Coherent control of atomic inner-shell x-ray lasing via perturbed valence-shell transitions

Atomic inner-shell x-ray lasers pumped by an x-ray free-electron laser generate ultrashort, intense, monochromatic pulses with temporal coherence. Coherent control of lasing in monovalent magnesium ions is investigated theoretically, where valence-shell transitions are driven by optical lasers. Modulated high-order sidebands and attosecond pulses are generated with quasi-continuous-wave and few-cycle control lasers, respectively. The general manipulation scheme involves fast Auger decay, limited pump coherence, diverse coupling channels, and collisions in the plasma. Our approach shows potential applications in high-resolution spectroscopy, nonlinear x-ray studies, metrology, and ultrafast science in keV regime.

Figure 1

Schematic of the control scheme for atomic inner-shell x-ray lasing with Na-like Mg ions. The fine-structure states are uniformly illustrated by $\left[\mathrm{Ne}\right]3p$, $1s3p$ and $2p^{5}3p$. Notice that two control schemes are presented by the quasi-CW and few-cycle laser, marked as (1) and (2). The legend shows all transitions channels involved in the model.

Figure 2

(a), (b) Temporal pulse envelope and energy spectra of a modulated x-ray laser (XRL) dressed by a quasi-continuous-wave control laser with ${\omega }_{\text{c}}$=0.7 eV and $I_{\text{c}}=5\times {10}^{13}$ $\mathrm{W}/{\mathrm{cm}}^2$. and (c) and (d) are, respectively, the temporal and energy structures of x-ray lasing pulses using XFEL pump pulses in the SASE mode, with an average spike ${\tau }_s=0.26$ fs. The blue (dark gray) and green (light gray) lines, respectively, denote two lasing pulses in the example of specific incoming SASE pulses. The black lines show the ensemble of pulses after a 100-simulation average.

Figure 3

(a) Energy spectra of modulated x-ray lasers pumped by coherent Gaussian x-ray pulses using the quasi-continuous-wave control laser with ${\omega }_{\text{c}}$=0.7 eV and $I_{\text{c}}=5\times {10}^{13}$ $\mathrm{W}/{\mathrm{cm}}^2$ during the propagation. (b) Integrated photon number as a function of propagation distance (mm). Here the photon numbers in the three regions defined by the white lines in (a) are plotted.

Figure 4

Dependence of energy spectra and integrated photon numbers for the x-ray lasing transition on the intensities of the pump pulse (a), (b), duration, (c), (d) and the quasi-continuous-wave control laser (e),(f). Other parameters are fixed to the corresponding values in Fig. 2. A Gaussian-type pump laser is used in all calculations.

Figure 5

Isolated attosecond x-ray pulse controlled by a few-cycle pulse with duration ${\tau }_{\text{c}}=5$ fs and intensity $I_{\text{c}}=1\times {10}^{14}$ $\mathrm{W}/{\mathrm{cm}}^2$. (a) Energy spectra of the lasing transition irradiated by a control laser with carrier-envelope phase (CEP) = 0 and Gaussian-type pump pulses, and two cases of self-amplified spontaneous emission (SASE) spikes with width ${\tau }_s$= 0.26. (b) and (c)Temporal pulses and corresponding temporal phase extracted from the region $\mathrm{\Delta }\omega /\omega =-60$ to $-18.6$ (light-green region in (a) of transmission window of Tb metal). (d)–(i) Attosecond pulse extracted from irradiation of the Gaussian pump pulse and the control laser for various CEPs. Other parameters are consistent with Fig. 1.