Light-induced Conical Intersections Research Articles

Classical and quantum light-induced non-adiabaticity in molecular systems

The exchange of energy between electronic and nuclear motion is the origin of non-adiabaticity and plays an important role in many molecular phenomena and processes. Conical intersections (CIs) of different electronic potential energy surfaces lead to the most singular non-adiabaticity and have been intensely investigated. The coupling of light and matter induces conical intersections, which are termed light-induced conical intersections (LICIs). There are two kinds of LICIs, those induced by classical (laser) light and those by quantum light like that provided by a cavity. The present work reviews the subject of LICIs, discussing the achievements made so far. Particular attention is paid to comparing classical and quantum LICIs, their similarities and differences and their relationship to naturally occurring CIs. In contrast to natural CIs, the properties of which are dictated by nature, the properties of their light-induced counterparts are controllable by choosing the frequency and intensity (or coupling to the cavity) of the external light source. This opens the door to inducing and manipulating various kinds of non-adiabatic effects. Several examples of diatomic and polyatomic molecules are presented covering both dynamics and spectroscopy. The computational methods employed are discussed as well. To our opinion, the young field of LICIs and their impact shows much future potential.

Floquet Engineering of a Diatomic Molecule through a Bichromatic Radiation Field.

We report on a theoretical study of a Cs2 molecule illuminated by two lasers and show how this can result in novel quantum dynamics. We reveal that these interactions facilitate the bypass of the non-crossing rule, forming light-induced conical intersections and modifiable avoided crossings. Our findings show how laser field orientation and strength, along with initial phase differences, can control molecular-state transitions, especially on the micromotion scale. We also extensively discuss how the interaction of radiation with matter gives rise to the emergence of potential energy surfaces of hybrids of radiation and molecular states. This research advances a technique for manipulating photoassociation processes in Cs2 molecules, offering potential new avenues in quantum control.

Quantum Control of Atom-Ion Charge Exchange via Light-Induced Conical Intersections

Quantum Control of Atom-Ion Charge Exchange via Light-Induced Conical Intersections

Directly revealing the geometric phase effect of dissociative D2+ by two-color strong field photodissociation.

We study the geometric phase (GP) effect of D2+ produced by the encirclement of the dissociated nuclear wavefunction around the light-induced conical intersection (LICI) using a linearly polarized two-color (800 nm and its third harmonic at 266 nm) synthesized laser field. We calculate the photofragment momentum distribution of D2+ with the random orientation by solving the time-dependent Schrödinger equation. We reveal the GP effect that manifests as the Aharonov-Bohm-like interference in the photofragment angular distribution along the direction perpendicular to the linear polarization axis. Our work deepens the understanding of the physical mechanisms of the molecular dynamics when driven by the synthesized strong laser field.

Competition between collective and individual conical intersection dynamics in an optical cavity

Light-induced nonadiabatic phenomena arise when molecules or molecular ensembles are exposed to resonant external electromagnetic fields. The latter can either be classical laser or quantized cavity radiation fields, which can couple to either the electronic, nuclear or rotational degrees of freedom of the molecule. In the case of quantized radiation fields, the light–matter coupling results in the formation of two new hybrid light–matter states, namely the upper and lower ‘polaritons’. Light-induced avoided crossings and light-induced conical intersections (CIs) between polaritons exist as a function of the vibrational and rotational coordinates of single molecules. For ensembles of N molecules, the N − 1 dark states between the two optically active polaritons feature, additionally, so-called collective CIs, involving the coordinates of more than one molecule to form. Here, we study the competition between intramolecular and collective light-induced nonadiabatic phenomena by comparing the escape rate from the Franck–Condon region of a single molecule and of a molecular ensemble coupled to a cavity mode. In situations where the polaritonic gap would be large and the dark-state decay channels could not be reached effectively, the presence of a seam of light-induced CI between the polaritons facilitates again the participation of the dark manifold, resulting in a cooperative effect that determines the overall non-radiative decay rate from the upper into the lower polaritonic states.

Probing Light-Induced Conical Intersections by Monitoring Multidimensional Polaritonic Surfaces.

The interaction of a molecule with the quantized electromagnetic field of a nanocavity gives rise to light-induced conical intersections between polaritonic potential energy surfaces. We demonstrate for a realistic model of a polyatomic molecule that the time-resolved ultrafast radiative emission of the cavity enables following both nuclear wavepacket dynamics on, and nonadiabatic population transfer between, polaritonic surfaces without applying a probe pulse. The latter provides an unambiguous (and in principle experimentally accessible) dynamical fingerprint of light-induced conical intersections.

The role of geometric phase in dissociation dynamics of the molecule

AbstractThis work explores the role of geometric phase (GP), which results from light induced conical intersection (LICI), in photodissociation process of the molecule through solving the time‐dependent Schrödinger equation. The dissociation results between two cases including GP and excluding GP are compared. Different from the case including GP, the angular distribution of photofragments excluding GP is non‐vanishing at which is the angle between the molecular axis and the polarization direction of laser field. Furthermore, in strong field, when the initial vibrational energy is higher than the energy of LICI point, not only the photofragments distributions present obvious quantum interference structures, but also the angular distributions of the photofragments of two cases have opposite oscillatory structure around . This also shows that the GP effect and nonadiabatic effect of LICI are unified in photodissociation processes.

Polaritonic States of Matter in a Rotating Cavity.

The interaction of quantum light with matter like that inside a cavity is known to give rise to mixed light-matter states called polaritons. We discuss the impact of rotation of the cavity on the polaritons. It is shown that the number of polaritons increases because of this rotation. The structure of the original polaritons is modified, and new ones are induced by the rotation that strongly depend on the angular velocity and the choice of axis of rotation. In molecules the rotation can change the number of light-induced conical intersections and their dimensionality and hence strongly impact their quantum dynamics. General consequences are discussed.

Characterization of light-induced potentials in the strong-field dissociation of O2+

We investigate theoretically the imprints of light-induced potentials (LIPs) on the dissociation dynamics of ${\mathrm{O}}_{2}{}^{+}$ molecular ions, as observable in angle-resolved fragment kinetic-energy-release (KER) spectra. Following the vibrational and rotational dynamics of the initial pump-laser-excited cationic nuclear wave packet, while accounting for the dipole coupling between the ${\mathrm{O}}_{2}{}^{+}(a{\phantom{\rule{0.16em}{0ex}}}^{4}{\mathrm{\ensuremath{\Pi}}}_{u})$ and ${\mathrm{O}}_{2}{}^{+}(f{\phantom{\rule{0.16em}{0ex}}}^{4}{\mathrm{\ensuremath{\Pi}}}_{g})$ electronic states in 800-nm 40-fs probe-laser pulses with peak intensities between ${10}^{13}$ and ${10}^{14} \mathrm{W}/{\mathrm{cm}}^{2}$, we calculate angle-resolved KER spectra which reveal characteristic energy- and angle-dependent fringe structures. These fringes shift downward in energy as the molecular alignment angle $\ensuremath{\theta}$ relative to the probe-pulse polarization direction increases from 0 to $\ensuremath{\pi}/2$. The angle-dependent shifts in the KER fringes increase for larger probe-pulse peak intensities and follow the angle and light-wave-intensity dependence of the vibrational spectrum in the associated Floquet bond-hardening well, which is a manifestation of transient ${\mathrm{O}}_{2}{}^{+}$ nuclear-probability trapping in the LIP during dissociation. By examining the rovibrational dynamics of the dissociating molecular cation near the light-induced conical intersection (LICI) in the cationic LIP surface at $\ensuremath{\theta}=\ensuremath{\pi}/2$, we identify related angle-dependent structures in the KER spectra, suggesting a means for assessing the significance of LICIs in molecular dissociation pathways.

Striking Generic Impact of Light-Induced Non-Adiabaticity in Polyatomic Molecules.

Non-adiabaticity, i.e., the effect of mixing electronic states by nuclear motion, is a central phenomenon in molecular science. The strongest nonadiabatic effects arise due to the presence of conical intersections of electronic energy surfaces. These intersections are abundant in polyatomic molecules. Laser light can induce in a controlled manner new conical intersections, called light-induced conical intersections, which lead to strong nonadiabatic effects similar to those of the natural conical intersections. These effects are, however, controllable and may even compete with those of the natural intersections. In this work we show that the standard low-energy vibrational spectrum of the electronic ground state can change dramatically by inducing non-adiabaticity via a light-induced conical intersection. This generic effect is demonstrated for an explicit example by full-dimensional high-level quantum calculations using a pump-probe scheme with a moderate-intensity pump laser and a weak probe laser.

Probing multiphoton light-induced molecular potentials

The strong coupling between intense laser fields and valence electrons in molecules causes distortions of the potential energy hypersurfaces which determine the motion of the nuclei and influence possible reaction pathways. The coupling strength varies with the angle between the light electric field and valence orbital, and thereby adds another dimension to the effective molecular potential energy surface, leading to the emergence of light-induced conical intersections. Here, we demonstrate that multiphoton couplings can give rise to complex light-induced potential energy surfaces that govern molecular behavior. In the laser-induced dissociation of H2+, the simplest of molecules, we measure a strongly modulated angular distribution of protons which has escaped prior observation. Using two-color Floquet theory, we show that the modulations result from ultrafast dynamics on light-induced molecular potentials. These potentials are shaped by the amplitude, duration and phase of the dressing fields, allowing for manipulating the dissociation dynamics of small molecules.

Ultrafast dynamics in the vicinity of quantum light-induced conical intersections

Nonadiabatic effects appear due to avoided crossings or conical intersections (CIs) that are either intrinsic properties in field-free space or induced by a classical laser field in a molecule. It was demonstrated that avoided crossings in diatomics can also be created in an optical cavity. Here, the quantized radiation field mixes the nuclear and electronic degrees of freedom creating hybrid field-matter states called polaritons. In the present theoretical study we go further and create CIs in diatomics by means of a radiation field in the framework of cavity quantum electrodynamics. By treating all degrees of freedom, that is the rotational, vibrational, electronic and photonic degrees of freedom on an equal footing we can control the nonadiabatic quantum light-induced dynamics by means of CIs. First, the pronounced difference between the the quantum light-induced avoided crossing and the CI with respect to the nonadiabatic dynamics of the molecule is demonstrated. Second, we discuss the similarities and differences between the classical and the quantum field description of the light for the studied scenario.

Geometric phase effects on photodissociation dynamics of diatomics

We investigated the effect of the geometric phase (GP) on photodissociation dynamics at a light-induced conical intersection (LICI) through exact quantum dynamical calculations. By taking the one-photon photodissociation of ionic molecules as an example, we explored the conditions wherein the LICI associated GP affects dissociation dynamics. We found that GP leads to a phase shift between the angular distributions of GP included and GP excluded photofragments. This effect is more pronounced when the energy of the initial vibrational level is above the energy of the LICI point.

Communication: Substantial impact of the orientation of transition dipole moments on the dynamics of diatomics in laser fields

The formation of light-induced conical intersections (LICIs) between electronic states of diatomic molecules has been thoroughly investigated over the past decade. In the case of running laser waves, the rotational, vibrational, and electronic motions couple via the LICI giving rise to strong nonadiabatic phenomena. In contrast to natural conical intersections (CIs) which are given by nature and hard to manipulate, the characteristics of LICIs are easily modified by the parameters of the laser field. The internuclear position of the created LICI is determined by the laser energy, while the angular position is given by the orientation of the transition dipole moment (TDM) with respect to the molecular axis. In the present communication, using MgH+ as a showcase example, we exploit the strong impact of the orientation of the TDMs exerted on the light-induced nonadiabatic dynamics. Comparing the photodissociations induced by parallel or perpendicular transitions, a clear signature of the created LICIs is revealed in the angular distribution of the photofragments.

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.

Mapping of the light-induced conical intersections in the photoelectron spectra of K2 molecules.

In the strong field regime, exploring the physical nature of molecular dynamics is still a challenge due to the dramatic change of molecular potentials. Here, we perform a quantum wave packet study on the pump-probe ionization of K2 molecules and show how the light-induced conical intersections (LICIs) are imprinted into the molecular photoelectron spectra. We demonstrate that the energy and angular distributions of photoelectron spectra provide an accurate mapping of the electronic structure under the influence of the strong laser field. The determination of correct characterization of LICIs can help us to better explore alternative ways to control dynamics.

Direct Signatures of Light-Induced Conical Intersections on the Field-Dressed Spectrum of Na2.

Rovibronic spectra of the field-dressed homonuclear diatomic Na2 molecule are investigated to identify direct signatures of the light-induced conical intersection (LICI) on the spectrum. The theoretical framework formulated allows the computation of the (1) field-dressed rovibronic states induced by a medium-intensity continuous-wave laser light and the (2) transition amplitudes between these field-dressed states with respect to an additional weak probe pulse. The field-dressed spectrum features absorption peaks resembling the field-free spectrum as well as stimulated emission peaks corresponding to transitions not visible in the field-free case. By investigating the dependence of the field-dressed spectra on the dressing-field wavelength, in both full- and reduced-dimensional simulations, direct signatures of the LICI can be identified. These signatures include (1) the appearance of new peaks and the splitting of peaks for both absorption and stimulated emission and (2) the manifestation of an intensity-borrowing effect in the field-dressed spectrum.

Unambiguous Signature of the Berry Phase in Intense Laser Dissociation of Diatomic Molecules.

We report strong evidence of Berry phase effects in intense laser dissociation of D2+ molecules, manifested as Aharonov-Bohm-like oscillations in the photofragment angular distribution (PAD). Our calculations show that this interference pattern strongly depends on the parity of the diatom initial rotational state, (-1) j. Indeed, the PAD local maxima (minima) observed in one case ( j odd) correspond to local minima (maxima) in the other case ( j even). Using simple topological arguments, we clearly show that such interference conversion is a direct signature of the Berry phase. The sole effect of the latter on the rovibrational wave function is a sign change of the relative phase between two interfering components, which wind in opposite senses around a light-induced conical intersection (LICI). Therefore, encirclement of the LICI leads to constructive ( j odd) or destructive ( j even) self-interference of the initial nuclear wavepacket in the dissociative limit. To corroborate our theoretical findings, we suggest an experiment of strong-field indirect dissociation of D2+ molecules, comparing the PAD of the ortho and para molecular species in directions nearly perpendicular to the laser polarization axis.

Geometric phase of light-induced conical intersections: adiabatic time-dependent approach

ABSTRACTConical intersections are degeneracies between electronic states and are very common in nature. It has been found that they can also be created both by standing or by running laser waves. The latter are called light-induced conical intersections. It is well known that conical intersections are the sources for numerous topological effects which are manifested, e.g. in the appearance of the geometric or Berry phase. In one of our former works by incorporating the diabatic-to-adiabatic transformation angle with the line-integral technique, we have calculated the Berry-phase of the light-induced conical intersections. Here, we demonstrate that by using the time-dependent adiabatic approach suggested by Berry the geometric phase of the light-induced conical intersections can also be obtained and the results are very similar to those of the time-independent calculations.

Competition between Light-Induced and Intrinsic Nonadiabatic Phenomena in Diatomics.

Nonadiabatic effects arise due to avoided crossings or conical intersections that are either present naturally in field-free space or induced by a classical laser field in a molecule. Recently, it was demonstrated that nonadiabatic effects in diatomics can also be created in an optical cavity. Here, the quantized radiation field mixes the nuclear and electronic degrees of freedom. We show the equivalence of using the cavity's quantized field and the classical laser field as usually done for molecules. This is demonstrated for NaI, which exhibits a pronounced natural (intrinsic) avoided crossing that competes with the avoided crossing induced by the field. Furthermore, rotating molecules exhibit light-induced conical intersections (LICIs) in classical laser light, and we also investigate the impact of these intersections. For NaI, we undoubtedly demonstrate a significant difference between the impact of the laser-induced avoided crossing and that of the LICI on the dynamics of the molecule.