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Physical Review A

XUV superfluorescence from helium gas in the paraxial three-dimensional approximation

Špela Krušič, A. Mihelič, K. Bučar, Andrei Benediktovitch, Stasis Chuchurka, M. Žitnik

Published Jan 24, 2023• 4 citations

Abstract

We present the results of a theoretical study of XUV superfluorescence from doubly excited states of helium resonantly pumped by free-electron laser (FEL) pulses. Our model allows us to predict both the spectrum and angular distribution of emitted XUV radiation in a wide range of experimentally accessible parameters. This is achieved by going beyond two key deficiencies of most previous models: The one-dimensional treatment in space is upgraded to three dimensions with electromagnetic fields treated in the paraxial approximation and spontaneous emission is modeled by a recently developed approach that avoids the unrealistic delayed response but preserves the expected characteristics of the emitted field in the spontaneous emission limit. The case study of $3a{\phantom{\rule{0.16em}{0ex}}}^{1}{P}^{o}$ resonance in helium with $63.66\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$ excitation energy is presented for realistic parameters of seeded light pulses from the FERMI FEL facility and a recently developed high-pressure gas cell. Results of numerical simulations show that both the spectral width and angular divergence of emitted radiation vary with gas pressure and pump pulse intensity in a complex way.

DOI: 10.1103/physreva.107.013113

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•Mar 17, 2019•0 citations

We present the results of a theoretical study of XUV superfluorescence from doubly excited states of helium resonantly pumped by free-electron laser (FEL) pulses. Our model allows us to predict both the spectrum and angular distribution of emitted XUV radiation in a wide range of experimentally accessible parameters. This is achieved by going beyond two key deficiencies of most previous models: The one-dimensional treatment in space is upgraded to three dimensions with electromagnetic fields treated in the paraxial approximation and spontaneous emission is modeled by a recently developed approach that avoids the unrealistic delayed response but preserves the expected characteristics of the emitted field in the spontaneous emission limit. The case study of

3a{\phantom{\rule{0.16em}{0ex}}}^{1}{P}^{o}

resonance in helium with

63.66\phantom{\rule{0.28em}{0ex}}\mathrm{eV}

excitation energy is presented for realistic parameters of seeded light pulses from the FERMI FEL facility and a recently developed high-pressure gas cell. Results of numerical simulations show that both the spectral width and angular divergence of emitted radiation vary with gas pressure and pump pulse intensity in a complex way.

Using multilevel (161-level) numerical simulations beyond the rotating-wave approximation, we investigate the single-atom response of helium to intense pulses of radiation with properties characteristic of a self-amplified spontaneous emission (SASE) free-electron laser (FEL) source, and central wavelengths resonant with

1snp

excitation (

n=3

,4). The results show a complete breakdown of the two-level approximation and suggest that, under typical experimental conditions, levels other than the resonant level are significantly populated. We discuss the implications for the subsequent development of superfluorescence (a collective effect) from the excited atomic medium and compare the results to recent experiments.

We present a theoretical study of self-amplification of extreme ultraviolet light in a helium gas target. Resonant excitation to the

3a\phantom{\rule{0.16em}{0ex}}^{1}P^{o}

doubly excited state below the

N=2

threshold by

100\phantom{\rule{0.28em}{0ex}}\mathrm{fs}

free-electron laser pulses is followed by fluorescence at

40.7\phantom{\rule{0.28em}{0ex}}\mathrm{eV}

photon energy. The process is modeled by a three-level atomic system coupled to the continuum and described by the Maxwell-Bloch equations. The evolution of state populations and radiation fields is studied over a wide range of pump intensities and target pressures, clearly showing the regions of spontaneous emission, amplification, and saturation of light emitted in the forward direction. The treatment includes both coherent and SASE pump pulses. In both cases the amplified pulses are temporally coherent and exhibit a duration similar to that of the pump pulses.

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.

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.

We present a comprehensive experimental and theoretical study on superfluorescence in the extreme ultraviolet wavelength regime. Focusing a free-electron laser pulse in a cell filled with Xe gas, the medium is quasi-instantaneously population inverted by 4d-shell ionization on the giant resonance followed by Auger decay. On the timescale of ∼10 ps to ∼100 ps (depending on parameters) a macroscopic polarization builds up in the medium, resulting in superfluorescent emission of several Xe lines in the forward direction. As the number of emitters in the system is increased by either raising the pressure or the pump-pulse energy, the emission yield grows exponentially over four orders of magnitude and reaches saturation. With increasing yield, we observe line broadening, a manifestation of superfluorescence in the spectral domain. Our novel theoretical approach, based on a full quantum treatment of the atomic system and the irradiated field, shows quantitative agreement with the experiment and supports our interpretation.