Determination of the photoemission position in single-photon ionization with attosecond streaking spectroscopy

Attosecond metrology can directly measure attosecond emission time of photoexcited electrons from matter, providing unprecedented understanding of transition processes of electrons from bound to continuum states. However, some fundamental details of the electron dynamics in the entire emission process upon photoexcitation still remain debatable or unknown. The photoemission time delays deduced from attosecond streaking spectroscopy originate from photoelectron propagation in the coupled Coulomb-laser fields, encoding the spatial and spectral information of electrons upon photoexcitation. Here we demonstrate that attosecond photoemission delays can be used to image picometer-resolved photoemission position via a classical model. The electronic dynamics in the laser-assisted single-photon ionization process is fully captured by a quantum path-integral model. We trace the imaged photoemission position to the average position of spatially coherent superposition of electron waves upon photoexcitation and, in particular, predict emission position coinciding with the orbital radius of the ground state of hydrogen-like atoms, in contrast with previous predictions.

Figure 1

(a) The Coulomb potential (blue solid lines) and radial probability density function $W\left(r_0\right)$ (red solid line) of the ground state of a H atom as a function of $r_0$. (b)–(d) Classically calculated normalized streaking traces of electron photoionized from the ground state of H atoms by absorption of one 25 eV photon in the presence of an IR laser pulse at different initial emission positions. The inset provides an enlarged view of the relative temporal shift between normalized streaking trace and the normalized negative IR vector potential $-A_{\text{IR}}\left(\tau \right)$ as a function of the XUV-IR relative delay $\tau$ (red dashed lines).

Figure 2

(a) Quantum-mechanically calculated streaking spectrogram of PEs from the ground state of H atoms. Corresponding centers of energy $E_{\text{COE}}\left(\tau \right)$ are represented by green solid line. (b) Normalized negative IR vector potential $-A_{\text{IR}}\left(\tau \right)$ and normalized $E_{\text{COE}}\left(\tau \right)$ as a function of $\tau$. The inset provides an enlarged view of their relative temporal shift. (c) Streaking spectrogram and centers of energy $E_{\text{COE}}\left(\tau \right)$ simulated by a quantum-path integral model.

Figure 3

(a) Classical model predicts photoemission time delays of electrons from the ground state of H atom as a function of initial emission position at XUV photon energies ranging from 25 to 50 eV (solid curves). Also shown are the corresponding TDSE results (green solid circles). (b) Same as in panel (a) but for ${\mathrm{He}}^{+}$ and different XUV photon energies ranging from 65 to 90 eV. The red dashed lines represent the radially probability density $W\left(r_0\right)$ of the ground states as a function of $r_0$.

Figure 4

. Photoemission time delays of electron from the ground states of (a) H atom and (b) ${\mathrm{He}}^{+}$ ion as a function of XUV photon energy from TDSE (green solid circles), quantum-path integral model (yellow solid squares), our classical model (purple solid line), the eikonal approximation model (black dot-dashed line), and the improved eikonal approximation model (red dashed line). The initial emission position $r_0=1$ for H and 0.5 for ${\mathrm{He}}^{+}$ in the last three models.