Superradiant Thomson scattering from graphite in the extreme ultraviolet

Radiation-matter interaction is typically understood through low order perturbation theory, yet this framework falters in exotic environments, such as pulsars, where radiation exists in coherent states with large occupation numbers. Free Electron Lasers (FELs) provide a platform to investigate the interaction of matter with coherent radiation states at the laboratory scale in non-standard experimental conditions, for exciting photon densities and wavelength range.

Exploiting the high degree of coherence of FERMI FEL at the EIS-TIMEX beamline, a recent experiment from our group has unveiled an intrinsic nonlinear amplification in the extreme ultraviolet (EUV) Thomson scattering cross section from highly oriented pyrolytic graphite (HOPG), unrelated to FEL-induced alterations in the sample state. The exponential growth of the scattering cross section observed on increasing the intensity of the incident radiation reveals the occurrence of a process substantially deviating from linear Thomson scattering. In line with Dicke’s theory of superradiant emission, the phenomenon can be categorized as superradiant scattering. The scattering indeed involves the creation of low energy, low momentum coherent phonons in the system, which act as collective modes supporting the superradiance.

The observation can be considered as the first example of superradiant scattering by a crystal and is promoted by a remarkably low number of available channels for the scattering process. That produces the conditions for an increased (n>1) occupation of the final coherent radiation state, which in turn amplifies the scattering cross section. In the specific case, the reduction in the available scattering channels is ascribable to three fundamental conditions: (i) the high degree of coherence of the incident radiation, ensured by the seeded nature of FERMI FEL, (ii) the small fraction of Brillouin zone probed by EUV photons, and (iii) the reduced density of states in the reciprocal space sampled along the unique axis of HOPG.

Our Thomson scattering study on HOPG was carried out using the ~70 fs EUV pulses of FERMI in unprecedented experimental conditions for wavelength range (4-5 nm) and exciting photon densities (0.2 J/cm²). The intrinsic FEL emission fluctuations allow appreciating a positive exponential dependence of scattered intensity on the incident intensity (Fig. 1a). The measurement scheme adopted (Fig. 1b) enabled the study of the angular dependence of the scattered intensity, which points out a key role of phonons in the scattering process. The quantum-mechanical description of the scattering cross section precisely reproduces the measured trends (Fig. 1c), indicating the way to get useful information on the specimen. Our data allow obtaining quantitative results regarding the determination of the absorption and the combined analysis of absorption and scattering factors in the energy region across the absorption edge. They also point out the anisotropy of sound propagation in HOPG.

Figure 1: a) Semi-log plot of the ratio of scattered (I_scat) to incident (I₀) radiation intensity versus I₀. Data are shown for incident wavelength λ₀=4.08 nm (violet dots) and λ₀=4.74 nm (pink dots), vertical incident beam polarization to the scattering plane, and scattering angle θ=90°. Solid lines are single exponential fits to the data. b) Experimental setup at the TIMEX beamline (top view). The FEL beam impinges on the sample tilted by 65°. The scattered radiation is collected by the micro-channel plate detector, with a 10° angular opening, at variable scattering angle θ (60°-150°). c) Trend of the ratio of scattered to incident radiation intensity I_scat/I₀ as a function of I₀ and of θ (λ₀=4.08 nm, vertical incident beam polarization to the scattering plane). Violet dots: experimental points; surface plot: fitting function. 

The proposed framework sets the basis for designing novel EUV Thomson scattering experiments, opening promising routes for material investigations. Firstly, this kind of experiments can provide access to fundamental data, such as the absorption coefficient in the EUV spectrum, scattering factors across low energy absorption edges, and the dispersion curves of low-q phonons in thin films. Secondly, they enable the investigation of exotic phenomena, such as those arising from superradiant processes triggered by the intense and coherent EUV FEL pulses, particularly when combined with a reduced scattering volume in the reciprocal space.

This research was conducted by the following research team:

C. Fasolato^1,2, E. Stellino², E. Principi³, R. Mincigrucci³, J.S. Pelli-Cresi³, L. Foglia³, P. Postorino⁴, F. Sacchetti⁵, C. Petrillo^1,6
1 Dipartimento di Fisica e Geologia, Università degli Studi di Perugia, Italy.
² Istituto dei Sistemi Complessi (ISC), Consiglio Nazionale delle Ricerche (CNR), Rome, Italy.
³ Elettra - Sincrotrone Trieste S.C.p.A., Trieste, Italy.
⁴ Dipartimento di Fisica, Università Sapienza, Rome, Italy.
⁵ Istituto Officina dei Materiali (IOM), Consiglio Nazionale delle Ricerche (CNR), Perugia, Italy.
⁶ AREA Science Park, Padriciano, Trieste, Italy.

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