Figure 1

Intercycle (gray circles and dashed arrows) and subcycle (blue dots and full arrows) interferences of electron wave packets created and driven by sculpted $\omega \mathrm{\text{−}}2\omega$ laser pulses for relative two-color phases $\phi =0$ (a) and $\phi =\pi /2$ (b).Reuse & Permissions

Figure 2

(a)–(c) Measured two-dimensional interferograms extracted from electron momentum spectra for the single ionization of helium atoms by subtracting an overall Gaussian shape for various relative phases $\phi$ of the two-color laser field polarized along $p_z$. The gray bars blank out regions where our detector has no resolution for electrons. (d)–(f) Solutions of the TDSE for a single-cycle pulse for the same values of $\phi$ as in (a)–(c). In the lower halves of (d) and (f) we also show the TDSE results for a multicycle pulse for which also intercycle fringes appear. The white dashed lines and arrows in (a) and (c) indicate the integration range used for the correlated ion spectra in Fig. 3a, 3b.Reuse & Permissions

Figure 3

Control of subcycle interference patterns with a sculpted laser field. (a) Measured ion momentum spectra of ${\mathrm{He}}^{+}$ along the laser polarization direction for $\phi =0$ (blue full arrow) and $\pi$ (red dashed arrow). The thin vertical lines mark the position of the intercycle peaks. (b) Same as (a) but for $\phi =\pi /2$. The shaded dots mark the subcycle interference patterns. (c) Intercycle and subcycle interference fringes extracted from the measured ion momentum spectra as a function of the longitudinal momentum $p_z$ and the relative phase $\phi$. (d) Same as (c) but calculated using the TDSE. The upper half of the diagram ($p_z>0$) shows the simulated spectrum for a single-cycle pulse, the lower half ($p_z<0$) for a multicycle pulse. (e) Comparison of normalized spectra for $\phi =\pi /2$, calculated using the TDSE for a multicycle pulse (gray thin full line) and single-cycle pulse (red thick dashed line) with the measured spectrum (blue thick full line), obtained from (b) by subtracting a Gaussian fit with its amplitude multiplied by 0.6.Reuse & Permissions

Figure 4

(a) Phase of the bound-state wave function of helium as a function of the subcycle time difference $\Delta t$ between the emission bursts extracted from the interferometrically measured phase difference (red open squares) in comparison with the TDSE interferogram (green full lines). Error bars in time reflect the experimental momentum uncertainty $\Delta p\lesssim 0.05\mathrm{a}.\mathrm{u}.$. Inset upper left: Dependence of $\Delta \alpha$ on $p_z$. Also shown is the phase of the wave function near the tunnel exit obtained from the TDSE (blue dashed-dotted line), Eq. (5), and the unperturbed phase evolution in the ground state (dotted black line), and the first excited state (dashed gray line) with binding energies ${\epsilon }_g$ and ${\epsilon }_e$, respectively. (b) Same as (a) but for neon ($\Delta p\lesssim 0.08\mathrm{a}.\mathrm{u}.$). The shaded area shows the $\pi$ phase shift due to the odd parity of the neon ground state that is not present for the even parity of the helium ground state (see insets lower right).Reuse & Permissions