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arXiv:1911.00450 · Physical Review A

Transition between amplified spontaneous emission and superfluorescence in a longitudinally pumped medium by an x-ray free-electron-laser pulse

Yu-Hung Kuan, Wen-Te Liao

Published Feb 24, 2020• 7 citations
arXivHTMLPDF

Abstract

The transition from the amplification of spontaneous emission to superfluorescence in a three-level and swept-gain medium excited by an x-ray free-electron-laser pulse is theoretically investigated. Given the specific timescale of an x-ray free-electron-laser pulse, we investigate the swept pumping process in detail, and our results show that the temporal structure of an x-ray free-electron-laser pulse plays a more critical role than its peak intensity does for producing population inversion. The typical watershed of two radiant regions depends on the optical depth of the gain medium for a given coherence time, namely, the particle number density and medium length are equally important. However, we find that medium length plays a more important role than particle density for making the forward-backward asymmetry. The transient gain length and the total medium length are identified as two important factors to observe length-induced backward transition. The present results suggest an application of parametric controls over a single-pass-amplified light source.

DOI
10.1103/physreva.101.023836

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The transition from the amplification of spontaneous emission to superfluorescence in a three-level and swept-gain medium excited by an x-ray free-electron-laser pulse is theoretically investigated. Given the specific timescale of an x-ray free-electron-laser pulse, we investigate the swept pumping process in detail, and our results show that the temporal structure of an x-ray free-electron-laser pulse plays a more critical role than its peak intensity does for producing population inversion. The typical watershed of two radiant regions depends on the optical depth of the gain medium for a given coherence time, namely, the particle number density and medium length are equally important. However, we find that medium length plays a more important role than particle density for making the forward-backward asymmetry. The transient gain length and the total medium length are identified as two important factors to observe length-induced backward transition. The present results suggest an application of parametric controls over a single-pass-amplified light source.
Irradiation of a medium by short intense pulses from x-ray (XUV) free-electron lasers can result in saturated photoionization of inner electronic shells. As a result an inversion of populations between core levels appears. The resulting fluorescent radiation can be amplified during its propagation through the inverted medium and results in intense, quasi-transform-limited radiation bursts. While the optical counterpart of this phenomena, known as superfluorescence, was intensively investigated, a generalized treatment is needed in the x-ray (XUV) domain, where the dynamics of pumping and evolution due to fast decay processes play a crucial role. To provide a general theoretical approach, we start from the fundamental, quantized minimal coupling Hamiltonian of light-matter interaction and after a series of approximations arrive at a closed system of equations for the two-point correlation function of atomic coherences and the two-time correlation function of the emitted field. The obtained formalism enables us to investigate collective spontaneous emission in various regimes. It is extended consistently to include incoherent processes that are relevant in the x-ray (XUV) domain. These processes are introduced into the formalism by corresponding Lindblad superoperators. The connection to other approaches is discussed and numerical examples related to recent experiments are presented.
A one-dimensional model of the coherent amplification in a high- and swept-gain amplifier in the presence of strong spontaneous emission is presented and applied to seeding an x-ray laser with a high harmonic pulse. The atomic structure of the amplifying medium includes level degeneracy, and the Maxwell-Bloch equations are used to describe the propagation and interaction processes. This analysis elucidates, in the most comprehensive way, the influence of the random spontaneous emission on the coherent amplification process, as reflected in the basic pulse parameters such as its shape, polarization, and coherence.
We have observed and characterized 501.6 nm collective spontaneous emission (superfluorescence) following 1s(2) → 1s3p excitation of helium atoms by 53.7 nm free-electron laser radiation. Emitted pulse energies of up to 100 nJ are observed, corresponding to a photon number conversion efficiency of up to 10%. We observe the peak intensity to scale as ρ(2) and the emitted pulse width and delay to scale as ρ(-1), where ρ is the atom number density. Emitted pulses as short as 1 ps are observed, which corresponds to a rate around 75,000 times faster than the spontaneous 1s3p → 1s2s decay rate. To our knowledge, this is the first observation of superfluorescence following pumping in the extreme ultraviolet wavelength region, and extension of the technique to the generation of extreme ultraviolet and x-ray superfluorescence pulses should be straightforward by using suitable atomic systems and pump wavelengths.
An approach to modeling the dynamics of x-ray amplified spontaneous emission and superfluorescence -- the phenomenon of collective x-ray emission initiated by intense pulses of X-ray Free Electron Lasers -- is developed based on stochastic partial differential equations. The equations are derived from first principles, and the relevant approximations, derivation steps, and extensions specific to stimulated x-ray emission are presented. The resulting equations take the form of three-dimensional generalized Maxwell-Bloch equations augmented with noise terms for both field and atomic variables. The derived noise terms possess specific correlation properties that enable the correct reconstruction of spontaneous emission. Consequently, the developed theoretical formalism is universally suitable for describing all stages of stimulated x-ray emission: spontaneous emission, amplified spontaneous emission, and superfluorescence. We present numerical examples that illustrate various properties of the emitted field, including spatio-temporal coherence, spectral-angular and polarization characteristics. We anticipate that the proposed theoretical framework will establish a robust foundation for interpreting measurements in stimulated x-ray emission spectroscopy, modeling x-ray laser oscillators, and describing other experiments leveraging x-ray superfluorescence.
We study the compression of strong x-ray pulses from x-ray free-electron lasers (XFELs) propagating through the resonant medium of atomic argon. The simulations are based on the three-level model with the frequency of the incident x-ray pulse tuned in the $2{p}_{3/2}\text{\ensuremath{-}}4s$ resonance. The pulse propagation is accompanied by the self-seeded stimulated resonant Raman scattering (SRRS). The SRRS starts from two channels of amplified spontaneous emission (ASE), $4s\text{\ensuremath{-}}2{p}_{3/2}$ and $3s\text{\ensuremath{-}}2{p}_{3/2}$, which form the extensive ringing pattern and widen the power spectrum. The produced seed field triggers the Stokes ASE channel $3s\text{\ensuremath{-}}2{p}_{3/2}$. The population inversion is quenched for longer propagation distances where the ASE is followed by the lasing without inversion (LWI), which amplifies the Stokes component. Both ASE and LWI reshape the input pulse: The compressed front part of the pulse (up to 100 as) is followed by the long tail of the ringing and beating between the pump and Stokes frequencies. The pump pulse also generates weaker Stokes and anti-Stokes fields caused by four-wave mixing. These four spectral bands have fine structures caused by the dynamical Stark effect. A slowdown of the XFEL pulse up to 78% of the speed of light in vacuum is found because of a large nonlinear refractive index.
An approach to modeling the dynamics of x-ray amplified spontaneous emission and superfluorescence, the phenomenon of collective x-ray emission initiated by intense pulses of x-ray free-electron lasers, is developed based on stochastic partial differential equations. The equations are derived from first principles, and the relevant approximations, derivation steps, and extensions specific to stimulated x-ray emission are presented. The resulting equations take the form of three-dimensional generalized Maxwell-Bloch equations augmented with noise terms for both field and atomic variables. The derived noise terms possess specific correlation properties that enable the correct reconstruction of spontaneous emission. Consequently, the developed theoretical formalism is universally suitable for describing all stages of stimulated x-ray emission: spontaneous emission, amplified spontaneous emission, and superfluorescence. We present numerical examples that illustrate various properties of the emitted field, including spatiotemporal coherence and spectral-angular and polarization characteristics. We anticipate that the proposed theoretical framework will establish a robust foundation for interpreting measurements in stimulated x-ray emission spectroscopy, modeling x-ray laser oscillators, and describing other experiments leveraging x-ray superfluorescence.