  We investigate laser-induced nonsequential double ionization by a
polarization-gated laser pulse, constructed employing two counter-rotating
circularly polarized few cycle pulses with a time delay $T_{d}$. We address the
problem within a classical framework, and mimic the behavior of the
quantum-mechanical electronic wave packet by means of an ensemble of classical
electron trajectories. These trajectories are initially weighted with the
quasi-static tunneling rate, and with suitably chosen distributions for the
momentum components parallel and perpendicular to the laser-field polarization,
in the temporal region for which it is nearly linearly polarized. We show that,
if the time delay $T_{d}$ is of the order of the pulse length, the
electron-momentum distributions, as functions of the parallel momentum
components, are highly asymmetric and dependent on the carrier-envelope (CE)
phase. As this delay is decreased, this asymmetry gradually vanishes. We
explain this behavior in terms of the available phase space, the quasi-static
tunneling rate and the recollision rate for the first electron, for different
sets of trajectories. Our results show that polarization-gating technique may
provide an efficient way to study the NSDI dynamics in the single-cycle limit,
without employing few-cycle pulses.
