Asymmetry in attosecond streaking from a degenerate state

By the numerical solution to the time-dependent Schrödinger equation, we observe a remarkable asymmetry in the photoelectron streaking spectra when the ${\mathrm{He}}^{+}$ ion is ionized by an attosecond pulse from the $2s$ state in the presence of a weak infrared pulse. An analytical theory based on the modified perturbation theory is developed to quantitatively account for the underlying mechanism. We find that a transition occurs between the degenerate $2s$ and $2p$ states under the influence of the infrared electric field before the arrival of the attosecond pulse. The observed asymmetry in the attosecond streaking is formed by the interference of photoelectrons ionized from the $2s$ and $2p$ states. Using the sensitivity of the asymmetry to the infrared (IR) electric field at the moment of attosecond photoionization, we show that the present finding provides a highly reliable way to fully characterize the IR waveform in the streaking experiment.

Figure 1

The photoelectron momentum distribution $D\left(\mathbf{p}\right)$ (left column) and $D\left(p_z\right)$ (right column) from (a), (c) the $1s$ state of H and (b), (d) the $2s$ state of ${\mathrm{He}}^{+}$ from the attosecond streaking depicted in the top panel. In (a) and (b), $I_{\mathrm{IR}}=1\times {10}^{12} \mathrm{W}/\mathrm{cm}{}^2$ and the dashed circle is a reference to the momentum shift. In (c) and (d), by making $|p_z|$ the abscissa, $D\left(p_z\right)$ are shown for both the forward and backward directions at three indicated intensities of $I_{\mathrm{IR}}$.

Figure 2

(a) The streaking spectrum $D\left(p_z\right)$ calculated by the length and the velocity gauge in TDSE with the complete SSVP. The result from the length gauge calculation without (b) the rising part or (c) the falling part of the SSVP. Top: The total $A\left(t\right)$ and $E\left(t\right)$ for each respective case and the field parameters chosen so as to mimic one of the cases for the $2s$ state of ${\mathrm{He}}^{+}$, shown in Fig. 1.

Figure 3

(a) The same streaking spectra as in Fig. 2 calculated by the analytical theory [cf. Eq. (6)], compared with the TDSE result. (b) The asymmetric parameter extracted from the streaking spectrum and analytically calculated by Eq. (9) for the SSVP with various $A_0$. (c) The vector potential of the few-cycle IR pulse used in Fig. 1 is accurately retrieved by using the asymmetric parameter from the streaking spectrum.