Quantum dynamics, isotope effects, and power spectra of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msup><mml:mrow/><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mi>HD</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msup></mml:math> excited to the continuum by strong one-cycle laser pulses: Three-dimensional non-Born-Oppenheimer simulations

Non-Born-Oppenheimer quantum dynamics of ${\mathrm{H}}_{2}{}^{+}$ and ${\mathrm{HD}}^{+}$ excited by single one-cycle laser pulses linearly polarized along the molecular ($z$) axis have been studied within a three-dimensional model, including the internuclear distance $R$ and electron coordinates $z$ and $\ensuremath{\rho}$, by means of the numerical solution of the time-dependent Schr\"odinger equation on the timescale of about 200 fs. Laser carrier frequencies corresponding to the wavelengths of ${\ensuremath{\lambda}}_{l}=400$ and 50 nm have been used and the amplitudes of the pulses have been chosen such that the energies of ${\mathrm{H}}_{2}{}^{+}$ and ${\mathrm{HD}}^{+}$ are above the dissociation threshold after the ends of the laser pulses. It is shown that excitation of ${\mathrm{H}}_{2}{}^{+}$ and ${\mathrm{HD}}^{+}$ above the dissociation threshold is accompanied by formation of vibrationally ``hot'' and ``cold'' ensembles of molecules. Dissociation of vibrationally ``hot'' molecules does not prevent the appearance of post-laser-pulse electronic oscillations, parallel $z$ oscillations, and transversal $\ensuremath{\rho}$ oscillations. Moreover, dissociation of ``hot'' molecules does not influence characteristic frequencies of electronic $z$ and $\ensuremath{\rho}$ oscillations. The main difference between the laser-induced quantum dynamics of homonuclear ${\mathrm{H}}_{2}{}^{+}$ and its heteronuclear isotope ${\mathrm{HD}}^{+}$ is that fast post-laser-pulse electronic $z$ oscillations in ${\mathrm{H}}_{2}{}^{+}$ are regularly shaped with the period of ${\ensuremath{\tau}}_{\mathrm{shp}}\ensuremath{\approx}30$ fs corresponding to nuclear oscillations in ${\mathrm{H}}_{2}{}^{+}$, while electronic $z$ oscillations in ${\mathrm{HD}}^{+}$ arise as ``echo pulses'' of its initial excitation and appear with the period of ${\ensuremath{\tau}}_{\mathrm{echo}}\ensuremath{\approx}80$ fs corresponding to nuclear motion in ${\mathrm{HD}}^{+}$. Accordingly, corresponding power spectra of nuclear motion contain strong low-frequency harmonics at ${\ensuremath{\omega}}_{\mathrm{shp}}=2\ensuremath{\pi}/{\ensuremath{\tau}}_{\mathrm{shp}}$ in ${\mathrm{H}}_{2}{}^{+}$ and ${\ensuremath{\omega}}_{\mathrm{echo}}=2\ensuremath{\pi}/{\ensuremath{\tau}}_{\mathrm{echo}}$ in ${\mathrm{HD}}^{+}$. Power spectra related to both electronic and nuclear motion have been calculated in the acceleration form. Both higher- and lower-order harmonics are generated at the laser wavelength ${\ensuremath{\lambda}}_{l}=400$ nm, while only lower-order harmonics are well pronounced at ${\ensuremath{\lambda}}_{l}=50$ nm. It is also shown that a rationalized harmonic order, defined in terms of the frequency of the laser-induced electronic $z$ oscillations, agrees with the concept of inversion symmetry for electronic motion in diatomic molecules.

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