Quantum Trajectory Separation and Attosecond Mapping in Liquid High-Harmonic Generation

Abstract: High-harmonic generation (HHG) from liquids offers a potential pathway to attosecond spectroscopy in chemically complex and disordered environments, yet fundamental questions remain open: whether liquid harmonic emission preserves well-defined attosecond synchronization, and whether harmonic emission can involve simultaneous contributions from multiple quantum trajectories with distinct excursion times despite strong disorder and scattering. Here, we address these issues experimentally by resolving the trajectory-dependent temporal structure of liquid HHG. By optimizing the laser focusing geometry, we achieve clear spatial discrimination of short- and long-trajectory contributions, providing direct evidence for the existence of multiple quantum trajectories in liquids. Using a phase-controlled two-color driving field, we independently retrieve the attochirp associated with each trajectory and demonstrate opposite energy-time correlations for short and long trajectories, establishing a trajectory-resolved energy-time mapping in liquid HHG. All observations are well reproduced by semiclassical recollision simulations. These results place liquid HHG on the same conceptual footing as gas- and solid-phase HHG and establish a robust foundation for attosecond-resolved spectroscopy of ultrafast electronic and chemical dynamics in liquid environments.