ECAMP 15

X-ray free-electron lasers (XFELs) open new avenues towards studying collective x-ray emission and nonlinear x-ray matter interaction. In this talk I will present recent advancements on the experimental and theoretical exploration of collective spontaneous x-ray emission (x-ray superfluorescence) following ultrafast inner-shell photoinization. X-ray superfluorescence has been demonstrated in atomic gases in the soft x-ray range [1], in rare-gases [2] and clusters [3] in the XUV, and in solids and liquids in the hard x-ray range [4,5]. As opposed to the XFEL pulses that are based on the process of self-amplified spontaneous emission and have limited temporal coherence, x-ray superfluorescence produces phase-stable, ultrabright x-ray pulses of fs and sub-fs duration [6,7]. A quantitative theoretical prediction of this effect is intricate and computationally demanding, since it involves incoherent pumping of a large ensemble of atoms of several electronic states that undergo strong decoherence through electronic decay channels and pulse propagation effects, along with the need of a quantum-electrodynamical description of the field modes. I will present a theoretical framework [8,9] strongly linked to stochastic sampling of the time-dependent positive-P distribution of the multi-dimensional Liouville space. In this novel method, we extend a previous phenomenological treatment and treat quantum fluctuations of the electromagnetic field by appropriate stochastic contributions. The resulting set of coupled stochastic partial differential equations resemble the generalized Maxwell-Bloch equations to follow the evolution of the electromagnetic fields and the density matrix of the emitters [10]. The stability of the equations will be discussed and I address potential applications of the method in cavity and nonlinear quantum optics.

[1] N. Rohringer et al., Nature 481, 488 (2012).
[2] L. Mercadier et al., Physical Review Letters 123, 023201 (2019).
[3] A Benediktovitch et al. Physical Review A 101, 063412 (2020).
[4] T. Kroll et al., Physical Review Letters 120, 133203 (2018).
[5] T. Kroll et al., Physical Review Letters 125 (3), 037404 (2020).
[6] M. D. Doyle et al., Optica 10, 1602 (2023).
[7] T. M. Linker et al., Nature, accepted (2025). https://arxiv.org/abs/2409.06914
[8] S. Chuchurka, V. Sukharnikov, A. Benediktovitch and N. Rohringer, Phys. Rev. A 110, 053703 (2024).
[9] S. Chuchurka, V. Sukharnikov and N. Rohringer, Phys. Rev. A 109, 063705 (2024).
[10] S. Chuchurka, A. Benediktovitch, Š. Krušič, A. Halavanau, and N. Rohringer, Phys. Rev. A 109, 03375 (2024).