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Physical Review Letters

Nonlinear Dynamics of X-Ray Superradiant Burst via Cooperative Nuclear Excitations

Juntian Shan, Yue Chang, Lida Zhang, Fan Wang, Jianmin Yuan, Xiangjin Kong, Y. G.

Published Mar 2, 2026• 0 citations
Publisher

Abstract

Superradiant burst often arises from photon-mediated interactions within an excited ensemble of emitters, where collective emission leads to a sharp increase in photon intensity. Here, we focus on a nuclear ensemble with cooperative excitations and propose, for the first time, the generation of superradiant burst of x-ray photons. We establish the required excitation conditions to observe x-ray superradiant bursts, offering guidance for the experiments utilizing state-of-the-art x-ray sources. Building on this, we investigate the dynamics of the x-ray superradiant burst and reveal novel nonlinear relationships between the time required to reach the peak intensity and the excitation number, as well as between the peak intensity and the excitation number. Additionally, we introduce a dimensionless parameter that serves as an indicator of the system, reflecting how strongly the burst can occur in a given configuration. Our work provides fresh insights into the understanding of collective emission in many-body x-ray-nuclei systems within the nonlinear regime, opening new avenues for x-ray quantum optics.

DOI
10.1103/rfwb-sq72

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Superradiant burst often arises from photon-mediated interactions within an excited ensemble of emitters, where collective emission leads to a sharp increase in photon intensity. Here, we focus on a nuclear ensemble with cooperative excitations and propose, for the first time, the generation of superradiant burst of x-ray photons. We establish the required excitation conditions to observe x-ray superradiant bursts, offering guidance for the experiments utilizing state-of-the-art x-ray sources. Building on this, we investigate the dynamics of the x-ray superradiant burst and reveal novel nonlinear relationships between the time required to reach the peak intensity and the excitation number, as well as between the peak intensity and the excitation number. Additionally, we introduce a dimensionless parameter that serves as an indicator of the system, reflecting how strongly the burst can occur in a given configuration. Our work provides fresh insights into the understanding of collective emission in many-body x-ray-nuclei systems within the nonlinear regime, opening new avenues for x-ray quantum optics.
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Fully-excited two-level atoms separated by less than the transition wavelength cooperatively emit light in a short burst, a phenomenon called superradiance by R. Dicke in 1954. The burst is characterized by a maximum intensity scaling with the square of the number of atoms NNN and a temporal width reduced by NNN compared to the single atom spontaneous decay time. Both effects are usually attributed to a synchronization of the electric dipole moments of the atoms occurring during the process of light emission. Contrary to this explanation, it was recently shown by use of a quantum path description that the peak intensity results from the quantum correlations among the atoms when occupying symmetric Dicke states. Here we investigate from this perspective the temporal evolution of the ensemble, starting in the small sample limit, i.e., when the atoms have mutual separations much smaller than the transition wavelength λλλ and pass down the ladder of symmetric Dicke states. In addition, we explore the temporal evolution for the case of non-interacting atoms with mutual separations much larger than λλλ. We show that in this case a similar superradiant burst of the emitted radiation is observed if the quantum correlations of the atoms are generated by conditional photon measurements retaining the atomic ensemble within or close to the symmetric subspace.
We investigate the emergence of cooperative radiation phenomena in ensembles of two-level atoms coupled to a lossy resonant cavity beyond the Markovian and mean-field approximations. By deriving a complete analytical solution for the two-emitter case and employing a numerically exact method for larger ensembles, we characterize the full transition from Markovian to non-Markovian collective dynamics for systems of up to 10310^3103 emitters. Our results reveal three distinct regimes: a Markovian phase exhibiting the standard superradiant burst, a non-Markovian phase featuring spontaneous superabsorption of the emitted field, and a critical regime marked by pulsed collective emission. We show that the critical spectral width separating these behaviors increases monotonically with the number of emitters, demonstrating that environmental memory effects can be enhanced by cooperativity. Finally, we find that the superradiant scaling of the peak intensity progressively degrades with increasing system size, approaching a subquadratic law in the limit of a perfect cavity. In this regime, spontaneous superabsorption emerges as a distinct manifestation of non-Markovian cooperativity.
The interaction between super-intense coherent x-ray light and nuclei is studied theoretically. One of the main difficulties in driving nuclear transitions arises from the very narrow nuclear excited state widths, which limit the coupling between lasers and nuclei. In the context of direct laser–nucleus interaction, we consider the nuclear width broadening that occurs when in solid targets, when the excitation caused by a single photon is shared by a large number of nuclei, forming a collective excited state. Our results show that cooperative effects mostly contribute with a modest increase to the nuclear excited state population except in the case of 57 Fe, where the enhancement can reach almost two orders of magnitude. Additionally, an update is given of previous estimates of the nuclear excited state population and signal photons for x-ray lasers interacting with solid-state and ion beam nuclear targets taking into account the experimental advances of x-ray coherent light sources. The presented values are an improvement by orders of magnitude and are encouraging as to the future prospects of nuclear quantum optics.
Coherent control of nuclear pumping in a three-level system driven by x-ray light is investigated. In single nuclei the pumping performance is determined by the branching ratio of the excited state populated by the x-ray pulse. Our results are based on the observation that in ensembles of nuclei, cooperative excitation and decay leads to a greatly modified nuclear dynamics which we characterize by a time-dependent cooperative branching ratio. We discuss prospects of steering the x-ray pumping by coherently controlling the cooperative decay. First, we study an ideal case with purely superradiant decay and perfect control of the cooperative emission. A numerical analysis of x-ray pumping in nuclear forward scattering with coherent control of the cooperative decay via externally applied magnetic fields is presented. Next, we provide an extended survey of nuclei suitable for our scheme, and propose proof-of-principle implementations already possible with typical M\"ossbauer nuclei such as 57Fe^{57}\mathrm{Fe}57Fe. Finally, we discuss the application of such control techniques to the population or depletion of long-lived nuclear states.