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arXiv:0809.3249 · Physical Review A

X-ray refractive index of laser-dressed atoms

Christian Buth, Robin Santra

Published Oct 13, 2008• 17 citations
arXivHTMLPDF

Abstract

We investigated the complex index of refraction in the x-ray regime of atoms in laser light. The laser (intensity up to ${10}^{13}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}$, wavelength $800\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$) modifies the atomic states but, by assumption, does not excite or ionize the atoms in their electronic ground state. Using quantum electrodynamics, we devise an ab initio theory to calculate the dynamic dipole polarizability and the photoabsorption cross section, which are subsequently used to determine the real and imaginary part, respectively, of the refractive index. The interaction with the laser is treated nonperturbatively; the x-ray interaction is described in terms of a one-photon process. We numerically solve the resolvents involved using a single-vector Lanczos algorithm. Finally, we formulate rate equations to copropagate a laser and an x-ray pulse through a gas cell. Our theory is applied to argon. We study the x-ray polarizability and absorption near the argon $K$ edge over a large range of dressing-laser intensities. We find electromagnetically induced transparency (EIT) for x rays on the Ar $1s\ensuremath{\rightarrow}4p$ pre-edge resonance. We demonstrate that EIT in Ar allows one to imprint the shape of an ultrafast laser pulse on a broader x-ray pulse (duration $100\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$, photon energy $3.2\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$). Our work thus opens new opportunities for research with hard x-ray sources.

DOI
10.1103/physreva.78.043409

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We investigated the complex index of refraction in the x-ray regime of atoms in laser light. The laser (intensity up to 1013W∕cm2{10}^{13}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}1013W∕cm2, wavelength 800nm800\phantom{\rule{0.3em}{0ex}}\mathrm{nm}800nm) modifies the atomic states but, by assumption, does not excite or ionize the atoms in their electronic ground state. Using quantum electrodynamics, we devise an ab initio theory to calculate the dynamic dipole polarizability and the photoabsorption cross section, which are subsequently used to determine the real and imaginary part, respectively, of the refractive index. The interaction with the laser is treated nonperturbatively; the x-ray interaction is described in terms of a one-photon process. We numerically solve the resolvents involved using a single-vector Lanczos algorithm. Finally, we formulate rate equations to copropagate a laser and an x-ray pulse through a gas cell. Our theory is applied to argon. We study the x-ray polarizability and absorption near the argon KKK edge over a large range of dressing-laser intensities. We find electromagnetically induced transparency (EIT) for x rays on the Ar 1s\ensuremath→4p1s\ensuremath{\rightarrow}4p1s\ensuremath→4p pre-edge resonance. We demonstrate that EIT in Ar allows one to imprint the shape of an ultrafast laser pulse on a broader x-ray pulse (duration 100ps100\phantom{\rule{0.3em}{0ex}}\mathrm{ps}100ps, photon energy 3.2keV3.2\phantom{\rule{0.3em}{0ex}}\mathrm{keV}3.2keV). Our work thus opens new opportunities for research with hard x-ray sources.
Abstract Experiments on free–free electron scattering, specifically the absorption or emission of 1.17 eV photons from a Nd:YAG laser field by an unbound electron when it is scattered by an atom or molecule, are reviewed. For large scattering angles such experiments are well described by a simple analytical theory that is independent of the properties of the target. At small scattering angles this theory breaks down for targets with a high dipole polarizability α , and an additional term needs to be incorporated in the scattering amplitude. This term is proportional to the dipole polarizability, and hence introduces the properties of the target into the free–free cross section—i.e., the laser field ‘dresses’ the atom. A progress report is given of free–free experiments designed to look for such ‘dressed atom’ effects during the electron-impact excitation of argon in the presence of a laser field; the lowest excited states of argon have α ≈ 300 atomic units.
We studied experimentally and theoretically the evolution of open atomic systems in the constant intensity laser field. The study is performed by analyzing the line shapes of Hanle electromagnetically induced transparency (EIT) obtained in different segments of a laser beam cross section of constant intensity, i.e., a $\ensuremath{\Pi}$-shaped laser beam. Such Hanle EIT resonances were measured using a small movable aperture placed just in front of the photodetector, i.e., after the entire laser beam had passed through the vacuum Rb cell. The laser was locked to the open transition ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=1$ at the D1{D}_{1}D1​ line of 87{}^{87}87Rb with laser intensities between 0.5 and 4 mW/cm2{}^{2}2. This study shows that the profile of the laser beam determines the processes governing the development of atomic states during the interaction. The resonances obtained near the beam center are narrower than those obtained near the beam edge, but the significant changes of the linewidths occur only near the beam edge, i.e., right after the atom enters the beam. The Hanle EIT resonances obtained near the beam center exhibit two pronounced minima next to the central maximum. The theoretical model reveals that the occurrence of these transmission minima is a joint effect of the preparation of atoms into the dark state and the optical pumping into the uncoupled ground level Fg=1{F}_{g}=1Fg​=1. The appearance of the transmission minima, although similar to that observed in the wings of a Gaussian beam [A. J. Krmpot et al., Opt. Express 17, 22491 (2009)], is of an entirely different nature for the $\ensuremath{\Pi}$-shaped laser beam.
The recent development of laser cooling and trapping techniques has made possible the controlled realization of dense and cold atomic samples, thus opening the way for spectroscopic investigations in the low and ultra-low temperature regimes not accessible with conventional techniques. In our lab, an apparatus for laser cooling and Bose-Einstein condensation of rubidium atoms is in operation, producing a sample large enough to perform reliable investigations by absorption or emission techniques. Moving from previous photoionization experiments of laser-cooled atoms in a magneto-optical trap irradiated by cw-laser radiation [1] and stimulated by the interest grown recently on ultra-cold plasma [2], we have started a series of experiments aimed at investigating the interaction of intense laser pulses with the ultra-cold neutral sample, boty aboeand below the condensation temperature. Radiation from an excimer-pumped dye laser was used at a wavelength close to 594 nm, corresponding to the ionization threshold of rubidium for two photon non-resonant absorption from the ground state, with intensities in the tens of MW/cm^2 range and a pulse duration of 16 ns. Preliminary results, attained through the dynamical analysis (atom number, temperature) of the cold atom sample after the arrival of the laser pulse, suggest the occurrence of different processes, initiated by multi-photon ionization, involving collisions between cold electrons and ultra-cold neutrals, recombination at low temperatures and collective processes in the weak and cold plasma. Interpretation of those results demonstrates that this class of experiments, based on a variety of topics typical of atomic, plasma and statistical physics, can open the way for novel and intriguing investigations of laser-matter interaction. Further experimental developments will include duplication of the laser pulse frequency and one photon ionization of ground state rubidium laser-cooled atoms. [1] O. Maragò et al., Phys. Rev. A 57 R4110 (1998); E., Arimondo et al., Appl. Surf. Sci. 154-155 527 (2000); F. Fuso et al., Opt. Commun. 173 223 (2000). [2] T.C. Killian et al., Phys. Rev. Lett. 83 4776 (1999); S. Kulin et al., Phys. Rev. Lett. 85 318 (2000).
We develop a large scale quantum master equation approach to describe dynamical processes of practical open quantum systems driven by both coherent and stochastic interactions by including more than one thousand true states of the systems, motivated by the development of highly bright and fully coherent lasers in the X-ray wavelength regime. The method combines the processes of coherent dynamics induced by the X-ray laser and incoherent relaxations due to spontaneous emissions, Auger decays, and electronic collisions. As examples, theoretical investigation of {\it real} coherent dynamics of inner-shell electrons of a neon gas, irradiated by a high-intensity X-ray laser with a full temporal coherence, is carried out with the approach. In contrast to the rate equation treatment, we find that coherence can suppress the multiphoton absorptions of a neon gas in the ultra-intense X-ray pulse, due to coherence-induced Rabi oscillations and power broadening effects. We study the influence of coherence on ionization processes of neon, and directly prove that sequential single-photon processes for both outer- and inner-shell electrons dominate the ionizations for the recently typical experiments with a laser intensity of ≈1018\approx10^{18}≈1018 W/cm2{\rm W/cm^2}W/cm2. We discuss possible experimental implementations such as signatures for coherent evolution of inner-shell electrons via resonance fluorescence processes. The approach can also be applied to many different practical open quantum systems in atomic, quantum optical, and cold matter systems, which are treated qualitatively by a few-level master equation model before.