Cavity Controls Core-to-Core Resonant Inelastic X-ray Scattering

X-ray cavity quantum optics with inner-shell transitions has been hindered by the overlap between resonant and continuum states. Here, we report the first experimental demonstration of cavity-controlled co-to-core resonant inelastic x-ray scattering (RIXS). We eliminate the effects of the absorption edge by monitoring the RIXS profile, thereby resolving the resonant state from the overlapping continuum. We observe distinct cavity-induced energy shifts and cavity-enhanced decay rate in the $2p3d$ RIXS spectra of WSi$_{2}$. These effects, manifesting as stretched or shifted profiles in the RIXS planes, enable novel spectroscopic applications by cavity-controlled core-hole states. Our results establish core-to-core RIXS as a powerful tool for manipulating inner-shell dynamics in x-ray cavities, offering new avenues for integrating quanutm optical effects with x-ray spectroscopy.

💡 Research Summary

This paper reports the first experimental demonstration of cavity‑controlled core‑to‑core resonant inelastic X‑ray scattering (RIXS) using a thin‑film planar X‑ray cavity. The authors address a long‑standing obstacle in X‑ray cavity quantum optics: the spectral overlap between resonant inner‑shell transitions and the continuum, which has prevented the observation of quantum‑optical effects in hard‑X‑ray regimes. By recording two‑dimensional RIXS planes (incident photon energy versus emitted photon energy or energy transfer) with a high‑resolution von Hamos spectrometer, they separate the resonant Raman feature (constant energy transfer) from the diagonal continuum emission (constant emission energy).

The cavity consists of a multilayer stack (Pt/C/WSi₂/C/Pt) deposited on silicon, with WSi₂ providing a strong 2p‑5d dipole‑allowed transition that gives rise to the Lα emission (2p → 3d). Quantum Green‑function theory predicts that the cavity modifies the intermediate core‑hole state through two parameters: a cavity‑induced energy shift (CIS, δ_c) and a cavity‑enhanced decay rate (CER, γ_c). Both depend sensitively on the angular detuning Δθ of the incident beam from the first‑order cavity mode. Calculations show that at Δθ≈0 rad (the cavity mode) the decay rate is maximized while the energy shift is small, whereas at Δθ≈70 µrad the energy shift peaks and the decay enhancement is modest.

Experiments were performed at the GALAXIES beamline of the SOLEIL synchrotron, using a vertically collimated 30 µrad‑divergent beam (≈60 µm spot) and eight von Hamos crystal analyzers to achieve ~1 eV energy resolution and a large solid angle. A reference RIXS plane was first recorded at a large grazing incidence (8.7 mrad) where cavity effects are negligible. Subsequent measurements at the two selected detunings reveal clear cavity signatures:

1. Cavity‑Enhanced Decay (CER) – At the cavity mode, the Raman peak broadens dramatically along the energy‑transfer axis, producing extended tails on both sides of zero detuning. This broadening reflects the additional decay channel γ_c introduced by the cavity, effectively shortening the core‑hole lifetime.

2. Cavity‑Induced Shift (CIS) – At the 70 µrad offset, the Raman peak is displaced by ~‑0.2 eV relative to the reference, indicating a negative energy shift δ_c of the intermediate state caused by the modified photonic density of states.

3. Intensity Boost of the Diagonal Feature – The constant‑emission‑energy line (diagonal in the RIXS plane) becomes significantly brighter at the cavity mode, consistent with the formation of a standing‑wave field that enhances the spontaneous emission probability (∝ Im G).

These observations demonstrate that the cavity can independently tune the energy and lifetime of a core‑hole state, thereby disentangling the resonant transition from the absorption edge and continuum background that have plagued previous TFY or reflectivity studies. By selecting a constant energy‑transfer slice, the authors isolate the Raman component and suppress edge contributions, effectively realizing a high‑resolution, cavity‑engineered RIXS spectroscopy.

The work opens several avenues for advanced X‑ray spectroscopies. The demonstrated control of decay rates and transition energies can be leveraged in high‑energy‑resolution off‑resonant spectroscopy (HEROS) and high‑energy‑resolution fluorescence‑detected absorption (HERFD), where precise line‑shape manipulation is essential. Moreover, the ability to shape the intermediate state suggests possibilities for coherent control of inner‑shell dynamics, quantum‑optical gating, and even the generation of non‑classical X‑ray light via super‑radiant or sub‑radiant channels in tailored cavities.

In summary, by integrating a planar X‑ray cavity with core‑to‑core RIXS, the authors provide a powerful experimental platform that overcomes the intrinsic overlap of resonant and continuum states, directly visualizes cavity‑induced energy shifts and decay enhancements, and paves the way for cavity‑controlled X‑ray quantum optics and next‑generation spectroscopic techniques.