Holographic Angular Streaking of Electrons and the Wigner-Time Delay

Abstract

For a circularly polarized single-color field at a central frequency of $2\omega$ the final electron momentum distribution upon strong field ionization does not carry any information about the phase of the initial momentum distribution. Adding a weak, co-rotating, circularly polarized field at a central frequency of $\omega$ gives rise to a sub-cycle interference pattern (holographic angular streaking of electrons (HASE)). This interference pattern allows for the retrieval of the derivative of the phase of the initial momentum distribution after tunneling $\phi^{\prime}_{\mathrm{off}}(p_i)$. A trajectory-based semi-classical model (HASE model) is introduced which links the experimentally accessible quantities to $\phi^{\prime}_{\mathrm{off}}(p_i)$. It is shown that a change in $\phi^{\prime}_{\mathrm{off}}$ is equivalent to a displacement in position space $\Delta x$ of the initial wave packet after tunneling. This offset in position space allows for an intuitive interpretation of the Wigner time delay $\Delta \tau_W$ in strong field ionization for circularly polarized single-color fields. The influence of Coulomb interaction after tunneling is investigated quantitatively.