Quantum entanglement during single-cycle nonsequential ionization

In order to elucidate the correlated motion of atomic electrons, we investigate the attosecond-scale dynamics of their entanglement arising due to nonsequential ionization driven by a strong, linearly-polarized laser field. The calculation is based on numerical integration of the time-dependent Schr\"{o}dinger equation for helium irradiated by a one-cycle, near-infrared field whose intensity is in the neighborhood of $1\textrm{ PW/cm}^2$. The entanglement measure (Schmidt weight) is resolved on a sub-cycle timescale, and its key dependency on the field profile is exposed for the first time by tuning the carrier-envelope phase (CEP) to control the ionization-recollision timing. We find that between CEP cases, this can result in a $20\%$ enhancement in the peak entanglement. A connection is made between the entanglement, the probability current, and the correlation coefficient for the two electron momenta, providing new insights into the nonsequential ionization mechanism.