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arXiv:2607.18854

Quantum Dynamics of $H_2^+$ in Orthogonal Two-Color Fields

Jinzhen Zhu

physics.atom-phmath-phquant-phSubmitted Jul 21, 2026• Announced Jul 22, 2026
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Abstract

We present full-dimensional quantum simulations of $H_2^+$ dissociative ionization driven by strong orthogonal laser fields. We consider equal-frequency orthogonal components, which generate elliptical or circular polarization depending on their relative phase and amplitude, as well as orthogonal $800$- and $400$-nm two-color fields. These two-dimensional fields strongly modify the fragmentation dynamics. Most notably, we identify a high-energy peak in the proton kinetic-energy-release (KER) spectrum at approximately $4-5$ eV that is absent from the corresponding single-color, linearly polarized calculations. The yield of this peak can be coherently controlled by varying the relative carrier-envelope phase of the perpendicular field component. The perpendicular field also disrupts the clear electron-proton energy-sharing pattern observed in the main $3-3.5$ eV dissociation channel, indicating more complex multichannel dynamics. Time-dependent state projections and calculations initiated from individual excited states attribute the additional peak to laser-induced vibrational excitation of $H_2^+$. Furthermore, the perpendicular field rotates the fragment angular distributions, causing the most probable proton and electron emission directions to deviate substantially from the principal $z$ axis. These findings demonstrate that the spatial and temporal geometry of orthogonal laser fields provides an additional degree of freedom for controlling ultrafast electron-nuclear dynamics.

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Quantum Dynamics of H2+H_2^+H2+​ in Orthogonal Two-Color Fields
We present full-dimensional quantum simulations of H2+H_2^+H2+​ dissociative ionization driven by strong orthogonal laser fields. We consider equal-frequency orthogonal components, which generate elliptical or circular polarization depending on their relative phase and amplitude, as well as orthogonal 800800800- and 400400400-nm two-color fields. These two-dimensional fields strongly modify the fragmentation dynamics. Most notably, we identify a high-energy peak in the proton kinetic-energy-release (KER) spectrum at approximately 4−54-54−5 eV that is absent from the corresponding single-color, linearly polarized calculations. The yield of this peak can be coherently controlled by varying the relative carrier-envelope phase of the perpendicular field component. The perpendicular field also disrupts the clear electron-proton energy-sharing pattern observed in the main 3−3.53-3.53−3.5 eV dissociation channel, indicating more complex multichannel dynamics. Time-dependent state projections and calculations initiated from individual excited states attribute the additional peak to laser-induced vibrational excitation of H2+H_2^+H2+​. Furthermore, the perpendicular field rotates the fragment angular distributions, causing the most probable proton and electron emission directions to deviate substantially from the principal zzz axis. These findings demonstrate that the spatial and temporal geometry of orthogonal laser fields provides an additional degree of freedom for controlling ultrafast electron-nuclear dynamics.
Orthogonally polarized two-color sequential laser pulses are used to control the electron localization in the dissociation of H2+{}_{2}{}^{+}2​+. The first single attosecond pulse, whose polarization axis is perpendicular to the molecular axis, excites H2+{}_{2}{}^{+}2​+ from $1s{\ensuremath{\sigma}}_{g}$ to $2p{\ensuremath{\pi}}_{u}$, and the time-delayed infrared pulse, whose polarization axis is parallel to the molecular axis, steers the electron between two nuclei. The simulation of the time-dependent Schr\"odinger equation predicts the control degree of the electron localization can be up to 90% with the current laser technology. In this article, we reveal that the mechanism for this asymmetric localization is due to the mixture of $2p{\ensuremath{\pi}}_{g}$ and $2p{\ensuremath{\pi}}_{u}$, instead of $1s{\ensuremath{\sigma}}_{g}$and $2p{\ensuremath{\sigma}}_{u}$ in the previous studies.
Within the Born-Oppenheimer approximation, we build a multichannel model to simulate the dissociation of H2+{\mathrm{H}}_{2}{}^{+}H2​+ in strong laser fields. Two applications of this model are presented: first, orthogonally polarized UV and infrared pulses are used to dissociate H2+{\mathrm{H}}_{2}{}^{+}H2​+ into $2p{\ensuremath{\pi}}_{u}$ and $3d{\ensuremath{\pi}}_{g}$ states, whose superposition results in asymmetric electron localization after the dissociation; second, two orthogonally polarized UV pulses are introduced to trigger competing Rabi oscillations among $1s{\ensuremath{\sigma}}_{g}$, $2p{\ensuremath{\sigma}}_{u}$, $3d{\ensuremath{\sigma}}_{g}$ and $2p{\ensuremath{\pi}}_{u}$ states. This study shows the dissociation of H2+{\mathrm{H}}_{2}{}^{+}H2​+ can be steered into selected electronic states with controllable probabilities with state-of-the-art laser technologies.
We theoretically investigate strong-field ionization of hydrogen atoms by orthogonally polarized two-color (OTC) laser pulses consisting of a fundamental field that is resonant with the 1s - 2p transition and its second harmonic. Numerical simulations are performed by solving the two-dimensional time-dependent Schrödinger equation and recording the photoelectron momentum distribution. In this strong-field resonant ionization, the atom undergoes many Rabi cycles and the electron can be emitted within a completed Rabi-cycle leading to the splitting of the localized momentum distribution. Here, the splitting is attributed to dynamic Rabi-splitting as a result of the dynamic Stark effect. The employed OTC scheme is shown to be efficient for controlling the dynamic Rabi-splitting through the control of quantum-path interferences involved in one-photon and two-photon absorption processes. The control scheme is accomplished by varying the relative ratio intensity and optical phase between the two pulses, and its footprint is mapped in the momentum distribution. This is shown to lead to an asymmetric distribution and suppression of the ionization process. The obtained results suggest the OTC scheme as a tool for coherent control of dynamic Rabi-oscillations via the controlled quantum-path interferences, thus opening new directions towards designing quantum states via the control OTC scheme.
Coherent control of the fragmentation of van der Waals--bound rare-gas dimers is crucial for gaining insights into the properties of weakly bound complexes. In this study, we experimentally investigate the directional dissociative single ionization of argon dimers, employing relative phase-controlled linearly and elliptically polarized two-color femtosecond laser fields. The emission direction of the ionic fragments is manipulated by adjusting the relative phase of the two-color laser fields. We attribute the observed asymmetric pattern to the interference between different dissociation pathways, corresponding to the nuclear wave packet propagating on the gerade and ungerade states, respectively. The relative phase-dependent asymmetries observed in linearly and elliptically polarized two-color laser fields exhibit similarities, suggesting a limited role of electron recollision. Our results highlight the role of nuclear wave-packet interference in the directional fragmentation of rare-gas dimers, and they promote the possibility of coherent control of van der Waals bond cleavage in chemical reactions.
Multiphoton resonant excitation and frustrated tunneling ionization, manifesting the photonic and optical nature of the driving light via direct excitation and electron recapture, respectively, are complementary mechanisms to access Rydberg state excitation (RSE) of atoms and molecules in an intense laser field. However, clear identification and manipulation of their individual contributions in the light-induced RSE process remain experimentally challenging. Here, we bridge this gap by exploring the dissociative and nondissociative RSE of H2 molecules using bicircular two-color laser pulses. Depending on the relative field strength and polarization helicity of the two colors, the RSE probability can be boosted by more than one order of magnitude by exploiting the laser waveform-dependent field effect. The role of the photon effect is readily strengthened with increasing relative strength of the second-harmonic field of the two colors regardless of the polarization helicity. As compared to the nondissociative RSE forming H2 * , the field effect in producing the dissociative RSE channel of ( H + , H * ) is moderately suppressed, which is primarily accessed via a three-step sequential process separated by molecular bond stretching. Our work paves the way toward a comprehensive understanding of the interplay of the underlying field and photon effects in the strong-field RSE process, as well as facilitating the generation of Rydberg states optimized with tailored characteristics.
The single ionization of H2{\mathrm{H}}_{2}H2​ in strong laser fields creates the correlated electron-H2+{{\mathrm{H}}_{2}}^{+}H2​+ pair. Based on such a correlation, we conceive a strategy to control the energy spectra of the freed electron or dissociative fragments by simulating the time-dependent Schr\"odinger equation. Two attosecond pulses in a train produce the replica of electron-H2+{{\mathrm{H}}_{2}}^{+}H2​+ pairs, which are to be steered by a time-delayed phase-stabilized (mid)infrared laser pulse. By controlling the behavior of the freed electron, the dissociation of H2+{{\mathrm{H}}_{2}}^{+}H2​+ can be controlled even though there is no direct laser-H2+{{\mathrm{H}}_{2}}^{+}H2​+ coupling. On the other hand, the photoelectron energy spectra can be manipulated via laser-H2+{{\mathrm{H}}_{2}}^{+}H2​+ coupling. This study demonstrates the entanglement of molecular quantum wave packets, and affords a route to remotely control molecular dissociative ionization.