Elettra | GasPhase In 1924, physicist Wilhelm Hanle investigated an unusual phenomenon in resonantly scattered photons and its associated polarization. He studied how the polarization of light resonantly scattered at a 90° angle from atomic mercury vapor appeared completely unpolarized. This phenomenon was first observed a decade earlier by Robert Wood. However, a similar experiment performed by Lord Rayleigh in 1922 showed the scattered light retaining part of its initial polarization. Two similar experiments lead to a seemingly contradictory result. This discrepancy puzzled researchers. In 1923, Wood revisited the issue and discovered that the observed polarization depended on the orientation of the setup relative to Earth’s magnetic field. Once the magnetic field was compensated using a solenoid, the scattered light became almost fully polarized. Hanle offered the first semiclassical interpretation. He linked the excitation of magnetic sublevels to oscillations in electron motion. Although helpful, his model could not be reconciled with the thenprevailing (old) quantum theory, which only allowed atoms to exist in pure states. A full explanation required the new concept of coherent excitation. Coherent excitation of multiple magnetic sublevels allowing them to interfere if their energy separation is on the order of ℏ/τ, with τ being the lifetime of the excited state. This interference can be significantly influenced by a weak external magnetic field, modulating the angular distribution and polarization of emitted fluorescence. This Hanle effect is typically observed through Hanle curves, which are recorded by varying the magnetic field using the fluorescence yield as signal. The lifetime τ of the excited state that is encoded in the angular distribution can thereby be extracted. Traditionally, the Hanle effect has been used in optical spectroscopy to determine atomic lifetimes. Recent advances in high-resolution x-ray sources, such as synchrotron radiation, now allow this technique to be applied at much shorter wavelengths. In this work, we demonstrate the use of the Hanle effect as a novel tool for determining excited-state lifetimes in highly charged ions in the soft x-ray regime. Highly charged ions refer to atoms with most of their electrons removed, resulting in a simple electronic structure. Their tightly bound electrons are sensitive probes for fundamental interactions. Precise measurements of their microscopic properties, the level energies and transition matrix elements, are excellent tests for quantum electrodynamics (QED) in strong fields and are essential in fields ranging from laboratory astrophysics to nextgeneration lithography. However, accurately measuring the lifetimes of their excited states that often lie in the femtosecond to picosecond range remains experimentally difficult. Conventional approaches probe the natural linewidths, which is analogous to the lifetime. However, sub-meV natural linewidths resulting from picosecond lifetimes in the soft x-ray regime are challenging to resolve. Here, we successfully translated the Hanle effect into the soft x-ray regime and demonstrated its use as an alternative to established methods. We probe N⁵⁺ (helium-like) nitrogen ions, generated and trapped using a compact electron beam ion trap (EBIT). The EBIT also exposes the ions to a static magnetic field of 0.8 T. At the Elettra synchrotron in Trieste, we used linearly polarized, monochromatic soft x-rays from the GasPhase beamline to perform x-ray absorption spectroscopy (XAS) on the trapped ions (Fig. 1 a). Fluorescence from the excited ions was detected using two silicon drift detectors (SDD) placed in and perpendicular to the plane of x-ray polarization (Fig. 1 b). This detector configuration allows us to quantify the angular distribution of the emitted light. The Hanle effect is sensitively controlled by the small Zeeman shift induced by the external magnetic field and the natural linewidth of the excited state. Furthermore, the Zeeman shift is known to be, to first order, independent of the principal quantum number while the natural linewidth decreases (lifetime increases) with it. Therefore, resonant excitation of the series of 1s–np ¹P₁ ground state transitions probes the magnitude of the Hanle effect. For low n, where the Zeeman splitting is negligible compared to the natural linewidth, the emission follows the characteristic dipole pattern. However, a systematic variation is observed in the angular distribution for increasing n, which is a clear signature of the Hanle effect in the soft x-ray domain (Fig. 1 c). Based on accurate modeling of the observed resonant elastic photon scattering by highly charged ions, we determined lifetimes ranging from hundreds of femtoseconds to tens of picoseconds. These values showed excellent agreement with theoretical predictions for helium-like ions, validating the Hanle effect as a sensitive and reliable probe for such short-lived states (Fig. 1 d). As a next step, we aim to apply this method to more complex systems such as lithium-like ions and other isoelectronic sequences, where theoretical models are less certain. The ability to measure lifetimes in such systems is crucial not only for refining atomic models but also for interpreting x-ray spectra from space-based observatories like XRISM. Moreover, these measurements contribute to magnetic field diagnostics andpolarization studies in hot astrophysical plasmas. Soft x-ray Hanle effect: A century old technique, rediscovered with x-rays Elettra Highlights 2024–2025 44
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