Nondipole Time Delay and Double-Slit Interference in Tunneling Ionization

Recently two-center interference in single-photon molecular ionization was employed to observe a zeptosecond time delay due to the photon propagation of the internuclear distance in a molecule [Grundmann et al., Science 370, 339 (2020)]. We investigate the possibility of a comparable nondipole time delay in tunneling ionization and decode the emerged time delay signal. With the here newly developed Coulomb-corrected nondipole molecular strong-field approximation, we derive and analyze the photoelectron momentum distribution, the signature of nondipole effects, and the role of the degeneracy of the molecular orbitals. We show that the ejected electron momentum shifts and interference fringes efficiently imprint both the molecule structure and laser parameters. The corresponding nondipole time delay value significantly deviates from that in single-photon ionization. In particular, when the two-center interference in the molecule is destructive, the time delay is independent of the bond length. We also identify the double-slit interference in tunneling ionization of atoms with nonzero angular momentum via a nondipole momentum shift.

Figure 1

Tunneling exit distribution when the molecular axis angle is ${\theta }_m=\pi /4$: (a) for ${\mathrm{H}}_2^{+}$ with nondegenerate molecular orbitals $({\sigma }_{g}1s)$, where the vertical lines mark the position $z_e=\pm R_z/2$; (b) ${\mathrm{Ne}}_2$ with degenerate molecular orbitals $({\sigma }_{g}2p)$; in (a),(b) the ionization phase is $\mathrm{\Phi }=0$ (black solid), $\mathrm{\Phi }=\pi /2$ (blue dashed), and $\mathrm{\Phi }=\pi$ (red dotted-dashed); (c) PMD of ${\mathrm{Ne}}_2$ $({\sigma }_{g}2p)$ in the polarization plane. The dark fringe (d) has double peaks, while the bright fringe (e) has a single peak in the longitudinal PMD. The probability of the dark fringe is 10 times smaller than the bright one. The laser vector potential is $\mathbf{A}(\eta )=-A_0(\sin \mathrm{\Phi },\cos \mathrm{\Phi },0)$ with wavelength 3000 nm and intensity $I=4\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$; $\mathbf{R}=R(\sin {\theta }_m,0,\cos {\theta }_m)$.

Figure 2

The tunneling exit and longitudinal momentum distributions for ${\mathrm{He}}_2$ with degenerate molecular orbitals, with the molecular axis angle ${\theta }_m=0$: (a)–(c) Exit distribution; (d)–(f) Longitudinal PMD; (a,d) for the electronic state ${\sigma }_g$ $1s$ with $R=5$ a.u.; (b),(e) for the state ${\sigma }_u$ 1s with $R=5$ a.u. (black); for the atom with $(l=1,m=0)$ (red); (c),(f) for ${\sigma }_g$ $1s$ (black), and ${\sigma }_u$ $1s$ (blue), with $R=100$ a.u. Laser parameters are the same as in Fig. 1. The inset is the enlargement around $p_{-}=I_p/c$. The nondipole shift of the dark fringe in PMD is $I_p/c$.

Figure 3

Nondipole momentum shift $\delta ⟨p_{-}⟩$ (black solid lines) due to the molecular contribution and the ionization yield (blue dashed lines) vs molecular axis angle ${\theta }_m$: (a),(b) Ionization from ${\sigma }_g$ $1s$; (c),(d) Ionization from ${\sigma }_u$ 1s; (a),(c) Ionization of ${\mathrm{H}}_2^{+}$; (b),(d) Ionization of ${\mathrm{He}}_2$; Laser parameters are the same as in Fig. 1; $\mathbf{R}=R(\sin {\theta }_m,0,\cos {\theta }_m)$, $R=5$ a.u.