Nonsequential Double Ionization at the Single-Optical-Cycle Limit

We report differential measurements of ${\mathrm{A}\mathrm{r}}^{++}$ ion momentum distributions from nonsequential double ionization in phase-stabilized few-cycle laser pulses. The distributions depend strongly on the carrier-envelope (CE) phase. Via control over the CE phase one is able to direct the nonsequential double-ionization dynamics. Data analysis through a classical model calculation reveals that the influence of the optical phase enters via (i) the cycle dependent electric field ionization rate, (ii) the electron recollision time, and (iii) the accessible phase space for inelastic collisions. Our model indicates that the combination of these effects allows a look into single cycle dynamics already for few-cycle pulses.

Figure 1

Schematic view of the experimental setup. W1, W2: two pairs of glass wedges; MCP: position sensitive microchannel plate detector; M: mirror; E: extraction electric field; SAB: supersonic atomic beam.

Figure 2

Experimental momentum distribution of ${\mathrm{A}\mathrm{r}}^{2+}$ ions from NSDI of Ar at different CE phases $\phi$. The laser pulse parameters are $\approx 5\mathrm{f}\mathrm{s}$ pulse width and $\approx 350\mathrm{T}\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$ peak light intensity. The distributions are integrated over the Cartesian momentum components perpendicular to the light beam polarization axis. ${\phi }_0$, shown on the panels, is determined from comparison with a theoretical model to be $0.2\pi$. The spectrum in panel (f) was taken with the phase unstabilized at otherwise unchanged experimental parameters.

Figure 3

Upper panel: electric field $E(t)$ (solid line) and the quasistatic field ionization rate [18] (dashed line) for a four-cycle laser pulse (760 nm center wavelength, ${3.5\times {10}^{14}\mathrm{W}/\mathrm{c}\mathrm{m}}^2$ peak intensity). Lower panel: classically accessible final phase space upon recollision ($p_{1\parallel }=p_{2\parallel }=p_{e,\parallel }$) for electrons liberated at tunneling time $t_0$ (in units of the optical period $T=2.6\mathrm{f}\mathrm{s}$). $\phi$ denotes the corresponding CE phase.

Figure 4

Numerical simulation of the ion momentum distribution induced by few-cycle pulses at different CE phases. A four-cycle laser pulse is used in the calculation for (a)–(e) and an eight-cycle pulse in (f). The other parameters are the same as in Fig. 3.