Use of Electron Correlation to Make Attosecond Measurements without Attosecond Pulses

We describe how correlations between electrons can be used to trace the dynamics of correlated two-electron ionization with attosecond precision, without using attosecond pulses. The approach is illustrated using the example of Auger or Coster-Kronig decay triggered by photoionization with an extreme ultraviolet pulse. It requires correlated measurements of angle-resolved energy spectra of both the photo- and Auger electrons in the presence of a laser pulse. To reconstruct the dynamics, we use not only classical time and energy correlation, but also entanglement between the two electrons.

Figure 1

(a) Energy diagram of the Auger process: absorption of XUV photon $\Omega$ creates a free photoelectron $k_X$ and a hole state $E_h$ which autoionizes to create the second free electron $k_A$. (b) Linear contour plot of the field-free correlated two-electron spectrum. Energy is measured in units of laser frequency $\omega$; $E_X^0$, $E_A^0$ are the central energies of the photoelectron and the Auger spectra.

Figure 2

(a) Correlated two-electron spectrum $|C(k_x,k_A){|}^2$ in the presence of the laser field. $E_X^0$, $E_A^0$ are the central energies of the field-free photoelectron spectrum and the Auger line. (b) Slice for fixed energy of the photoelectron.

Figure 3

(a)  Model of the decay via an intermediate state $|2⟩$. (b) Exact (solid line) and reconstructed decay for $N={10}^5$ counts (circles), $N={10}^6$ counts (empty circles), and 100 asec pump-probe jitter.

Figure 4

Correlated spectra (a),(b) and reconstructed Auger lines in the frequency domain (c),(d) for $N={10}^5$ and $N={10}^6$ counts and 100 asec jitter. In (a),(b) shades of gray (color) code spectral intensity on a linear scale, with lighter color coding showing the higher signal (except for the high central spot). In panels (c),(d) the exact spectral phase is shown with a smooth solid line.