F. Glerean1,2,3, E. M. Rigoni1,2,4, G. Jarc1,2,4, S. Y. Mathengattil1,2,4, A. Montanaro1,2,4 F. Giusti1,2, M. Mitrano3, F. Benatti1,5, D. Fausti1,2,4 1 Physics Department, University of Trieste, Trieste, Italy 2 Elettra - Sincrotrone Trieste S.C.p.A., Trieste, Italy 3 Physics Department, Harvard University, Cambridge, MA, USA 4 Physics Department, University of Erlangen-Nürnberg, Erlangen, Germany 5 Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Trieste, Italy e-mail: daniele.fausti@fau.de, fglerean@fas.harvard.edu Acknowledgments The research leading to this result has been supported by the project INCEPT under grant agreement no. 677488 from the European Research Council. D.F., E.M.R., A.M., and G.J. acknowledge the support of the Gordon and Betty Moore Foundation through the grant CENTQC. Original paper F. Glerean et al., Light Sci. Appl. 14, 115 (2025); DOI:10.1038/s41377-025-01789-y. Fig. 1 Figure 1. (a) Ultrafast pump-probe spectroscopy of fluctuations measuring the quantum optical statistics of few-photon pulses. By observing how lightmatter interactions modify the photon number distribution of the probe, we access the intrinsic fluctuations of the material; (b) Equilibrium photon number distribution (left) measured for probes with an average of 13.8 (top) and 2.9 (bottom) photons per pulse. Pump-probe modulations of the photon number distribution induced by the coherent phonon oscillations (right); (c) Phonon-dependent mean photon number and variance (top). The Mandel parameter Q (bottom) quantifies the deviations from the coherent Poissonian statistics (Q =0). Qdet represents a baseline accounting for the detector excess noise; (d) Phonon and photon observables calculated as a function of pump delay for coherent, thermal, and squeezed phonon states. The top panels compare the average phonon displacement and its variance. The middle panels report the optical response (average and variance of the photon number). The bottom panels show the Mandel parameter. Adapted from F. Glerean et al., Light Sci. Appl. 14, 115 (2025); DOI:10.1038/s41377-025-01789-y; CC BY 4.0. (d) (c) (a) (b) sample pump probe N 0 5 10 15 20 0.0 0.2 0.4 0.6 0.8 1.0 p(N) Fock coherent squeezed 0 5 10 15 20 N N=13.8 0.0 0.2 p(N) 0 5 10 N N=2.9 0.0 0.5 1.0 pump delay (ps) 0.00 0.05 0.10 0.0 0.1 0.2 p(N) 3 4 5 6 7 8 9 experiment σ2 N N 0.0 0.5 1.0 pump delay (ps) −0.03 0.00 0.03 0.06 Q=σ2 N/N−1 Qdet −2 0 2 coherent q σ2 q thermal q σ2 q squeezed q σ2 q 2.5 3.0 3.5 N σ2 N N σ2 N N σ2 N 0.00 0.25 0.50 0.75 (ps) −0.05 0.00 0.05 Q=σ2 N/N−1 0.00 0.25 0.50 0.75 (ps) Q=σ2 N/N−1 0.00 0.25 0.50 0.75 (ps) Q=σ2 N/N−1 Structure and Dynamics Elettra Highlights 2024–2025 81
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