Optical control of an atomic inner-shell x-ray laser

X-ray free-electron lasers have had an enormous impact on x-ray science by achieving femtosecond pulses with unprecedented intensities. However, present-day facilities operating by the self-amplified spontaneous emission principle have a number of shortcomings; namely, their radiation has a chaotic pulse profile and short coherence times. We put forward a scheme for a neon-based atomic inner-shell x-ray laser (XRL) which produces temporally and spatially coherent subfemtosecond pulses that are controlled by and synchronized to an optical laser with femtosecond precision. We envision that such an XRL will allow for numerous applications such as nuclear quantum optics and the study of ultrafast quantum dynamics of atoms, molecules, and condensed matter.

Figure 1

Schematic of x-ray lasing in core-excited neon with pumping by an x-ray FEL. (a) Neon atoms are excited by x rays from a FEL from the ground state to the $1s^{-1}2p3p$ core-excited state. (b) X-ray lasing occurs on the $1s^{-1}2p3p\to 1s2p^{-1}3p$ transition. Furthermore, ${\Gamma }_{\mathrm{U}}$ and ${\Gamma }_{\mathrm{L}}$ are the decay widths of the upper and lower lasing states, respectively.

Figure 2

X-ray absorption cross section by core electrons of neon near the $K$ edge for the field-free case (top) and for optical laser dressing at ${10}^{13}$ W/cm${}^2$ (bottom) with an 800 nm laser. The x rays and the optical light are linearly polarized and have parallel polarization vectors. The dashed green line indicates the central FEL photon energy at ${\omega }_{\mathrm{P}}=868.2$ eV. Adapted from Ref. [22].

Figure 3

(a) The dashed black line is the amplitude of a single SASE FEL x-ray pulse. The dashed red, blue, and green lines are five-optical-cycle (13 fs) FWHM duration pulses of the optical dressing laser at three different positions with respect to the FEL x-ray pulse. The solid black line is the average over 500 SASE FEL pulses. We assume $3\times {10}^{13}$ x rays in, on average, 21.5 fs FWHM long pulses, focused to a 10 $\mu$m spot at a bandwidth of 0.4 eV. (b) The solid black line shows the single-shot SSG in the field-free case if the XRL is pumped with the dashed black SASE FEL pulse from (a) which has a FWHM duration of 7.3 fs; the solid red, blue, and green lines show the single-shot SSG for laser dressing with the optical laser pulse of matching color from (a). The average of the SSG over 500 SASE FEL pulses for the field-free case is given by the dashed black line and for optical laser dressing by the dashed red, blue, and green lines.

Figure 4

Dependence of the XRL output intensity on the interaction length (or propagation distance) in a macroscopic medium. The XRL is pumped by the dashed black FEL pulse displayed in Fig. 3, which leads to the XRL output intensity that is given by the solid black line. The XRL output intensities with dressing by the optical laser pulses from Fig. 3 are shown as dashed lines of the same color here.

Figure 5

The temporal profile of the XRL pulses after saturation. The XRL is pumped with the dashed black FEL pulse from Fig. 3. The solid black line corresponds to the FEL-x-ray-only case and the dot-dashed green line displays the optical laser-dressed case by the dashed red optical laser pulse from Fig. 3, which is shown here as well.