Time double-slit interferences in strong-field tunneling ionization

Oscillations in the electron emission spectrum of atoms ionized by few-cycle laser pulses were recently identified as a time double-slit interference [F. Lindner et al., Phys. Rev. Lett. 95, 040401 (2005)]. We extend this analysis to three-dimensional momentum images. We show that different portions of the wave packet released at different times interfere, forming interference fringes in the momentum distributions. The complex interference pattern observable in momentum space maps out information on the scattering potential.

Figure 1

(Color online) (a) Electric field of frequency $\omega =0.05$, duration $\tau =2\pi ∕\omega =126\mathrm{a.u.}$, and amplitude $F_0=0.075\mathrm{a.u.}$ as a function of time (one cycle corresponding to a square envelope function). (b) Momentum for different classical trajectories: electron detached at time $t=-\pi ∕\omega$, $-\pi ∕2\omega$, 0, $\pi ∕2\omega$, and $\pi ∕\omega$, as indicated. The momenta of the trajectories of electrons released at $t=\mp \pi ∕2\omega$ coincide in the time interval $t⩾\pi ∕2\omega$ and give rise to interferences.

Figure 2

(Color online) (a) Ab initio photoelectron spectra for a two-cycle electric field of frequency $\omega =0.05\mathrm{a.u.}$, peak field $F_0=0.075\mathrm{a.u.}$, and duration $\tau =4\pi ∕\omega =251$ (with a ${\cos }^2$ envelope function). Inset: electric field as a function of time. The shaded areas correspond to the two temporal slits. (b) Doubly differential electron momentum distribution in cylindrical coordinates $(k_z,k_{\rho })$ in logarithmic scale for the same laser pulse.

Figure 3

(Color online) Same as Fig. 2 but for a cosine-envelope pulse, all other parameters unchanged.

Figure 4

(Color online) (a) Ab initio photoelectron spectra for the case of the electric field in Fig. 1a: after a half-cycle pulse $(\tau =\pi ∕\omega )$ and one-cycle pulse $(\tau =2\pi ∕\omega )$. (b) Ab initio doubly differential electron momentum distribution after the half-cycle pulse (one slit). (c) Ab initio doubly differential electron momentum distribution after the one-cycle pulse (two slits).

Figure 5

(Color online) (a) Semiclassical photoelectron spectrum corresponding to the field in Fig. 1a. (b) Semiclassical doubly differential electron momentum distribution after the pulse. (c) Schematic diagram of the interference process.

Figure 6

(Color online) (a) Photoelectron spectra by solving the TDSE removing the excited states and by using the semiclassical (sc) model corresponding to the field in Fig. 1a. (b) Longitudinal momentum distributions by the two methods. (c) Close-up of (a) showing the phase shift between two consecutive peaks. (d) Distance between two consecutive peaks of the longitudinal momentum distribution of (c).