Ramsey method for Auger-electron interference induced by an attosecond twin pulse

We examine the archetype of an interference experiment for Auger electrons: two electron wave packets are launched by inner-shell ionizing a krypton atom using two attosecond light pulses with a variable time delay. This setting is an attosecond realization of the Ramsey method of separated oscillatory fields. Interference of the two ejected Auger-electron wave packets is predicted, indicating that the coherence between the two pulses is passed to the Auger electrons. For the detection of the interference pattern an accurate coincidence measurement of photo- and Auger electrons is necessary. The method allows one to control inner-shell electron dynamics on an attosecond timescale and represents a sensitive indicator for decoherence.

Figure 1

The XUV intensity $I_{\mathrm{X}}\left(t\right)$ (dashed, red) and krypton $3d$ hole population $\varrho \left(t\right)$ (solid, black) [Eq. (1)] for two attosecond pulses $({\tau }_{\mathrm{X}}=500\mathrm{as})$ separated by a variable delay of $\tau$.

Figure 2

Probability density $|{\overline{c}}_{\mathrm{A}}^{{\vec{k}}_{\mathrm{P}}{\vec{k}}_{\mathrm{A}}}{\left(\tau \right)|}^2$ [Eq. (2)] to find a photoelectron with $k_{\mathrm{P}}$ and an Auger electron with $k_{\mathrm{A}}$. We average the photoelectron over the full solid angle and view the Auger electrons along the $z$ axis (linear XUV polarization axis). The left panel is for a delay of $\tau =0$ and the right panel is for $\tau =5{\tau }_{3d}$. The color scale is linear.

Figure 3

Auger-electron spectrum viewed along the $z$ axis for an attosecond twin pulse with a separation of $\tau =5{\tau }_{3d}$. The interference fringes are diminished for a decreasing accuracy of the photoelectron measurement; the energy uncertainties are $\pm 0.04\mathrm{eV}$ (solid, black), $\pm 0.1\mathrm{eV}$ (dashed, red), and $\pm 0.4\mathrm{eV}$ (dotted, green).

Figure 4

Interference of the Auger-electron waves (dotted, green) from an attosecond twin pulse for a precisely known photoelectron momentum $k_{\mathrm{P}}^2/2={\Omega }_{\mathrm{P}}$. The interference pattern is decomposed into the scaled lineshape function (solid, black) and the scaled XUV spectral envelope square (dashed, red).

Figure 5

Interference of the Auger-electron waves for different time delays $\tau$ between the two attosecond pulses in Fig. 1: $\tau =0$ (solid, black), $\tau =3{\tau }_{3d}$ (dashed, red), and $\tau =5{\tau }_{3d}$ (dotted, green) for a photoelectron momentum which is known with an uncertainty of ${\left(\Delta k\right)}^2/2={10}^{-5}\mathrm{eV}$.