Physical Review A

Dissociation of H2+ into selected electronic states in strong laser fields

Xinyuan You, Feng He

Published Jun 9, 2014• 8 citations

Abstract

Within the Born-Oppenheimer approximation, we build a multichannel model to simulate the dissociation of ${\mathrm{H}}_{2}{}^{+}$ in strong laser fields. Two applications of this model are presented: first, orthogonally polarized UV and infrared pulses are used to dissociate ${\mathrm{H}}_{2}{}^{+}$ 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 ${\mathrm{H}}_{2}{}^{+}$ can be steered into selected electronic states with controllable probabilities with state-of-the-art laser technologies.

DOI: 10.1103/physreva.89.063405

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Control of electron localization in the dissociation of H 2+ using orthogonally polarized two-color sequential laser pulses

Feng He

Physical Review ADec 20, 201234 citations

Laser Induced Dissociation Control of $H_2^+$ and $H_3^{2+}$

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The Journal of Atomic and Molecular SciencesAug 1, 20170 citations

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

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physics.atom-phCross-listedarXiv:2607.18854Jul 22, 2026

Electron localization of ${{\rm{H}}}_{2}^{+}$ in a dc electric field

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Physical Review AApr 11, 20188 citations

Manipulating dynamical Rabi-splitting with two-color laser pulses

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Physical Review A

Dissociation of H2+ into selected electronic states in strong laser fields

Xinyuan You, Feng He

Published Jun 9, 2014• 8 citations

Publisher

Abstract

Within the Born-Oppenheimer approximation, we build a multichannel model to simulate the dissociation of

{\mathrm{H}}_{2}{}^{+}

in strong laser fields. Two applications of this model are presented: first, orthogonally polarized UV and infrared pulses are used to dissociate

{\mathrm{H}}_{2}{}^{+}

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

{\mathrm{H}}_{2}{}^{+}

can be steered into selected electronic states with controllable probabilities with state-of-the-art laser technologies.

DOI: 10.1103/physreva.89.063405

Related papers

Control of electron localization in the dissociation of H 2+ using orthogonally polarized two-color sequential laser pulses

Feng He

Orthogonally polarized two-color sequential laser pulses are used to control the electron localization in the dissociation of H ${}_{2}{}^{+}$ . The first single attosecond pulse, whose polarization axis is perpendicular to the molecular axis, excites H ${}_{2}{}^{+}$ 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.Orthogonally polarized two-color sequential laser pulses are used to control the electron localization in the dissociation of H${}_{2}{}^{+}$. The first single attosecond pulse, whose polarization axis is perpendicular to the molecular axis, excites H${}_{2}{}^{+}$ 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.

Physical Review ADec 20, 201234 citations

Laser Induced Dissociation Control of $H_2^+$ and $H_3^{2+}$ Laser Induced Dissociation Control of $H_2^+$ and $H_3^{2+}$

Z.-M. Jia, Zhinan Zeng

Laser induced dissociation control of the symmetric diatomic molecular ion $H_2^+$ and the triatomic molecular ion $H_3^{2+}$ is discussed. The simulation results demonstrate that a long-wavelength terahertz or mid-infrared laser pulse can be used to control the electrons of the dissociative states after the excitation of an ultrashort ultraviolet (UV) laser pulse. For $H_2^+,$ there exists an effective time, which increases with increasing pulse duration of the UV laser pulse, for controlling the molecular dissociation. For the electrons of the $1sσ_g$ state, they move along the polarization direction of the dissociation control electric field. In contrast, for the electrons of the $2pσ_u$ state, they move in the opposite direction to that of the electric force. And for the triatomic molecule $H_3^{2+}$ , the electron dissociation control can also be realized by changing the central wavelength of the exciting UV pulse.Laser induced dissociation control of the symmetric diatomic molecular ion $H_2^+$ and the triatomic molecular ion $H_3^{2+}$ is discussed. The simulation results demonstrate that a long-wavelength terahertz or mid-infrared laser pulse can be used to control the electrons of the dissociative states after the excitation of an ultrashort ultraviolet (UV) laser pulse. For $H_2^+,$ there exists an effective time, which increases with increasing pulse duration of the UV laser pulse, for controlling the molecular dissociation. For the electrons of the $1sσ_g$ state, they move along the polarization direction of the dissociation control electric field. In contrast, for the electrons of the $2pσ_u$ state, they move in the opposite direction to that of the electric force. And for the triatomic molecule $H_3^{2+}$, the electron dissociation control can also be realized by changing the central wavelength of the exciting UV pulse.

The Journal of Atomic and Molecular SciencesAug 1, 20170 citations

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

Jinzhen Zhu

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.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.

physics.atom-phCross-listedarXiv:2607.18854Jul 22, 2026

Electron localization of ${{\rm{H}}}_{2}^{+}$ in a dc electric fieldElectron localization of ${{\rm{H}}}_{2}^{+}$ in a dc electric field

Zhengmao Jia, Zhinan Zeng, W T Tang +1 more

A dc electric field is utilized to steer the electron motion after the molecular ion H 2 + is excited by an ultrashort ultraviolet laser pulse. The numerical simulation shows that the electron localization distribution and the dissociation control ratio are dependent on the polarization direction and amplitude of the dc electric field. Most electrons of the dissociation state move opposite to the dc electric field and stabilize at the dressed-up potential well, for the dressed-down well is occupied by the electrons of the 1s σ g state.A dc electric field is utilized to steer the electron motion after the molecular ion H 2 + is excited by an ultrashort ultraviolet laser pulse. The numerical simulation shows that the electron localization distribution and the dissociation control ratio are dependent on the polarization direction and amplitude of the dc electric field. Most electrons of the dissociation state move opposite to the dc electric field and stabilize at the dressed-up potential well, for the dressed-down well is occupied by the electrons of the 1s σ g state.

Chinese Physics BJan 1, 20170 citations

Remote control of the dissociative ionization of H 2 based on electron- H 2 + entanglement

Junping Wang, Feng He

The single ionization of ${\mathrm{H}}_{2}$ in strong laser fields creates the correlated electron- ${{\mathrm{H}}_{2}}^{+}$ 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- ${{\mathrm{H}}_{2}}^{+}$ 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 ${{\mathrm{H}}_{2}}^{+}$ can be controlled even though there is no direct laser- ${{\mathrm{H}}_{2}}^{+}$ coupling. On the other hand, the photoelectron energy spectra can be manipulated via laser- ${{\mathrm{H}}_{2}}^{+}$ coupling. This study demonstrates the entanglement of molecular quantum wave packets, and affords a route to remotely control molecular dissociative ionization.The single ionization of ${\mathrm{H}}_{2}$ in strong laser fields creates the correlated electron-${{\mathrm{H}}_{2}}^{+}$ 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-${{\mathrm{H}}_{2}}^{+}$ 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 ${{\mathrm{H}}_{2}}^{+}$ can be controlled even though there is no direct laser-${{\mathrm{H}}_{2}}^{+}$ coupling. On the other hand, the photoelectron energy spectra can be manipulated via laser-${{\mathrm{H}}_{2}}^{+}$ coupling. This study demonstrates the entanglement of molecular quantum wave packets, and affords a route to remotely control molecular dissociative ionization.

Physical Review AApr 11, 20188 citations

Manipulating dynamical Rabi-splitting with two-color laser pulses

Hicham Agueny, Abdelmalek Taoutioui, Younes Adnani +1 more

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.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.

Optics ExpressJul 12, 20197 citations

Within the Born-Oppenheimer approximation, we build a multichannel model to simulate the dissociation of

{\mathrm{H}}_{2}{}^{+}

in strong laser fields. Two applications of this model are presented: first, orthogonally polarized UV and infrared pulses are used to dissociate

{\mathrm{H}}_{2}{}^{+}

into

2p{\ensuremath{\pi}}_{u}

and

3d{\ensuremath{\pi}}_{g}

1s{\ensuremath{\sigma}}_{g}

2p{\ensuremath{\sigma}}_{u}

3d{\ensuremath{\sigma}}_{g}

and

2p{\ensuremath{\pi}}_{u}

states. This study shows the dissociation of

{\mathrm{H}}_{2}{}^{+}

can be steered into selected electronic states with controllable probabilities with state-of-the-art laser technologies.

Orthogonally polarized two-color sequential laser pulses are used to control the electron localization in the dissociation of H

{}_{2}{}^{+}

. The first single attosecond pulse, whose polarization axis is perpendicular to the molecular axis, excites H

{}_{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.

Laser Induced Dissociation Control of

H_2^+

and

H_3^{2+}

Laser induced dissociation control of the symmetric diatomic molecular ion

H_2^+

and the triatomic molecular ion

H_3^{2+}

is discussed. The simulation results demonstrate that a long-wavelength terahertz or mid-infrared laser pulse can be used to control the electrons of the dissociative states after the excitation of an ultrashort ultraviolet (UV) laser pulse. For

H_2^+,

there exists an effective time, which increases with increasing pulse duration of the UV laser pulse, for controlling the molecular dissociation. For the electrons of the

1sσ_g

state, they move along the polarization direction of the dissociation control electric field. In contrast, for the electrons of the

2pσ_u

state, they move in the opposite direction to that of the electric force. And for the triatomic molecule

H_3^{2+}

, the electron dissociation control can also be realized by changing the central wavelength of the exciting UV pulse.

Quantum Dynamics of

H_2^+

in Orthogonal Two-Color Fields

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.

Electron localization of

{{\rm{H}}}_{2}^{+}

in a dc electric field

The single ionization of

{\mathrm{H}}_{2}

in strong laser fields creates the correlated electron-

{{\mathrm{H}}_{2}}^{+}

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-

{{\mathrm{H}}_{2}}^{+}

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

{{\mathrm{H}}_{2}}^{+}

can be controlled even though there is no direct laser-

{{\mathrm{H}}_{2}}^{+}

coupling. On the other hand, the photoelectron energy spectra can be manipulated via laser-

{{\mathrm{H}}_{2}}^{+}

coupling. This study demonstrates the entanglement of molecular quantum wave packets, and affords a route to remotely control molecular dissociative ionization.