Lewenstein and Colleagues Presents Two-Electron Model for keV High-Harmonic Generation

Isobel McSweeney and colleagues from ICFO, Guangdong Technion, Israel Institute of Technology, fUniversity College London, 6Foundation for Research and Technology-Hellas, Technische Universität Wien, Institute of Electronic Structure & Laser, Center for Quantum Science and Technologies, have investigated how accounting for the behaviour of multiple electrons expands the range of high-harmonic generation into the kiloelectronvolt regime. The refined theoretical model demonstrates that incorporating two-electron processes extends harmonic cutoffs to 4.7 and 5.5 times the ponderomotive energy. This sharply surpasses the conventional single-electron limit. Calculations reveal the potential to generate soft x-ray photons with energies up to approximately 1.2 keV, enabling the creation of sub-attosecond pulses suitable for probing ultrafast processes in materials and biological systems via core-level spectroscopy and imaging.

Two-electron processes extend high-harmonic generation beyond single-electron limitations

Harmonic cutoffs now reach 5.5 times the ponderomotive energy, a substantial increase from the previously established single-electron scaling of 3.17. The ponderomotive energy, a crucial parameter in strong-field physics, represents the average kinetic energy an electron acquires from the oscillating electromagnetic field of the driving laser. Conventional methods were unable to generate harmonics beyond this threshold. This was due to the constraints of modelling only a single electron’s behaviour. This effectively neglected the complex interplay between electrons within the atom. By incorporating two-electron processes into a refined theoretical model, access to the soft x-ray region of the electromagnetic spectrum has been unlocked. Specifically, generating photons with energies up to 1.2 keV is now possible. Achieving stable and efficient harmonic generation at these energies remains a key engineering challenge, despite this broadened spectral bandwidth supporting the generation of sub-attosecond pulses. Calculations reveal photon energies up to approximately 1.2 keV, firmly within the soft x-ray region and extending far beyond the water window. The water window, a range between 2.3 and 4.4 keV, is particularly important for sensitive material analysis due to the high absorption cross-section of water. This extended range allows for increased contrast in imaging hydrated biological samples. The ability to generate such high-energy harmonics opens possibilities for advanced techniques like angle-resolved photoemission spectroscopy, providing detailed information about the electronic structure of materials.

Two-electron modelling of high-harmonic generation in helium atoms

A refined theoretical model, a two-electron generalisation of the strong-field approximation, was employed to simulate high-harmonic generation in helium atoms. The strong-field approximation (SFA) is a semi-classical method used to describe the interaction of intense laser fields with atoms. It typically treats the atom as a potential well. Explicitly accounting for the simultaneous behaviour of two electrons within the atom moves beyond the conventional single-active-electron model. This model assumes only one electron participates in the harmonic generation process. This two-electron model considers the correlated motion of both electrons under the intense laser field. It includes processes where one electron ionises, and the other participates in the harmonic generation. The model predicts harmonic cutoffs scaling at 4.7 and 5.5 times the ponderomotive energy. This exceeds the standard single-electron scaling of 3.17, and enabling the potential for sub-attosecond soft x-ray pulse generation. The researchers employed the saddle-point method, an analytical technique used to approximate integrals, to analyse the resulting expressions and determine the extended cutoff. This method allows for a more efficient calculation of the harmonic spectrum and provides insights into the underlying physical mechanisms. Further investigation will focus on adapting the model to more complex atomic structures and optimising the process for practical applications. This potentially involves the exploration of different laser parameters and atomic species.

High-harmonic generation extends soft x-ray production to complex atomic systems

High-harmonic generation, a technique with potential for detailed material analysis and biological imaging, is now able to generate soft x-rays. The behaviour of many-electron atoms and molecules presents a considerable challenge, as the team acknowledges their current model, successful with helium, doesn’t automatically translate to more complex systems. Helium, with its simple atomic structure, serves as an ideal test case for developing and validating the two-electron model. However, the increased complexity of atoms with multiple valence electrons introduces significant computational hurdles and requires a more sophisticated treatment of electron correlation effects. This limitation highlights a broader tension within the field, with alternative theoretical approaches, such as those focusing on the intricacies of electron correlation, remaining computationally demanding and difficult to implement effectively. Accurately capturing the interactions between all electrons in a complex atom requires significantly more computational resources and advanced theoretical techniques.

Significant computational power is required to accurately describe the behaviour of many-electron atoms and molecules. The broadened spectral bandwidth enables the creation of sub-attosecond pulses, vital for probing ultrafast processes in materials and potentially revolutionising biological imaging techniques. Sub-attosecond pulses, lasting only a fraction of a femtosecond, are necessary to resolve the extremely rapid dynamics of electrons in atoms and molecules. Extending the reach of high-harmonic generation, a process used to create extremely high-frequency light, involves considering the simultaneous behaviour of multiple electrons within atoms. This advancement surpasses limitations inherent in previous models, which focused solely on the behaviour of a single electron when exposed to intense laser pulses. As a result, the generated light now reaches the soft x-ray region of the electromagnetic spectrum, achieving photon energies up to 1.2 keV, and opening new avenues for research in diverse fields. The development of more efficient and compact high-harmonic sources could lead to widespread applications in materials science, chemistry, and biology, providing unprecedented insights into the fundamental processes governing matter.

Researchers demonstrated that considering the behaviour of two electrons simultaneously during high-harmonic generation significantly extends the range of achievable photon energies. This finding explains recent experimental observations of an extended harmonic spectrum in helium, reaching approximately 1.2 keV in the soft x-ray region and exceeding previous limitations. The broadened spectral bandwidth allows for the creation of sub-attosecond pulses, which are useful for investigating ultrafast dynamics in materials. The authors suggest that future work will need to address the increased computational challenges presented by atoms with multiple valence electrons.