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Excitation of H$_{2}^{+}$ with one-cycle laser pulses: Shaped post-laser-field electronic oscillations, generation of higher- and lower-order harmonics
Atomic and Molecular Clusters · Submitted 29 Oct 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It is shown that there exists a characteristic oscillation frequency $\omega_{\rm osc} \simeq 0.2265$~au (corresponding to the period of $\tau_{\rm osc} \simeq 0.671$~fs and the wavelength of $\lambda_{\rm osc} \simeq 200$~nm) that manifests itself as a "carrier" frequency of temporally shaped oscillations of the time-dependent expectation values $\langle z \rangle$ and $\langle \partial V/\partial z \rangle$ that emerge at the ends of the laser pulses and exist on a timescale of at least 50~fs.
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The abstract, sentence by sentence
Non Born-Oppenheimer quantum dynamics of H$_{2}^{+}$ excited by shaped one-cycle laser pulses linearly polarized along the molecular axis have been studied by the numerical solution of the time-dependent Schr\"odinger equation within a %three-body three-dimensional model, including the internuclear separation, $R$, and the electron coordinates $z$ and $\rho$. Laser carrier frequencies corresponding to the wavelengths $\lambda_{l}=25$~nm through $\lambda_{l}=400$~nm were used and the amplitudes of the pulses were chosen such that the energy of H$_{2}^{+}$ was close to its dissociation threshold at the end of any laser pulse applied. It is shown that there exists a characteristic oscillation frequency $\omega_{\rm osc} \simeq 0.2265$~au (corresponding to the period of $\tau_{\rm osc} \simeq 0.671$~fs and the wavelength of $\lambda_{\rm osc} \simeq 200$~nm) that manifests itself as a "carrier" frequency of temporally shaped oscillations of the time-dependent expectation values $\langle z \rangle$ and $\langle \partial V/\partial z \rangle$ that emerge at the ends of the laser pulses and exist on a timescale of at least 50~fs. Time-dependent expectation values $\langle \rho \rangle$ and $\langle \partial V/\partial \rho \rangle$ of the optically-passive degree of freedom, $\rho$, demonstrate post-laser-field oscillations at two basic frequencies $\omega^{\rho}_{1} \approx \omega_{\rm osc}$ and $\omega^{\rho}_{2} \approx 2\omega_{\rm osc}$. Power spectra associated with the electronic motion show higher- and lower-order harmonics with respect to the driving field.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Non Born-Oppenheimer quantum dynamics of H$_{2}^{+}$ excited by shaped one-cycle laser pulses linearly polarized along the molecular axis have been studied by the numerical solution of the time-dependent Schr\"odinger equation within a %three-body three-dimensional model, including the internuclear separation, $R$, and the electron coordinates $z$ and $\rho$. | method 0.72 | 0.95 | 0.04 | asserted 0.97 |
| s1 | Laser carrier frequencies corresponding to the wavelengths $\lambda_{l}=25$~nm through $\lambda_{l}=400$~nm were used and the amplitudes of the pulses were chosen such that the energy of H$_{2}^{+}$ was close to its dissociation threshold at the end of any laser pulse applied. | method 1.00 | 0.92 | 0.03 | asserted 0.94 |
| s2 | It is shown that there exists a characteristic oscillation frequency $\omega_{\rm osc} \simeq 0.2265$~au (corresponding to the period of $\tau_{\rm osc} \simeq 0.671$~fs and the wavelength of $\lambda_{\rm osc} \simeq 200$~nm) that manifests itself as a "carrier" frequency of temporally shaped oscillations of the time-dependent expectation values $\langle z \rangle$ and $\langle \partial V/\partial z \rangle$ that emerge at the ends of the laser pulses and exist on a timescale of at least 50~fs. | result 1.00 | 0.95 | 0.67 | asserted 1.00 |
| s3 | Time-dependent expectation values $\langle \rho \rangle$ and $\langle \partial V/\partial \rho \rangle$ of the optically-passive degree of freedom, $\rho$, demonstrate post-laser-field oscillations at two basic frequencies $\omega^{\rho}_{1} \approx \omega_{\rm osc}$ and $\omega^{\rho}_{2} \approx 2\omega_{\rm osc}$. | result 1.00 | 0.94 | 0.15 | asserted 1.00 |
| s4 | Power spectra associated with the electronic motion show higher- and lower-order harmonics with respect to the driving field. | result 1.00 | 0.92 | 0.13 | asserted 0.99 |
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Original abstract
Non Born-Oppenheimer quantum dynamics of H$_{2}^{+}$ excited by shaped one-cycle laser pulses linearly polarized along the molecular axis have been studied by the numerical solution of the time-dependent Schr\"odinger equation within a %three-body three-dimensional model, including the internuclear separation, $R$, and the electron coordinates $z$ and $\rho$. Laser carrier frequencies corresponding to the wavelengths $\lambda_{l}=25$~nm through $\lambda_{l}=400$~nm were used and the amplitudes of the pulses were chosen such that the energy of H$_{2}^{+}$ was close to its dissociation threshold at the end of any laser pulse applied. It is shown that there exists a characteristic oscillation frequency $\omega_{\rm osc} \simeq 0.2265$~au (corresponding to the period of $\tau_{\rm osc} \simeq 0.671$~fs and the wavelength of $\lambda_{\rm osc} \simeq 200$~nm) that manifests itself as a "carrier" frequency of temporally shaped oscillations of the time-dependent expectation values $\langle z \rangle$ and $\langle \partial V/\partial z \rangle$ that emerge at the ends of the laser pulses and exist on a timescale of at least 50~fs. Time-dependent expectation values $\langle \rho \rangle$ and $\langle \partial V/\partial \rho \rangle$ of the optically-passive degree of freedom, $\rho$, demonstrate post-laser-field oscillations at two basic frequencies $\omega^{\rho}_{1} \approx \omega_{\rm osc}$ and $\omega^{\rho}_{2} \approx 2\omega_{\rm osc}$. Power spectra associated with the electronic motion show higher- and lower-order harmonics with respect to the driving field.
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