Two-Color Fields Induce New Peak in H₂⁺ Fragmentation

Researchers have identified a high-energy peak in the proton kinetic-energy-release spectrum of dissociating hydrogen molecular ions, a finding made possible through the use of orthogonal two-color laser fields. This peak was absent in simulations using single-color, linearly polarized light, indicating a significant alteration in fragmentation dynamics when employing these more complex field geometries. The yield of this peak can be coherently controlled by varying the relative carrier-envelope phase of the perpendicular field component, demonstrating a new method for precise manipulation of molecular fragmentation. Further analysis reveals the perpendicular field disrupts typical energy-sharing patterns in the main dissociation channel, shifting the process towards more complex multichannel dynamics and rotating fragment angular distributions away from the principal axis. The hydrogen molecular ion, the simplest molecule containing one electron and two protons, is a benchmark system for studying molecular dynamics in intense laser fields Krausz and Ivanov (2009); Bucksbaum et al. (1990). Its principal fragmentation mechanisms, including dissociative ionization (DI), above-threshold dissociation (ATD), and bond softening (BS), have been investigated extensively in both experiments and theory Giusti-Suzor et al. (1995); Odenweller et al. (2011, 2014); Wu et al. (2013); Gong et al. (2016). These studies have shown that strong laser fields reshape molecular potential-energy surfaces and thereby control both the fragment kinetic energies and the direction of bond breaking Pavičić et al. (2005); Madsen et al. (2012); Scrinzi (2012). A characteristic example is the KER peak near eV that is frequently observed when dissociates in strong infrared fields Bucksbaum et al. (1990); Wu et al. (2013); Odenweller et al. (2014); Gong et al. (2016). The initial vibrational state also strongly affects molecular excitation, ionization, and fragmentation Kulander et al. (1996). In particular, fragmentation from excited vibrational states can produce additional features in the KER spectrum Zhou and Chu (2005), and excited-state populations can be essential for interpreting the structure of the joint energy spectrum (JES) Yue and Madsen (2014). More complex laser fields provide additional control over these ultrafast processes. Tailoring the polarization and combining multiple frequencies introduce new degrees of freedom into the laser, molecule interaction Peng et al. (2015). Circularly and elliptically polarized fields, for example, can suppress electron recollision with the parent ion and thereby reveal signatures of direct ionization and below-threshold dissociation (BTD) that may be obscured by interference effects in linearly polarized fields Znakovskaya et al.

Quantum Simulations of H₂⁺ in Orthogonal Two-Color Fields

Simulations reveal that manipulating the polarization of laser light can create new pathways for molecular dissociation, offering increased control over the fragments produced. Researchers employing full-dimensional quantum simulations of the hydrogen molecular ion, H₂⁺, have discovered a previously unseen peak in the proton kinetic-energy-release (KER) spectrum at approximately eV when using orthogonal two-color laser fields, a configuration where two laser beams intersect at right angles. The team, based at Ludwig Maximilians Universität and the Shanghai Artificial Intelligence Laboratory, utilized the tRecX code to model the complex interactions. Their approach involved solving the time-dependent Schrödinger equation in six spatial dimensions, a computationally demanding task. The simulations considered equal-frequency orthogonal components, generating elliptical or circular polarization depending on the relative phase and amplitude of the beams. Further analysis revealed that the perpendicular field doesn’t simply add energy; it fundamentally alters the fragmentation process. Time-dependent state projections and calculations initiated from individual excited states attribute the additional peak to laser-induced vibrational excitation of H₂⁺. This suggests that the orthogonal field is not only breaking the molecule apart but also selectively exciting specific vibrational modes before dissociation.

The simulations show that the perpendicular field rotates the fragment angular distributions, causing the most probable proton and electron emission directions to deviate substantially from the principal axis. This deviation from the expected alignment indicates a significant change in the directional control of the fragments. These findings demonstrate that the spatial and temporal geometry of orthogonal laser fields provides an additional degree of freedom for controlling ultrafast electron and nuclear dynamics, opening possibilities for steering molecular reactions with light. The research builds on previous work exploring the influence of polarization and multi-frequency fields on molecular fragmentation, but represents a significant step towards harnessing these effects for precise control over chemical processes.

Dissociative Ionization and KER Spectra in Strong Laser Fields

The manipulation of molecular fragmentation with laser light has become increasingly precise, and recent simulations reveal previously unseen control mechanisms at play when employing orthogonal two-color laser fields. Researchers are now able to sculpt the kinetic energy release (KER) spectrum of dissociating hydrogen molecular ions, identifying and coherently controlling new dissociation pathways. This research builds upon decades of work examining how strong laser fields reshape molecular potential-energy surfaces and dictate bond-breaking dynamics, originating with studies by Krausz and Ivanov (2009) and Bucksbaum et al. (1990). A key finding centers around a newly identified high-energy peak within the proton kinetic-energy-release (KER) spectrum, appearing at approximately eV when utilizing orthogonal two-color laser configurations. This isn’t simply about creating more fragmentation events, but directing energy distribution with precision.

The simulations, conducted using the tRecX code, model the full-dimensional quantum dynamics of the dissociation process, accounting for the complex interplay of electron and nuclear motion. Related implementations of this code have previously been applied to studies of helium double ionization and molecular single ionization, establishing a robust foundation for these new findings. Further analysis reveals that the introduction of a perpendicular field fundamentally alters the energy-sharing dynamics typically observed in the main eV dissociation channel. Instead of a predictable distribution of energy between the departing proton and electron, the perpendicular field induces “more complex multichannel dynamics.” This disruption extends beyond energy distribution, impacting the direction of fragment emission.

tSurff Method for Calculating Joint Energy Spectra

Full-dimensional quantum simulations of molecular dissociation are computationally demanding, yet crucial for understanding and ultimately controlling chemical reactions. Researchers are increasingly turning to advanced computational methods to model these complex processes, and a technique called tSurff is proving particularly effective in mapping the energy released during molecular fragmentation. Developed to streamline calculations of joint energy spectra, tSurff offers a way to accurately predict how molecules break apart under intense laser irradiation, with implications for fields ranging from attosecond science to chemical imaging. The tSurff method, applied to the hydrogen molecular ion, neglects interactions between all particles beyond a certain radius. This simplification allows researchers to focus computational power on the most critical regions of the simulation, as the authors write, outlining the core principle of the technique.

By partitioning configuration space into distinct regions, tSurff efficiently tracks the evolution of the molecular fragments as they separate. This approach, initially applied to helium double ionization and subsequently adapted for more complex molecules, relies on defining surfaces that delineate the boundaries where different physical models apply. Specifically, the method calculates the joint energy spectrum by propagating the molecular wave function until it crosses these surfaces, effectively transitioning from a full quantum treatment to a simplified description based on asymptotic states. The accuracy of this approximation hinges on the consistent use of the asymptotic Hamiltonian and sufficiently long propagation times. The researchers explain that this ensures the calculated energy spectra are not artificially influenced by the computational boundaries. The technique employs infinite-range exterior complex scaling to absorb outgoing flux, further enhancing the accuracy and stability of the simulations.

The power of tSurff lies in its ability to accurately predict the energy distribution of the fragments, providing insights into the underlying dynamics of the dissociation process. This is particularly valuable when studying complex scenarios, such as those involving orthogonal laser fields, where traditional computational methods can struggle. The method’s efficiency allows for detailed investigations of how laser parameters influence molecular fragmentation.

Molecular Dynamics with Protons Fixed at ±R and Electron Coordinate System

Rather than treating the entire molecular system as a fluid, dynamic entity, the team employed a unique computational approach, placing the protons at and while focusing on the electron’s coordinate system. This methodology, which builds on the tSurff method detailed in work focusing on the hydrogen molecular ion, allowed for a more focused analysis of the electron’s role in the dissociation process. This methodology proved crucial in identifying a high-energy peak in the proton kinetic-energy-release (KER) spectrum at approximately eV, a clear deviation from expected fragmentation pathways, suggesting a new channel for dissociation driven by the specific geometry of the laser field.

The significance of this finding extends beyond mere observation; the researchers discovered that this newly identified peak isn’t a passive consequence of the laser field, but can be actively manipulated. This coherent control arises from the perpendicular field’s ability to disrupt the typical energy distribution in the main dissociation channel. The perpendicular field doesn’t just alter energy distribution; it fundamentally changes the direction of fragmentation.