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

TL;DR

This work tackles the long-standing challenge of observing quantum-optical effects in inner-shell x-ray transitions due to overlap between resonant and continuum states. It introduces a thin-film x-ray cavity and a core-to-core RIXS measurement scheme guided by a Green's-function quantum optical model to access cavity-modified intermediate states, enabling control via cavity detuning. The key findings are the observation of a cavity-induced energy shift $\delta_c$ (CIS) and a cavity-enhanced decay rate $\gamma_c$ (CER) in the $2p-5d$ RIXS of WSi$_2$, manifested in 2D RIXS planes. This work establishes core-to-core RIXS as a versatile probe of x-ray cavity effects and points to future high-resolution spectroscopies (e.g., HEROS, HERFD) enabled by next-generation coherent x-ray sources for manipulating inner-shell dynamics.

Abstract

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.

Figures (4)

• Figure 1: Experimental scheme. (a) Cavity structure and RIXS energy-level diagram. Left: multilayer cavity composed of Pt mirrors, carbon (C) guiding layers, and a WSi$_2$ atomic ensemble. Right: simplified energy-level diagram for the core-to-core RIXS. The driving field resonantly excites the system to an intermediate core-hole state, which subsequently decays to the final state by emitting a characteristic x-ray. During the process, cavity effects induce an energy shift and an enhanced decay rate to the intermediate state. (b) Measurement geometry. The thin-film cavity sample is aligned at grazing incidence, resulting in a large footprint on the surface. A von Hamos (VH) spectrometer (energy resolution $\sim$1 eV) disperses and focuses the emitted x-rays onto a 2D detector, recording energy-resolved spectral images. A silicon drift detector (energy resolution $\sim$200 eV) collects the total fluorescence yield in the vertical direction, while a downstream 2D detector monitors cavity reflectivity. (c) 2D RIXS planes shown as a function of emission energy (left) or energy transfer (right). A constant background, estimated from off-resonant spectral tails, has been subtracted. The incident angle (8.7 mrad) was set to be above the critical angle, a condition under which the x-ray can penetrate the sample; thus, the cavity effect is minimized. Pink dashed lines indicate the resonant Raman peaks at constant energy transfer, and yellow dashed lines mark the constant emission energy.
• Figure 2: The CER and CIS as a function of angle offset calculated by the quantum Green's function model. An angle divergence of 30 $\mu$rad is convolved with the theoretical calculation. The pink cross and blue star indicate the specific angle offsets used in the experimental measurements, corresponding to the cavity-mode angle and an angle offset of $70~\mu$rad, respectively.
• Figure 3: The RIXS planes displayed with energy transfer axis. (a) The incident angle is at the first order of the cavity mode, where CER is strong and CIS is weak. (b) The incident angle is set to have an offset of $70~\mu$rad from (a), where CIS is strong and CER is weak. The vertical pink dashed lines indicate the peak intensities of the Raman feature.
• Figure 4: The extracted resonant spectrum of the Raman feature. The spectra are integrated within a 2-eV band centered around the energy transfer peak in the corresponding RIXS plane. (a) The incident angle is at 0.5°. (b) The incident angle is close to the cavity mode angle ($\Delta\theta \sim 0~\mu$rad) and (c) detuned to an angle offset of about $70~\mu$rad. The fittings are performed using a Lorentzian function with a constant background. The shaded curves indicate the fitted profile of panel (a).