Resolving vibrational wave-packet dynamics of D2(+) using multicolor probe pulses

Attosecond Probing of Nuclear Vibrations in the D2+ and HeH+ Molecular Ions

We study the ultrafast photodissociation of small diatomic molecules using attosecond laser pulses of moderate intensity in the (extreme) ultraviolet regime. The simultaneous application of subfemtosecond laser pulses with different photon energies─resonant in the region of the molecular motion─allows one to monitor the vibrational dynamics of simple diatomics, like the D2+ and HeH+ molecular ions. In our real-time wave packet simulations, the nuclear dynamics is initiated either by sudden ionization (D2+) or by explicit pump pulses (HeH+) via distortion of the potential energy of the molecule. The application of time-delayed attosecond pulses leads to the breakup of the molecules, and the information on the underlying bound-state dynamics is imprinted in the kinetic energy release (KER) spectra of the outgoing fragments. We show that the KER-delay spectrograms generated in our ultrafast pump-probe schemes are able to reconstruct the most important features of the molecular motion within a given electronic state, such as the time period or amplitude of oscillations, interference patterns, or the revival and splitting of the nuclear wave packet. The impact of probe pulse duration, which is key to the applicability of the presented mapping scheme, is investigated in detail.

Tracing the vibrational dynamics of sodium iodide via the spectrum of emitted photofragments

We study by real-time wave packet simulations the ultrafast photodissociation dynamics of the sodium iodide molecule with the aim to trace molecular vibrational motion in a bound electronic state. Applying a few-cycle infrared pump laser pulse, a nuclear wave packet is created in the ground electronic state via the dynamic Stark shift of the potential energy curves of the molecule. To probe this coherent motion in the ground state, we propose to use a series of ultrashort laser pulses with different photon energies that resonantly promote the spread-out wave packet to the repulsive excited state. As the kinetic energy release (KER) spectrum of the dissociating photofragments is sensitive to the shape of the vibrational wave packet, in our pump-probe scheme, KER-delay spectrograms generated for different probe photon energies are used to monitor the molecular motion in the bound state. In our numerical analysis supported by a simple analytical model, we show that for sufficiently long probe pulses the proposed mapping scheme reaches its limits as nuclear wave packet interferences wash out the observed images. The appearance of these interferences is attributed to nuclear wave packet amplitudes that are generated at the first and second half of the probe pulse with the same energy but with a certain time delay. In our detailed numerical survey on the laser parameter dependence of the presented scheme, we find that resonant probe pulses with a few femtosecond duration are suitable for a qualitative mapping of the bound-state molecular motion.

Toward the Full Quantum Dynamical Description of Photon Induced Processes in D2. J Phys Chem A 2016;120:9411-9421. [PMID: 27934332 DOI: 10.1021/acs.jpca.6b09623]

The dissociative ionization (multiphoton regime) of the D₂⁺ ion by ultrashort laser pulses has been studied theoretically using ab initio calculations. The combined ionization and dissociation spectrum was explored for fixed molecular axis orientations. In accordance with previous investigations, the dominant features in the obtained joint energy spectrum were multiphoton peaks. In addition to this, in the present work, photoelectron angular distributions were analyzed as well. By performing a partial wave analysis for each multiphoton peak, we have identified the number of absorbed photons. Moreover, we also found that the angular distribution can significantly change inside a multiphoton peak as a function of electron and nuclear kinetic energy.

Sub-10-fs control of dissociation pathways in the hydrogen molecular ion with a few-pulse attosecond pulse train

The control of the electronic states of a hydrogen molecular ion by photoexcitation is considerably difficult because it requires multiple sub-10 fs light pulses in the extreme ultraviolet (XUV) wavelength region with a sufficiently high intensity. Here, we demonstrate the control of the dissociation pathway originating from the 2pσu electronic state against that originating from the 2pπu electronic state in a hydrogen molecular ion by using a pair of attosecond pulse trains in the XUV wavelength region with a train-envelope duration of ∼4 fs. The switching time from the peak to the valley in the oscillation caused by the vibrational wavepacket motion in the 1sσg ground electronic state is only 8 fs. This result can be classified as the fastest control, to the best of our knowledge, of a molecular reaction in the simplest molecule on the basis of the XUV-pump and XUV-probe scheme.

Settling time of a vibrational wavepacket in ionization

The vibrational wavepacket of a diatomic molecular ion at the time of ionization is usually considered to be generated on the basis of the Franck–Condon principle. According to this principle, the amplitude of each vibrational wavefunction in the wavepacket is given by the overlap integral between each vibrational wavefunction and the ground vibrational wavefunction in the neutral molecule, and hence, the amplitude should be a real number, or equivalently, a complex number the phase of which is equal to zero. Here we report the observation of a non-trivial phase modulation of the amplitudes of vibrational wavefunctions in a wavepacket generated in the ground electronic state of a molecular ion at the time of ionization. The phase modulation results in a group delay of the specific vibrational states of order 1 fs, which can be regarded as the settling time required to compose the initial vibrational wavepacket.

Instantaneous generation of a vibrational wavepacket in a molecular ion is usually assumed in an ionization process. Here, by means of frequency-resolved optical gating, the authors observe a non-trivial phase modulation in a H₂⁺ molecule, which is interpreted as a ∼1-fs settling time.

Frequency-resolved optical gating technique for retrieving the amplitude of a vibrational wavepacket

We propose a novel method to determine the complex amplitude of each eigenfunction composing a vibrational wavepacket of / molecular ions evolving with a ~10 fs time scale. We find that the two-dimensional spectrogram of the kinetic energy release (KER) of H⁺/D⁺ fragments plotted against the time delay of the probe pulse is equivalent to the spectrogram used in the frequency-resolved optical gating (FROG) technique to retrieve the complex amplitude of an ultrashort optical pulse. By adapting the FROG algorithm to the delay-KER spectrogram of the vibrational wavepacket, we have successfully reconstructed the complex amplitude. The deterioration in retrieval accuracy caused by the bandpass filter required to process actual experimental data is also discussed.

Direct Signature of Light-Induced Conical Intersections in Diatomics

Nonadiabatic effects are ubiquitous in physics, chemistry, and biology. They are strongly amplified by conical intersections (CIs), which are degeneracies between electronic states of triatomic or larger molecules. A few years ago it was revealed that CIs in molecular systems can be formed by laser light, even in diatomics. Because of the prevailing strong nonadiabatic couplings, the existence of such laser-induced conical intersections (LICIs) may considerably change the dynamical behavior of molecular systems. By analyzing the photodissociation process of the D2+ molecule carefully, we found a robust effect in the angular distribution of the photofragments that serves as a direct signature of the LICI, providing undoubted evidence of its existence.