Displacement effect in strong-field atomic ionization by an XUV pulse

We study strong-field atomic ionization driven by an XUV pulse with a non\-zero displacement, the quantity defined as the integral of the pulse vector potential taken over the pulse duration. We demonstrate that the use of such pulses may lead to an extreme sensitivity of the ionization process to subtle changes of the parameters of a driving XUV pulse, in particular, the ramp-on/off profile and the carrier envelope phase. We illustrate this sensitivity for atomic hydrogen and lithium driven by few-femto\-second XUV pulses with intensity in the $\rm 10^{14}~W/cm^2$ range. We argue that the observed effect is general and should modify strong-field ionization of any atom, provided the ionization rate is sufficiently high.