Light’s Quantum Paths Interfere in Unexpected Two-Dimensional Patterns

Scientists at King’s College London in collaboration with The Extreme Light Infrastructure ERIC, Czech Technical University and Universit´e Claude Bernard Lyon 1, led by Xiaozhou Zou, have experimentally observed a novel form of quantum-path interference in two dimensions during high-harmonic generation. This interference is achieved using a highly-bichromatic field, characterised by comparable intensities of two orthogonal colours. The research details how the resulting harmonic intensity modulations encode information about this two-dimensional quantum-path interference (2D-QPI), revealing differing behaviours between odd and even harmonics, monomodal for the former and bimodal for the latter. Through the application of strong-field approximation and the saddle-point method to disentangle contributions from multiple quantum orbits, the study establishes a connection between the dipole response and the symmetry of the driving field, potentially offering a new approach to HHG spectroscopy and the study of attosecond electron dynamics by expanding the dimensionality of quantum paths.

Orthogonally polarised light unlocks two-dimensional electron interference pathways

A laser system employing two distinct colours of light with comparable intensity was central to observing this new interference pattern. High-harmonic generation (HHG) is a non-linear process where intense laser fields drive electrons to return to their parent atoms, emitting high-frequency photons. Traditionally, this process is driven by a single frequency, but this research deviates from that norm. Instead of simply adding a second, weaker colour as a perturbative element, the two colours were carefully balanced to actively and coherently alter electron behaviour during HHG, effectively converting a low-frequency input wave into many higher-frequency harmonic waves. The orthogonally-polarised nature of these colours, meaning their light waves vibrate at right angles to each other, is crucial. This polarisation unlocked a two-dimensional pathway for electrons, significantly expanding the possibilities for quantum-path interference. Quantum-path interference, analogous to the interference patterns created by overlapping water waves, manifests as constructive and destructive interference between different electron trajectories within the atom. This approach enabled observation of a novel form of 2D-QPI in HHG, differing significantly from previous work that employed a weaker second colour merely as a perturbative probe. In those earlier studies, the second colour’s influence was minimal, whereas here, both colours actively reshape electron behaviour, offering substantial potential for advanced spectroscopic techniques capable of probing more complex systems.

Bichromatic field control elucidates two-dimensional quantum-path interference in high-harmonic

Harmonic intensity modulations now reveal a distinct 2D-QPI with a contrast exceeding previously observed one-dimensional interference patterns, representing a fundamental shift in control over electron dynamics previously unattainable with single-colour or perturbative two-colour fields. This 2D-QPI arises from a highly-bichromatic driving field where the intensities of the two orthogonally-polarised colours are comparable, a regime not previously explored with this level of precision. The intensity balance is critical; if one colour dominates, the interference pattern collapses into a more conventional one-dimensional form. Applying saddle-point methods to HHG for the first time in this specific intensity regime, the researchers disentangled contributions from multiple quantum orbits. The saddle-point method is an analytical technique used to approximate integrals, allowing for the identification of the most probable electron trajectories contributing to the harmonic signal. By separating these contributions, they demonstrated a direct link between the dipole response, the atom’s response to the electric field, and the symmetry of the driving field. This connection is fundamental to understanding how the laser field influences the generated harmonics.

Detailed analysis of harmonic intensity modulations confirmed the new 2D-QPI; odd-order harmonics exhibited a single, unimodal peak, while even harmonics displayed a bimodal structure, directly linking to the driving field’s symmetry. This difference in modulation patterns provides a clear signature of the 2D-QPI. Calculations utilising the strong-field approximation and saddle-point method successfully separated contributions from multiple quantum orbits, demonstrating that the dipole response for both odd and even harmonics reflects the active symmetry of the orthogonally-polarised driving field. The intensity ratio of the second harmonic to the fundamental was measured at 0.12, with respective intensities of 1.8x 10¹³ W/cm² and 1.5x 10¹⁴ W/cm², conditions vital for observing this 2D-QPI. These specific intensity values are crucial, as they ensure that both colours contribute significantly to the HHG process. Although current experiments are limited to argon gas and do not yet demonstrate the scalability needed for probing more complex materials or achieving practical applications, this unlocks potential for attosecond electron dynamics spectroscopy, allowing for the observation of electron motion on attosecond timescales (1 attosecond = 10⁻¹⁵ seconds).

Two-dimensional quantum-path interference steers attosecond electron control

Precisely controlling electron behaviour within atoms and molecules is vital for unlocking the full potential of attosecond spectroscopy, offering a new dimension to that control. Attosecond spectroscopy aims to capture the incredibly fast dynamics of electrons, providing insights into fundamental chemical and physical processes. Demonstrating practical application beyond argon gas remains a significant hurdle, a limitation acknowledged within the work. Argon is a relatively simple atom, and extending these findings to more complex molecules will require overcoming significant technical challenges. This establishes a key step towards more detailed attosecond spectroscopy, a technique using extremely short bursts of light to observe electron behaviour. The ability to manipulate electron pathways with greater precision will enable the study of previously inaccessible phenomena.

Encoding information within harmonic intensity modulations provides scientists with a new way to map the pathways electrons take within atoms and molecules. Understanding these pathways allows for mapping electron behaviour with greater precision, potentially leading to the development of new materials and technologies. The demonstration of 2D-QPI expands understanding of how electrons behave during HHG, providing a more complete picture of this complex process. The distinct modulation observed in odd and even harmonics directly reflects the symmetry of the driving laser field, confirming a link between the dipole response and field polarisation. Consequently, this establishes a foundation for new spectroscopic methods capable of mapping attosecond electron dynamics with greater dimensionality, potentially revolutionising our understanding of chemical reactions and material properties at the atomic level.

Researchers observed a new form of quantum-path interference in high-harmonic generation using a highly-bichromatic field. This finding means scientists can now encode information about electron pathways within the intensity of generated harmonics, offering a new way to study attosecond electron dynamics. The observed modulations in odd and even harmonics reflect the symmetry of the driving laser field, confirming a connection between the electron response and field polarisation. The authors suggest this technique lifts the dimensionality of quantum paths involved in the interference, potentially enabling more detailed spectroscopic analysis.