Remote control of the dissociative ionization of ${\mathrm{H}}_2$ based on electron-${{\mathrm{H}}_2}^{+}$ entanglement

The single ionization of ${\mathrm{H}}_2$ in strong laser fields creates the correlated electron-${{\mathrm{H}}_2}^{+}$ pair. Based on such a correlation, we conceive a strategy to control the energy spectra of the freed electron or dissociative fragments by simulating the time-dependent Schrödinger equation. Two attosecond pulses in a train produce the replica of electron-${{\mathrm{H}}_2}^{+}$ pairs, which are to be steered by a time-delayed phase-stabilized (mid)infrared laser pulse. By controlling the behavior of the freed electron, the dissociation of ${{\mathrm{H}}_2}^{+}$ can be controlled even though there is no direct laser-${{\mathrm{H}}_2}^{+}$ coupling. On the other hand, the photoelectron energy spectra can be manipulated via laser-${{\mathrm{H}}_2}^{+}$ coupling. This study demonstrates the entanglement of molecular quantum wave packets, and affords a route to remotely control molecular dissociative ionization.

Figure 1

The sketch of remote control. Two attosecond XUV pulses in a train create the entangled free electron and ${{\mathrm{H}}_2}^{+}$ in the $2p{\sigma }_u$ state, and a time-delayed (mid)infrared laser pulse is adopted to steer either the free electron or ${{\mathrm{H}}_2}^{+}$. By manipulating the interference of the photoelectron, the dissociation of ${{\mathrm{H}}_2}^{+}$ can be remotely controlled, and vice versa.

Figure 2

The values of soft core parameters $\alpha \left(R\right)$ and $\beta \left(R\right)$ as a function of the internuclear distance $R$.

Figure 3

[(a)–(e)] Electron-nuclear JES obtained in the laser conditions of only one attosecond pulse, two attosecond pulses, and two attosecond pulses plus a MIR at the time delay 0, $T/8$, $T/4$, respectively. [(f)–(j)] The photoelectron spectra obtained by integrating the JES over $E_N$ in panels (a)–(e), respectively. Also shown is the corresponding laser field [(f)–(j)]. (k) Nuclear energy spectra obtained by integrating the JES in panels (b)–(d) over $E_e$. The two dashed lines in panel (e) indicate the analytical slopes for the two stripes. The attosecond pulse has the photon energy 1.6 a.u., and the MIR laser pulse has the intensity ${10}^{12}\mathrm{W}/{\mathrm{cm}}^2$ and wavelength 1600 nm.

Figure 4

Nuclear energy spectra obtained by integrating the JES in Figs. 3–3 over $E_e$ in the range of $11–11.5\mathrm{eV}$.

Figure 5

The snapshots of wave-packet distribution in $x_2\text{−}R$ space for cases without (a) and with (b) the IR field. [(c, d)] The electron-nuclear JES corresponding to panels (a) and (b), respectively. The IR laser pulse has the intensity $5\times {10}^{12}\mathrm{W}/{\mathrm{cm}}^2$ and wavelength 800 nm.

Figure 6

The photoelectron energy spectra obtained by integrating the JES over $E_N$ in the ranges of $16–17\mathrm{eV}$ in Figs. 5 and 5. The two curves are for the cases of without and with the IR pulse in the interaction.