Carrier-envelope-phase-induced asymmetries in double ionization of helium by an intense few-cycle XUV pulse

The carrier-envelope-phase (CEP) dependence of electron angular distributions in double ionization of He by an arbitrarily polarized, few-cycle, intense XUV pulse is formulated using perturbation theory (PT) in the pulse amplitude. Owing to the broad pulse bandwidth, interference of first- and second-order PT amplitudes produces asymmetric angular distributions sensitive to the CEP. The PT parametrization is shown to be valid by comparing with results of solutions of the full-dimensional, two-electron time-dependent Schrödinger equation for the case of linear polarization.

Figure 1

The TDP $d^{3}W/dEd{\Omega }_{{\widehat{\mathbf{p}}}_1}d{\Omega }_{{\widehat{\mathbf{p}}}_2}$ (in units of ${10}^{-7}$ a.u.) for DPI of He by a three-cycle attosecond pulse having a peak pulse intensity $I=2$ PW/cm${}^2$, a CEP $\varphi =\pi /2$, and carrier frequency $\omega =85$ eV for (a) EES and (b) UES. The electron energies $E_1$ and $E_2$ are specified in each panel. Solid (blue) curve, ${\theta }_1=0$ [solid (blue) arrow], $0\le {\theta }_2\le \pi$; dashed (red) curve, ${\theta }_1=\pi$ [dashed (red) arrow], $0\le {\theta }_2\le \pi$.

Figure 2

As Fig. 1 but in units of ${10}^{-5}$ a.u. for a carrier frequency $\omega =65$ eV for (a) EES and (b) UES.

Figure 3

Asymmetry $\Delta \mathcal{W}$ for DPI of He by a three-cycle pulse with peak intensity 2 PW/cm${}^2$ and CEP $\varphi$=$\pi /2$ for two carrier frequencies $\omega$. Both EES (a) and UES (b) cases are shown. Results for $\omega =85$ eV are increased by factors of 71 and 54 in (a) and (b), respectively.

Figure 4

The TDP $d^{3}W/dEd{\Omega }_{{\widehat{\mathbf{p}}}_1}d{\Omega }_{{\widehat{\mathbf{p}}}_2}$ (in units of ${10}^{-5}$ a.u.) for DPI of He by a three-cycle XUV pulse with carrier frequency $\omega =65$ eV and peak pulse intensity of $I=2$ PW/cm${}^2$ for three CEPs: (a) $\varphi =0$, (b) $\varphi =\pi /3$, and (c) $\varphi =2\pi /3$. In (d) we give for comparison the TDP obtained by including only the first-order PT amplitude. All results are for the EES case with $E_1=E_2=4$ eV and the color coding is the same as in Fig. 1.

Figure 5

As in Fig. 4 but for the UES case with $E_1=0.7$ eV and $E_2=3.3$ eV.

Figure 6

CEP dependence of the asymmetry $\Delta \mathcal{W}$ for DPI of He by a three-cycle pulse with $\omega =65$ eV, and $I=2$ PW/cm${}^2$. Three geometries with $E=4$ eV are shown, including both EES and UES cases, as specified in the figure legend. The symbols give our TDSE results. The lines are fits of the TDSE results to the PT parametrization (9).

Figure 7

CEP dependence of the DPI TDP for an orthogonal, back-to-back geometry (${\theta }_1=\pi /2$, ${\theta }_2=3\pi /2$) for two UES cases (indicated in each panel) and two carrier frequencies: (a) $\omega =85$ eV and (b) $\omega =65$ eV. The three-cycle XUV pulse has a peak intensity of $2\times {10}^{15}$ W/cm${}^2$. The red filled circles are the TDSE results and the blue lines are fits of the TDSE results to the PT parametrization in Eq. (10).