Light-induced vibrational structure in H2+ and D2+ in intense laser fields

Electro-Nuclear Dynamics of Single and Double Ionization of H2 in Ultrafast Intense Laser Pulses

We present an efficient method for modeling the single and double ionization dynamics of the H2 molecule in ultrashort, intense laser fields. This method is based on a semianalytical approach to calculate the time-dependent single and double molecular ionization rates and on a numerical approach to describe the vibrational motion that takes place in the intermediate molecular ion H2+. This model allows for the prediction of the single and double ionization probabilities of the H2 molecule to be made over a wide range of frequencies and laser intensities with limited computational time while providing a realistic estimate of the energy of the products of the dissociative ionization and of the Coulomb explosion of the H2 molecule. The effect of vibrational dynamics on ionization yields and proton kinetic energy release spectra is demonstrated and, in the case of the latter, is discussed in terms of basic strong-field molecular fragmentation mechanisms.

Phase transition-induced initial decomposition of nitrogen-rich binary CN compound 2,2'-azobis(5-azidotetrazole) and its precursor 2-amino-5-azidotetrazole via tetrazole ring opening under external electric fields: a comparative DFT-D study

A comparative DFT-D study was performed to investigate the external electric field-induced crystal structures, electronic features, Hirshfeld surfaces, vibrational properties and initial decomposition mechanisms of nitrogen-rich binary CN compound 2,2'-azobis(5-azidotetrazole) (C₂N₁₆) and its precursor 2-amino-5-azidotetrazole (CH₂N₈). The results show that there exist phase transitions at the critical points of 0.006 a.u. and 0.008 a.u. for CH₂N₈ and C₂N₁₆, respectively, which are embodied in various properties of these compounds and induce their initial decomposition of the tetrazole ring opening via the breaking of N-N single bonds. The analysis of band gaps and density of states suggests the external electric field-induced enhancing ability for electron transition from the occupied orbitals to empty ones and N-N bond breaking may be the initial decomposition pathway for them. The variations in Hirshfeld surfaces indicate the spatial change and adjustment of non-bonding interactions in the two crystals. The discussions on vibrational properties indicate that IR characteristic peaks of all vibrational modes in the two crystals show a gradual red shift toward a low frequency region. The external electric field-induced initial decomposition pathways of both crystals are tetrazole ring opening via the breaking of a N-N single bond. Our findings provide insights for a comprehensive understanding of external electric field-induced phase transition and initial decomposition mechanisms of nitrogen-rich binary CN energetic compounds.

Circularly polarized light-induced potentials and the demise of excited states

In the presence of strong electric fields, the excited states of single-electron molecules and molecules with large transient dipoles become unstable because of anti-alignment, the rotation of the molecular axis perpendicular to the field vector, where bond hardening is not possible. We show how to overcome this problem by using circularly polarized electromagnetic fields. Using a full quantum description of the electronic, vibrational, and rotational degrees of freedom, we characterize the excited electronic state dressed by the field and analyze its dependence on the bond length and angle and the stability of its vibro-rotational eigenstates. Although the dynamics is metastable, most of the population remains trapped in this excited state for hundreds of femtoseconds, allowing quantum control. Contrary to what happens with linearly polarized fields, the photodissociation occurs along the initial molecular axis, not perpendicular to it.

Anti-alignment driven dynamics in the excited states of molecules under strong fields

We develop two novel models of the H2+ molecule and its isotopes from which we assess quantum-mechanically and semi-classically whether the molecule anti-aligns with the field in the first excited electronic state. The results from both models allow us to predict anti-alignment dynamics even for the HD+ isotope, which possesses a permanent dipole moment. The molecule dissociates at angles perpendicular to the field polarization in both the excited and the ground electronic state, as the population is exchanged through a conical intersection. The quantum mechanical dispersion of the initial state is sufficient to cause full dissociation. We conclude that the stabilization of these molecules in the excited state through bond-hardening under a strong field is highly unlikely.

Control defeasance by anti-alignment in the excited state

We predict anti-alignment dynamics in the excited state of H₂⁺ or related homonuclear dimers in the presence of a strong field. This effect is a general indirect outcome of the strong transition dipole and large polarizabilities typically used to control or to induce alignment in the ground state. In the excited state, however, the polarizabilities have the opposite sign compared to those in the ground state, generating a torque that aligns the molecule perpendicular to the field, deeming any laser-control strategy impossible.

Imaging an isolated water molecule using a single electron wave packet

Observing changes in molecular structure requires atomic-scale Ångstrom and femtosecond spatio-temporal resolution. We use the Fourier transform (FT) variant of laser-induced electron diffraction (LIED), FT-LIED, to directly retrieve the molecular structure of H₂O⁺ with picometer and femtosecond resolution without a priori knowledge of the molecular structure nor the use of retrieval algorithms or ab initio calculations. We identify a symmetrically stretched H₂O⁺ field-dressed structure that is most likely in the ground electronic state. We subsequently study the nuclear response of an isolated water molecule to an external laser field at four different field strengths. We show that upon increasing the laser field strength from 2.5 to 3.8 V/Å, the O-H bond is further stretched and the molecule slightly bends. The observed ultrafast structural changes lead to an increase in the dipole moment of water and, in turn, a stronger dipole interaction between the nuclear framework of the molecule and the intense laser field. Our results provide important insights into the coupling of the nuclear framework to a laser field as the molecular geometry of H₂O⁺ is altered in the presence of an external field.

Transient absorption spectroscopy using high harmonic generation: a review of ultrafast X-ray dynamics in molecules and solids

Attosecond science opened the door to observing nuclear and electronic dynamics in real time and has begun to expand beyond its traditional grounds. Among several spectroscopic techniques, X-ray transient absorption spectroscopy has become key in understanding matter on ultrafast time scales. In this review, we illustrate the capabilities of this unique tool through a number of iconic experiments. We outline how coherent broadband X-ray radiation, emitted in high-harmonic generation, can be used to follow dynamics in increasingly complex systems. Experiments performed in both molecules and solids are discussed at length, on time scales ranging from attoseconds to picoseconds, and in perturbative or strong-field excitation regimes. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

Conical Intersections Induced by Quantum Light: Field-Dressed Spectra from the Weak to the Ultrastrong Coupling Regimes

In classical laser fields with frequencies resonant with the electronic excitation in molecules, it is by now known that conical intersections are induced by the field and are called light-induced conical intersections (LICIs). As optical cavities have become accessible, the question arises whether their quantized modes could also lead to the appearance of LICIs. A theoretical framework is formulated for the investigation of LICIs of diatomics in such quantum light. The eigenvalue spectrum of the dressed states in the cavity is studied, putting particular emphasis on the investigation of absorption spectra of the Na₂ molecule, that is, on the transitions between dressed states, measured by employing a weak probe pulse. The dependence of the spectra on the light-matter coupling strength in the cavity and on the frequency of the cavity mode is studied in detail. The computations demonstrate strong nonadiabatic effects caused by the appearing LICI.

Strong field transient manipulation of electronic states and bands

In the present review, laser fields are so strong that they become part of the electronic potential, and sometimes even dominate the Coulomb contribution. This manipulation of atomic potentials and of the associated states and bands finds fascinating applications in gases and solids, both in the bulk and at the surface. We present some recent spectacular examples obtained within the NCCR MUST in Switzerland.

Alignment dependent ultrafast electron-nuclear dynamics in molecular high-order harmonic generation

We investigated the high-order harmonic generation (HHG) process of diatomic molecular ion H₂⁺ in non-Born-Oppenheimer approximations (NBOA). The corresponding three-dimensional time-dependent Schrödinger equation is solved with arbitrary alignment angles. It is found that the nuclear motion can lead to spectral modulation of HHG in both the tunneling and multiphoton ionization regimes. The universal redshifts of the whole spectrum are unique in molecular HHG. The spectral width of HHG increases in NBOA. We calculated possible influences on redshifts of HHG in real experimental conditions and found that redshifts decrease with the increase of alignment angles of the molecules and are sensitive to the initial vibrational states. It can be used to extract the ultrafast electron-nuclear dynamics and image molecular structure. It will be instructive to related experiments.

Dissociation and Ionization of Quasi-Periodically Vibrating H2+ in Intense Few-Cycle Mid-Infrared Laser Fields

Using quantum mechanics calculations, we theoretically study the dissociation and ionization dynamics of the hydrogen-molecule ion in strong laser fields. Having prepared the nuclear wave packet of H₂⁺ in a specific vibrational state, a pump laser is used to produce a vibrational excitation, leading to quasi-periodical vibration without ionization. Then, a time-delayed few-cycle laser is applied to trigger the dissociation or ionization of H₂⁺. Both the time delay and the intensity of the probe laser alter the competition between dissociation and ionization. We also explore the dependence of kinetic-energy release spectra of fragments on the time delay, showing that the channels of above-threshold dissociation and below-threshold dissociation are opened and closed periodically. Also, dissociation from different channels is influenced by nuclear motion. The dissociation mechanism has been described in detail using the Floquet picture. This work provides a useful method for steering the electronic and nuclear dynamics of diatomic molecules in intense laser fields.

Selective bond breaking of CO2 in phase-locked two-color intense laser fields: laser field intensity dependence

One of the two equivalent C–O bonds of CO₂ can be selectively broken by phase-locked two-color intense laser fields.

Molecular vibrational trapping revisited: a case study with D2

The present theoretical study is concerned with the vibrational trapping or bond hardening, which is a well-known phenomenon predicted by a dressed state representation of small molecules like and in an intense laser field. This phenomenon is associated with a condition where the energy of the light induced, vibrational level coincides with one of the vibrational levels on the field-free potential curve, which at the same time maximizes the wave function overlap between these two levels. One-dimensional numerical simulations were performed to investigate this phenomenon in a more quantitative way than has been done previously by calculating the photodissociation probability of for a wide range of photon energy. The obtained results undoubtedly show that the nodal structure of the field-free vibrational wave functions plays a decisive role in the vibrational trapping, in addition to the current understanding of this phenomenon.

A theoretical study of the activation of nitromethane under applied electric fields

C–N activation is the key step of nitromethane decomposition.

Characterization of Molecular Breakup by Very Intense Femtosecond XUV Laser Pulses

We study the breakup of H2+ exposed to superintense, femtosecond laser pulses with frequencies greater than that corresponding to the ionization potential. By solving the time-dependent Schrödinger equation in an extensive field parameter range, it is revealed that highly nonresonant dissociation channels can dominate over ionization. By considering field-dressed Born-Oppenheimer potential energy curves in the reference frame following a free electron in the field, we propose a simple physical model that characterizes this dissociation mechanism. The model is used to predict control of vibrational excitation, magnitude of the dissociation yields, and nuclear kinetic energy release spectra. Finally, the joint energy spectrum for the ionization process illustrates the energy sharing between the electron and the nuclei and the correlation between ionization and dissociation processes.

Strong field laser control of photochemistry

Strong ultrashort laser pulses have opened new avenues for the manipulation of photochemical processes like photoisomerization or photodissociation. The presence of light intense enough to reshape the potential energy surfaces may steer the dynamics of both electrons and nuclei in new directions. A controlled laser pulse, precisely defined in terms of spectrum, time and intensity, is the essential tool in this type of approach to control chemical dynamics at a microscopic level. In this Perspective we examine the current strategies developed to achieve control of chemical processes with strong laser fields, as well as recent experimental advances that demonstrate that properties like the molecular absorption spectrum, the state lifetimes, the quantum yields and the velocity distributions in photodissociation processes can be controlled by the introduction of carefully designed strong laser fields.

Molecular interferometer to decode attosecond electron-nuclear dynamics

Understanding the coupled electronic and nuclear dynamics in molecules by using pump-probe schemes requires not only the use of short enough laser pulses but also wavelengths and intensities that do not modify the intrinsic behavior of the system. In this respect, extreme UV pulses of few-femtosecond and attosecond durations have been recognized as the ideal tool because their short wavelengths ensure a negligible distortion of the molecular potential. In this work, we propose the use of two twin extreme UV pulses to create a molecular interferometer from direct and sequential two-photon ionization processes that leave the molecule in the same final state. We theoretically demonstrate that such a scheme allows for a complete identification of both electronic and nuclear phases in the wave packet generated by the pump pulse. We also show that although total ionization yields reveal entangled electronic and nuclear dynamics in the bound states, doubly differential yields (differential in both electronic and nuclear energies) exhibit in addition the dynamics of autoionization, i.e., of electron correlation in the ionization continuum. Visualization of such dynamics is possible by varying the time delay between the pump and the probe pulses.

Clocking ultrafast wave packet dynamics in molecules through UV-induced symmetry breaking

We investigate the use of UV-pump-UV-probe schemes to trace the evolution of nuclear wave packets in excited molecular states by analyzing the asymmetry of the electron angular distributions resulting from dissociative ionization. The asymmetry results from the coherent superposition of gerade and ungerade states of the remaining molecular ion in the region where the nuclear wave packet launched by the pump pulse in the neutral molecule is located. Hence, the variation of this asymmetry with the time delay between the pump and the probe pulses parallels that of the moving wave packet and, consequently, can be used to clock its field-free evolution. The performance of this method is illustrated for the H(2) molecule.

THEORETICAL STUDY OF ABOVE THRESHOLD DISSOCIATION OF HD+ IN FEMTOSECOND LASER FIELDS

The above threshold dissociation (ATD) of the HD+ molecular ion in a linearly polarized femtosecond laser field is theoretically studied using three-dimensional time-dependent quantum wave packet method. Based on the Born–Oppenheimer approximation (BOA), calculations are performed on two electronic states, the ground state 1sσ and the excited state 2pσ. The energy-dependent distributions of the dissociated fragments, resulting from the ATD, are calculated by using an asymptotic-flow expression in the momentum space. The numerical results demonstrate that, in the laser field of wavelength λ = 800 nm and full-width at half-maximum (FWHM) τ = 30 fs , only two-photon dissociation is observable at a weaker pulse peak intensity, 5.0 × 1012 W cm -2, while at an intense intensity, 1.5 × 1015 W cm -2, the dissociated fragments resulting from four-photon absorption dominates over the photodissociation process. These results are consistent with the experimental observation of Orr et al. [Orr PA et al., Phys Rev Lett98:163001, 2007]. The ac Stark-shift caused by intense laser field will change the kinetic energies of the fragments. The ATD phenomena are quantitatively interpreted in terms of the concept of light-induced potential. The molecular rotation and alignment have some effects on the kinetic energy spectrum of the dissociated fragments. The molecular rotation reduces the ac Stark-shift and broadens the peaks of kinetic energy spectra of the dissociated fragments. However, the intense laser field can effectively align the molecule and is helpful to increase the ATD probability. The ATD spectrum is related to the initial quantum numbers J0 and M0 of the molecule. The ATD spectrum of HD+ is calculated at a limited thermal temperature.

Control of electron localization in deuterium molecular ions using an attosecond pulse train and a many-cycle infrared pulse

We demonstrate an experimental control of electron localization in deuterium molecular ions created and dissociated by the combined action of an attosecond pulse train and a many-cycle infrared (IR) pulse. The attosecond pulse train is synthesized using both even and odd high order harmonics of the driving IR frequency so that it can strobe the IR field once per IR cycle. An asymmetric ejection of the deuterium ions oscillates with the full IR period when the APT-IR time-delay is scanned. The observed control is due to the creation of a coherent superposition of 1s sigma{g} and 2p sigma{u} states via interference between one-photon and two-photon dissociation channels.

The long-term evolution of D2+ nuclear wave-packet with interaction of intense femtosecond laser pulse

We investigate the long-term evolution of D2+ nuclear wave-packet after interacting with a 5 fs, 800 nm laser pulse at an intensity of 0.5 x 10(14) W/cm2. The nuclear wave-packet evolves in field-free condition for very long time after the laser pulse. The collapse and revival of nuclear wave-packet is studied. The scale of the classical time (approximately 25 fs), the revival time (approximately 580 fs) and the super-revival time (approximately 12 ps) are determined from the simulation as well as the calculation. The constituents of long-standing nuclear wave-packet are also analyzed.

Photodissociation of H2(+) upon exposure to an intense pulsed photonic Fock state

Producing and controlling nonclassical light states are now the subject of intense experimental efforts. In this paper we consider the interaction of such a light state with a small molecule. Specifically, we develop the theory and apply it numerically to calculate in detail how a short pulse of nonclassical light, such as the high intensity Fock state, induces photodissociation in H(2)(+). We compare the kinetic energy distributions and photodissociation yields with the analogous results of quasi-classical light, namely a coherent state. We find that Fock-state light decreases the overall probability of dissociation for low vibrational states of H(2)(+) as well as the location of peaks and line shapes in the kinetic energy distribution of the nuclei.

Attosecond strobing of two-surface population dynamics in dissociating H2+

Using H2+ and D2+, we observe two-surface population dynamics by measuring the kinetic energy of the correlated ions that are created when H2+ (D2+) ionize in short (40-140 fs) and intense (10(14) W/cm2) infrared laser pulses. Experimentally, we find a modulation of the kinetic energy spectrum of the correlated fragments. The spectral progression arises from a hitherto unexpected spatial modulation on the excited state population, revealed by Coulomb explosion. By solving the two-level time-dependent Schrödinger equation, we show that an interference between the net-two-photon and the one-photon transition creates localized electrons which subsequently ionize.

Coherent control of light shifts in an atomic system: modulation of the medium gain

A sequence of two femtosecond coherent pulses--a strong pi-polarized pulse and a weak sigma-polarized pulse--excite the S1/2-P1/2 transition of atomic rubidium in an optically dense vapor. The sigma pulse induces transitions between the adiabatic states with a coupling strength that is different for identically and oppositely light-shifted coupled states, and that can be modified by tuning the relative phase between the pulses. An efficient control of the medium gain for the sigma pulse is experimentally demonstrated. It is shown to be the result of interference between the absorption and the stimulated emission paths for sigma photons.

Optical control of the singlet-triplet transition in Rb2

By controlling nonresonant dynamic Stark shifts it is possible to effectively decouple the intramolecular couplings of simple molecules. We have illustrated this effect in the 1 (1)Sigma(u)-->1 (3)Pi(u) transition in Rb(2). The laser scheme implies two important control knobs: the laser frequency, which must be chosen to avoid both single and multiphoton resonances and to select different electronic environments for the singlet and triplet states, and the pulse intensity, which must amplify the asymmetry in the dynamic polarizabilities that allows the decoupling, avoiding undesired strong-pulse effects. The mechanism of the scheme implies not only brute-force energy shifts but also light-induced reshaping of the potentials to avoid the undesired crossings. Quantitative aspects of the method are analyzed by using molecular models of increasing complexity for Rb(2).

Rapid proton transfer mediated by a strong laser field

Kinetic energy distributions of ejected from a polyatomic molecule, anthraquinone, subjected to 60 fs, 800 nm laser pulses of intensity between 0.2 and 4.0 x 10(14) W x cm(-2), reveal field-driven restructuring of the molecule prior to Coulomb explosion. Calculations demonstrate fast intramolecular proton migration into a field-dressed metastable potential energy minimum. The proton migration occurs in the direction perpendicular to the polarization of the laser field. Rapid field-mediated isomerization is an important new phenomenon in coupling of polyatomic molecules with intense lasers.

Adiabatic squeezing of molecular wave packets by laser pulses

Strong pulse sequences can be used to control the position and width of the molecular wave packet. In this paper we propose a new scheme to maximally compress the wave packet in a quasistatic way by freezing it at a peculiar adiabatic potential shaped by two laser pulses. The dynamic principles of the scheme and the characteristic effect of the different control parameters are presented and analyzed. We use two different molecular models, electronic potentials modeled by harmonic oscillators, with the same force constants, and the Na(2) dimer, to show the typical yield that can be obtained in compressing the initial (minimum width) molecular wave function.