Coulomb focusing in attosecond angular streaking

Light-induced ultrafast electron dynamics significantly impacts the fundamental processes in nature, such as molecular bond breaking and formation, chemical reactions, and biological metabolism. Observing and controlling these electron dynamics are crucial for understanding the essence and the development rule of the microscopic world. Attosecond optical metrology techniques, including attosecond streaking, attosecond photoelectron interferometry, and attosecond angular streaking, enable probing of electron dynamics on the atomic temporal and spatial scales. These techniques provide potential pathways for achieving quantum control in attosecond chemistry and for processing petahertz ultrafast photoelectric signals. The principle of attosecond angular streaking is to map the delay time of electron tunneling to the deflection angle corresponding to the maximum photoelectron yield through ionization in elliptically polarized laser fields, allowing for measurements with attosecond precision. One of the key assumptions in attosecond angular streaking is the one-to-one correspondence between the electron deflection angle and the tunneling ionization instant, though the universality of this assumption remains to be validated.

 

In a new paper published in Light: Science & Applications, a team of researchers, from Jilin University and Hainan University, China, has reported that in a combined study by energy-resolved angular streaking measurements and improved Coulomb-corrected strong-field approximation (ICCSFA) method including the under-barrier Coulombic interaction, the measured photoelectron angular offsets are determined jointly by  Coulomb interaction in quantum tunneling and the Coulomb focusing effect in classical continuum states. Through a comparison between the calculation  and experimental observations, they found that, under the influence of the joint Coulomb interactions, the most probable emission angle in attosecond angular streaking measurements arises from the coherent superposition of electrons with different initial ionization instants, rather than from the single ionization event corresponding to the maximum amplitude of the laser electric field, as commonly assumed in attosecond angular streaking measurements. The simulation methods base on Feynman path integrals and semiclassical statistical analysis of electron trajectories to trace the initial spatiotemporal distribution of tunneling electrons. The results indicate that the strong-field approximation model, which neglects Coulomb interactions, agrees with the single classical trajectory approximation simulations, showing a one-to-one correspondence between the highest-yield electrons and the peak of the electric field. However, the simulated results deviate significantly from the experimental results. Only by considering the Coulomb interaction in both quantum tunneling and continuum propagation (ICCSFA method) can the energy-dependent electron deflection angles be consistent with the experimental findings, and the highest-yield electrons were found originating from tunneling ionization within a few tens of attoseconds. The coherent superposition of electrons ionized at different initial times determines the final electron deflection angle. Additionally, statistical analysis of electron trajectory shows that Coulomb focusing alters the counts distribution of trajectories for electrons of different energies. The sub-barrier Coulomb attraction in nonadiabatic tunneling further enhances this effect, revealing the physical mechanism behind the counterintuitive energy dependence observed in angular streaking experiments.

 

This work indicates that attosecond angular streaking measurements are closely related to the statistical distribution of momentum/energy of electron wave packets generated by quantum tunneling. The Coulomb focusing effect disrupts the one-to-one correspondence between the emission angle of the highest-yield electrons and the tunneling ionization time. This research provides a crucial avenue for the intuitive interpretation of attosecond angular streaking experiments and offers new tools for decoding the sub-barrier tunneling dynamics in the classically forbidden region.

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