
Introduction
The determination of a complete quantum-state description for a given quantum-mechanical system is a fundamental task in quantum physics, and necessary to predict potential measurement outcomes. For any closed quantum system, the density matrix is such a quantity; it fully determines the state evolution and the probabilities of measurements with no need for prior knowledge of the individual pure states that build up the state. For photons, quantum-state reconstruction is routinely achieved by mixing an unknown state with a coherent reference and measuring field quadratures. Success in this context has been pivotal for establishing quantum optics. In contrast to photons, electrons are fermions and subject to the Pauli exclusion principle, rendering a measurement principle analogous to the one of photons impossible. Here, we propose and demon-strate a spectral shearing interferometry, which allows to measure the quantum state of free electrons in the time-energy domain for almost any ultrafast electron microscopy platforms.
Concept and results
Electron pulses are created by photoemission from a Schottky field-emitter source in a transmission electron microscope. We superimpose the electrons under scrutiny with two phase-stabilized probe laser pulses with ultra-narrow linewidth and slightly detuned wavelengths. By interaction with one of the two quasi-monochromatic laser pulses, the free-electron wave-packet can absorb or emit a photon, and its spectrum and spectral phase are shifted in energy. The interference pattern between the electron wavepacket and its duplicate manifests as a function of time delay between laser pulses and the electron pulse, which gives the explicit information of the quantum state of free electrons.
The experimental results show two main features. First, the sideband intensity are periodically modulated as a function of time delay, which directly evidences the two-path interference and the contrast of the modulation indicates the quantum coherence of electrons. Second, we observe strongly tilt sideband lobes, which result from the spectral shearing interference and re-veal the phase of the density matrix of the original electrons. Theory results nicely reproduces the proof-of-principle data. Our spectral shearing interferometry can therefore provide insight into the quantum state of free electrons.
By applying multiple combinations of the laser wavelength in spectral shearing interferometry, we show a full tomographic reconstruction of the free-electron quantum state. The reconstructed amplitude of the density matrix reveals the limited quantum coherence of our electrons. This decoherence arises primarily from the fact that electrons can be emitted at arbitrary times within the laser pulse (~250 fs) at an individual coherent emission time that is dictated by the bandwidth of the pho-ton-accepting emitter states. The possible emission time of electrons is much longer than the electron coher-ence length of the wavepacket and thus mixes many pure states of electrons, with a strong decay of their mu-tual coherence. The reconstructed phase of the density matrix reveals the phase difference between the energy component. Given the limited coherence of our electrons, the measured density-matrix phase reveals the group delay of our electrons. We can retrieve a linear chirp of approximately −94 fs/eV from the measured group delay of electrons.
Outlook
Our results imply a clear route toward generating electron pulses that approach a nearly pure state in the energy basis: using few-femtosecond laser pulses to trigger photoemission from a nanometric needle source can strongly reduce the (classical) emission-time uncertainty and therefore suppress quantum decoherence effects. Such a near-pure state would provide a quantum-enabled source for diffraction and microscopy use, where the measured results are not genuinely ensemble averages. In contrast, the quantum nature of free elec-trons emerges, and such a source can be potentially utilized to improve electron microscopy resolution [1] and the accessibility of quantum-state control protocols [2,3].
References
[1] K. X. Nguyen, Y. Jiang, C.-H. Lee, P. Kharel, Y. Zhang, A. M. van der Zande, P. Y. Huang, Achieving sub-0.5-angstrom–resolution ptychogra-phy in an uncorrected electron microscope. Science 383, 865–870 (2024).
[2] M. V. Tsarev, A. Ryabov, P. Baum, Free-electron qubits and maximum-contrast attosecond pulses via temporal Talbot revivals. Physical Review Research 3, 043033 (2021).
[3] O. Reinhardt, C. Mechel, M. Lynch, I. Kaminer, Free-electron qubits. Annalen der Physik 533, 2000254 (2021).