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Physical Review A

Characterization and detection method for x-ray excitation of Mössbauer nuclei beyond the low-excitation regime

Lukas Wolff, Jörg Evers

Published Oct 16, 2023• 3 citations
Publisher

Abstract

Up to now, experiments involving M\"ossbauer nuclei have been restricted to the low-excitation regime (LER). The reason for this is the narrow spectral linewidth of the nuclei. This defining feature enables M\"ossbauer spectroscopy with remarkable resolution and convenient control and measurements in the time domain, but at the same time implies that only a tiny part of the photons delivered by accelerator-based x-ray sources with orders-of-magnitude larger pulse bandwidth are resonant with the nuclei. X-ray free-electron lasers promise a substantial enhancement of the number of nuclear-resonant photons per pulse, such that excitations beyond the LER come within reach. This raises the question of how the onset of nonlinear excitations could be experimentally verified. Here, we develop and explore a method to detect an excitation of nuclear ensembles beyond the LER for ensembles of nuclei embedded in x-ray waveguides. It relies on the comparison of the x rays coherently and incoherently scattered off of the nuclei. As a key result, we show that the ratio of the two observables is constant within the LER, essentially independent of the details of the nuclear system and the characteristics of the exciting x rays. Conversely, deviations from this equivalence serve as a direct indication of excitations beyond the LER. Building upon this observation, we develop a variety of experimental signatures both, for near-instantaneous impulsive and for temporally extended nonimpulsive x-ray excitation. Correlating coherently and incoherently scattered intensities further allows one to compare theoretical models of nonlinear excitations more rigorously to corresponding experiments.

DOI
10.1103/physreva.108.043714

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Up to now, experiments involving M"ossbauer nuclei have been restricted to the low-excitation regime (LER). The reason for this is the narrow spectral linewidth of the nuclei. This defining feature enables M"ossbauer spectroscopy with remarkable resolution and convenient control and measurements in the time domain, but at the same time implies that only a tiny part of the photons delivered by accelerator-based x-ray sources with orders-of-magnitude larger pulse bandwidth are resonant with the nuclei. X-ray free-electron lasers promise a substantial enhancement of the number of nuclear-resonant photons per pulse, such that excitations beyond the LER come within reach. This raises the question of how the onset of nonlinear excitations could be experimentally verified. Here, we develop and explore a method to detect an excitation of nuclear ensembles beyond the LER for ensembles of nuclei embedded in x-ray waveguides. It relies on the comparison of the x rays coherently and incoherently scattered off of the nuclei. As a key result, we show that the ratio of the two observables is constant within the LER, essentially independent of the details of the nuclear system and the characteristics of the exciting x rays. Conversely, deviations from this equivalence serve as a direct indication of excitations beyond the LER. Building upon this observation, we develop a variety of experimental signatures both, for near-instantaneous impulsive and for temporally extended nonimpulsive x-ray excitation. Correlating coherently and incoherently scattered intensities further allows one to compare theoretical models of nonlinear excitations more rigorously to corresponding experiments.
Up to now, experiments involving Mössbauer nuclei driven by x-rays have been restricted to the low-excitation regime. Here, a setup is proposed which promises significant excitation, ideally exceeding full inversion of the nuclear ensemble, at x-ray light sources under construction. We further introduce a method to experimentally verify such inversions, in which population inversions manifest themselves in symmetry flips of suitably recorded spectra. It neither requires per-shot spectra of the incoming x-ray pulses, nor absolute measurements of the scattered light intensity.
Recent progress in accelerator-based x-ray sources brings higher excitation of ensembles of Mössbauer nuclei closer to experimental feasibility. Yet, a theoretical modeling of the decay dynamics of the interacting nuclear ensemble after the impulsive excitation is still an open challenge. Here, we derive a set of nonlinear equations which is capable of efficiently modeling large nuclear ensembles for arbitrary degrees of excitation. As key signature for higher excitation, we identify a non-linear time-evolution of the nuclear dipole phase, which can be tuned via the scattering geometry, and interferometrically be measured. Furthermore, we identify interesting finite-size effects in the nuclear dynamics of small ensembles. Our results provide important guidance for future experiments aiming at the non-linear excitation of nuclei. We further envision the exploration of finite size-effects in Mössbauer spectroscopy with highest spatial resolution, i.e., small sample volumes.
The direct interaction between nuclei and strong electromagnetic fields generated by novel coherent x-ray light sources such as the x-ray free electron laser is studied. We investigate the case of various stable or long-lived isotopes with energetically low-lying excited states, where the laser drives the nuclear transition from the ground to the first excited state. We therefore consider the nucleus as a two-level system including the corresponding hyperfine levels in our theoretical description. The performance of present and upcoming x-ray free electron laser facilities in coherently controlling the nuclear excited state population is analyzed for setups involving both solid state as well as accelerated nuclear targets to bridge the gap between photon and transition frequency. Current and predicted laser parameters are applied to calculate excited state populations and signal photon rates of nuclei after a radiation pulse, finding significant improvements compared to former calculations. Furthermore, we determine the parameters necessary to transfer substantial amounts of the nuclear ground state population to the excited state, and therefore to bring nuclear Rabi-oscillation within reach. Additionally, we take into account for the first time collective effects that take place in solid state targets and show that they may provide a significant effect in broadening natural linewidths of nuclear levels depending on the experimental setup. Our findings support the case of nuclear quantum optics for XFEL applications. Therefore, one hopes that eventually coherent control of nuclear transitions can be successfully applied in a number of areas in nuclear physics including preparation, control and detection methods.
The advent of x-ray free electron lasers (XFELs) has opened the door to exploring the x-ray-nuclei interaction in the multiexcitation regime. Here, we show the dependence of emission properties of x-ray photons from an ensemble of identical resonant nuclei on the number of excitations in the system, employing the theoretical methods we have introduced. Under the multiexcitation condition, the detection of x-ray quanta is emission-order selective. Our work presents an efficient approach to investigating the multiphoton emission of x-rays from cooperative resonant nuclei within and beyond weak-excitation regimes, offering valuable insights into nonlinear x-ray optics and many-body nuclear physics.
Waveguides offer a means to controllably couple atomic ensembles to the electromagnetic field therein. Here, we demonstrate x-ray propagation in planar thin-film waveguides coupled to Mössbauer nuclei under collective resonant excitation by short pulses of synchrotron radiation. We record x-ray photons that have been emitted into resonant modes of the waveguide. Depending on the geometry and mode of excitation, two fundamentally different signatures of the collective emission are observed, for which we present a unifying theoretical model. Our results form a new platform for waveguide quantum electrodynamics in the hard x-ray regime with the potential to provide a coherent narrow band source of x-rays on the nanometer scale.
The temporal dynamics of stimulated emission is studied, with particular emphasis on stimulated emission induced by x-ray pulses interacting with nuclei. In typical nuclear forward scattering experiments, the short incident x-ray pulse is accompanied by a huge number of off-resonant background photons. This prompts the question of whether stimulated emission can be observed in the delayed nuclear scattering signal which is emitted after the incident pulse has passed. We find that the stimulated photons essentially overlap with the stimulating pulse. To overcome this problem, we identify the reduction of the delayed scattered light intensity as an alternative signature for the stimulated emission. We further study a phase-sensitive variant of stimulated emission in the low-excitation regime, which provides convenient control parameters to facilitate the detection. Finally, we analyze the possibility of observing stimulated emission in nuclei driven by free electron lasers or synchrotron radiation sources.