Momentum mapping of continuum-electron wave-packet interference

We analyze the two-dimensional photoelectron momentum distribution of an Ar atom ionized by midinfrared laser pulses and mainly concentrate on the energy range below $2U_p$. By using a generalized quantum trajectory Monte Carlo simulation and comparing with the numerical solution of the time-dependent Schrödinger equation, we demonstrate that a profound ringlike pattern coming from the interplay between the intra- and the intercycle interferences of electron trajectories can be observed in the deep tunneling ionization regime. Moreover, we found that the rescattered electrons play a negligible role on the formation of a ringlike interference pattern, and the appearance of the ringlike interference pattern masks the holographic interference structure. Our results provide an appropriate experimental condition for the observation of the photoelectron holography and help to gain physical insight into the corresponding ultrafast electron dynamic process with attosecond temporal resolution.

Figure 1

Simulated two-dimensional (2D) photoelectron momentum spectra of an Ar atom. Upper panel: $\gamma =0.48$, lower panel: $\gamma =1.12$. (a) and (b) $I=2.13\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2,\lambda =1300\mathrm{nm}$, (c) and (d) $4.44\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2,\lambda =900\mathrm{nm}$, (e) and (f) $I=0.4\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2,\lambda =1300\mathrm{nm}$, and (g) and (h) $0.835\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2,\lambda =900\mathrm{nm}$.

Figure 2

Upper panel (a): Subcycle time windows from which photoelectrons are emitted. Lower panel: (b) the typical trajectory R, (c) the typical trajectory ID, and (d) the typical trajectory D.

Figure 3

Reconstructed photoelectron momentum spectra with EWPs from different time windows: (a) and (d) with EWPs from time windows A and B; (b) and (e) from time windows A and C; (c) and (f) from time windows A–C. (a)–(c) $\gamma =0.48$. (d)–(f) $\gamma =1.12$.

Figure 4

The same as with Fig. 3 but without considering the Coulomb potential.

Figure 5

(a) and (e) present zooms into Figs. 3 and 3 with three sampling points indicated. (b)–(d) and (f)–(h) show the probabilities of the summed trajectories ${\mathrm{\Psi }}_{\mathbf{p}}$ on the complex plane.

Figure 6

The same as with Fig. 5 but for three sampling points in Figs. 3 and 3.

Figure 7

(a) The temporal double-slit interference patten, (b) ATI rings, (c) the total momentum distribution reconstructed with EWPs from three time windows A–C. The red lines indicate the momentum spectrum for $p_r=0\mathrm{a}.\mathrm{u}.$

Figure 8

TDSE simulation in the deep tunneling regime: $\gamma =0.28,I=2.76\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2,\lambda =2000\mathrm{nm}$.