Spatiotemporal imaging of valence electron motion

Abstract

Electron motion on the (sub-)femtosecond time scale constitutes the fastest response in many natural phenomena such as light-induced phase transitions and chemical reactions. Whereas static electron densities in single molecules can be imaged in real space using scanning tunnelling and atomic force microscopy, probing real-time electron motion inside molecules requires ultrafast laser pulses. Here, we demonstrate an all-optical approach to imaging an ultrafast valence electron wave packet in real time with a time-resolution of a few femtoseconds. We employ a pump-probe-deflect scheme that allows us to prepare an ultrafast wave packet via strong-field ionization and directly image the resulting charge oscillations in the residual ion. This approach extends and overcomes limitations in laser-induced orbital imaging and may enable the real-time imaging of electron dynamics following photoionization such as charge migration and charge transfer processes.

Fig. 1

Schematic of the time-resolved orbital imaging experiment. a A coherent electron wave packet is prepared in Ar⁺ via strong-field ionization by a few-cycle pump pulse. As the wave packet evolves, a hole (vacancy) oscillates between the m = 0 and |m| = 1 states of the valence shell of the Ar⁺ ion with the spin orbit period T_SO = 23.3 fs. The electron density in Ar⁺ is probed after a variable time delay using a few-cycle probe pulse in the presence of a phase-stable, mid-infrared deflection field. The deflection field makes the centered momentum distributions produced by the pump pulse alone (b) distinguishable from the off-center distribution produced by the probe pulse (c). Panel c was generated by simulating the effect of the deflection field on the data presented in b. In the total electron distribution shown in d, the signal with p_x < −0.5 a.u. is dominated by electrons from the probe pulse, as indicated by the red oval. The colorscale indicates the electron yield. Each panel is normalized to its maximum. Source data are provided as a Source Data file

Fig. 2

Snapshots of a spin–orbit wave packet in the argon cation. a Measured Ar⁺ yield as a function of time delay between pump and probe pulses. The cartoons illustrate the electron configuration in Ar⁺ at the time of interaction with the probe pulse. For the positions marked with dotted lines and fractions of the spin–orbit period, T_SO, we present measured electron density plots in momentum space (b) and real space (c). The momentum space images show the positive part of the normalized differences of delay-dependent and delay-averaged electron momentum distributions. The data has been integrated over p_z and a delay range of ±3 fs. A low pass frequency filter has been applied. The real space images show the Fourier transform of the momentum space images. The theory plots show the normalized differences between calculated Ar⁺ momentum space orbitals corresponding to m = 0 and |m| = 1 vacancies, and their Fourier transforms, respectively. Source data are provided as a Source Data file

Fig. 3

Streaking ionization of an electron wave packet in Ar⁺. a Momentum distributions in the p_y/p_z plane for ionization from a coherent wave packet in Ar⁺. The left (right) half corresponds to delay values with a maximum (minimum) in the Ar²⁺ yield. Each spectrum is normalized to the same number of counts. The normalized difference between the left and right side is displayed in b. The dotted box indicates the momentum range for which the normalized difference is plotted along p_z in c. The experimental data are compared to the calculated difference in the instantaneous ionization probabilities for the m = 1 and |m| = 0 vacancies. Error bars are s.d. Source data are provided as a Source Data file

Fig. 4

Imaging time-dependent valence electron densities. a Normalized differences between the momentum distributions recorded for ionization of Ar⁺ at delays corresponding to yield maxima and yield minima. The data in each plane is integrated over the third dimension. Low-pass frequency filtering has been applied to the experimental data. b Results of an analytical imaging model. The color bar applies to both, experimental and theoretical results. c Modulus square of the Ar⁺ 3p orbital wave functions used in the simulation. Blue and red colors are chosen for presentational purposes. d Cut through the center of the measured and calculated 3D normalized differences along p_y. The experimental signal is multiplied by a factor of 2 to facilitate direct comparison of the measured and calculated widths of the signals. Source data are provided as a Source Data file