Multidimensional high-harmonic echo spectroscopy: Resolving coherent electron dynamics in the EUV regime.

We theoretically propose a multidimensional high-harmonic echo spectroscopy technique which utilizes strong optical fields to resolve coherent electron dynamics spanning an energy range of multiple electronvolts. Using our recently developed semi-perturbative approach, we can describe the coherent valence electron dynamics driven by a sequence of phase-matched and well-separated short few-cycle strong infrared laser pulses. The recombination of tunnel-ionized electrons by each pulse coherently populates the valence states of a molecule, which allows for a direct observation of its dynamics via the high harmonic echo signal. The broad bandwidth of the effective dipole between valence states originated from the strong-field excitation results in nontrivial ultra-delayed partial rephasing echo, which is not observed in standard two-dimensional optical spectroscopic techniques in a two-level molecular systems. We demonstrate the results of simulations for the anionic molecular system and show that the ultrafast valence electron dynamics can be well captured with femtosecond resolution.

Coherent x-ray spontaneous emission spectroscopy of conical intersections.

Conical intersections are known to play a vital role in many photochemical processes. The breakdown of the Born-Oppenheimer approximation in the vicinity of a conical intersection causes exciting phenomena, such as the ultrafast radiationless decay of excited states. The passage of a molecule through a conical intersection creates a coherent superposition of electronic states via nonadiabatic couplings. Detecting this coherent superposition may serve as a direct probe of the conical intersection. In this paper, we theoretically demonstrate the use of coherent spontaneous emission in samples with long-range order for probing the occurrence of a conical intersection in a molecule. Our simulations show that the spectrum contains clear signatures of the created coherent superposition of electronic states. We investigate the bandwidth requirements for the x-ray probes, which influence the observation of coherent superposition generated by the conical intersection.

Extending the Tavis-Cummings model for molecular ensembles-Exploring the effects of dipole self-energies and static dipole moments.

Strong coupling of organic molecules to the vacuum field of a nanoscale cavity can be used to modify their chemical and physical properties. We extend the Tavis-Cummings model for molecular ensembles and show that the often neglected interaction terms arising from the static dipole moment and the dipole self-energy are essential for a correct description of the light-matter interaction in polaritonic chemistry. On the basis of a full quantum description, we simulate the excited-state dynamics and spectroscopy of MgH+ molecules resonantly coupled to an optical cavity. We show that the inclusion of static dipole moments and the dipole self-energy is necessary to obtain a consistent model. We construct an efficient two-level system approach that reproduces the main features of the real molecular system and may be used to simulate larger molecular ensembles.

Cavity-Modified Chemiluminescent Reaction of Dioxetane.

Chemiluminescence is a thermally activated chemical process that emits a photon of light by forming a fraction of products in the electronic excited state. A well-known example of this spectacular phenomenon is the emission of light in the firefly beetle, where the formation of a four-membered cyclic peroxide compound and subsequent dissociation produce a light-emitting product. The smallest cyclic peroxide, dioxetane, also exhibits chemiluminescence but with a low quantum yield as compared to that of firefly dioxetane. Employing the strong light-matter coupling has recently been found to be an alternative strategy to modify the chemical reactivity. In the presence of an optical cavity, the molecular degrees of freedom greatly mix with the cavity mode to form hybrid cavity-matter states called polaritons. These newly generated hybrid light-matter states manipulate the potential energy surfaces and significantly change the reaction dynamics. Here, we theoretically investigate the effects of a strong light-matter interaction on the chemiluminescent reaction of dioxetane using the extended Jaynes-Cummings model. The cavity couplings corresponding to the electronic and vibrational degrees of freedom have been included in the interaction Hamiltonian. We explore how the cavity alters the ground- and excited-state path energy barriers and reaction rates. Our results demonstrate that the formation of excited-state products in the dioxetane decomposition process can be either accelerated or suppressed, depending on the molecular orientation with respect to the cavity polarization.

The role of dephasing for dark state coupling in a molecular Tavis-Cummings model.

The collective coupling of an ensemble of molecules to a light field is commonly described by the Tavis-Cummings model. This model includes numerous eigenstates that are optically decoupled from the optically bright polariton states. Accessing these dark states requires breaking the symmetry in the corresponding Hamiltonian. In this paper, we investigate the influence of non-unitary processes on the dark state dynamics in the molecular Tavis-Cummings model. The system is modeled with a Lindblad equation that includes pure dephasing, as it would be caused by weak interactions with an environment, and photon decay. Our simulations show that the rate of pure dephasing, as well as the number of two-level systems, has a significant influence on the dark state population.

Machine-learned correction to ensemble-averaged wave packet dynamics.

For a detailed understanding of many processes in nature involving, for example, energy or electron transfer, the theory of open quantum systems is of key importance. For larger systems, an accurate description of the underlying quantum dynamics is still a formidable task, and, hence, approaches employing machine learning techniques have been developed to reduce the computational effort of accurate dissipative quantum dynamics. A downside of many previous machine learning methods is that they require expensive numerical training datasets for systems of the same size as the ones they will be employed on, making them unfeasible to use for larger systems where those calculations are still too expensive. In this work, we will introduce a new method that is implemented as a machine-learned correction term to the so-called Numerical Integration of Schrödinger Equation (NISE) approach. It is shown that this term can be trained on data from small systems where accurate quantum methods are still numerically feasible. Subsequently, the NISE scheme, together with the new machine-learned correction, can be used to determine the dissipative quantum dynamics for larger systems. Furthermore, we show that the newly proposed machine-learned correction outperforms a previously handcrafted one, which, however, improves the results already considerably.

Triplet-triplet Annihilation Dynamics of Naphthalene.

Triplet-triplet annihilation (TTA) is a spin-allowed conversion of two triplet states into one singlet excited state, which provides an efficient route to generate a photon of higher frequency than the incident light. Multiple energy transfer steps between absorbing (sensitizer) and emitting (annihilator) molecular species are involved in the TTA based photon upconversion process. TTA compounds have recently been studied for solar energy applications, even though the maximum upconversion efficiency of 50 % is yet to be achieved. With the aid of quantum calculations and based on a few key requirements, several design principles have been established to develop the well-functioning annihilators. However, a complete molecular level understanding of triplet fusion dynamics is still missing. In this work, we have employed multi-reference electronic structure methods along with quantum dynamics to obtain a detailed and fundamental understanding of TTA mechanism in naphthalene. Our results suggest that the TTA process in naphthalene is mediated by conical intersections. In addition, we have explored the triplet fusion dynamics under the influence of strong light-matter coupling and found an increase of the TTA based upconversion efficiency.

Suppressing non-radiative decay of photochromic organic molecular systems in the strong coupling regime.

The lifetimes of electronic excited states have a strong influence on the efficiency of organic solar cells. However, in some molecular systems a given excited state lifetime is reduced due to the non-radiative decay through conical intersections. Several strategies may be used to suppress this decay channel. The use of the strong light-matter coupling provided in optical nano-cavities is the focus of this paper. Here, we consider the meso-tert-butyl-4,4-difluoro-4-bora-3a,4a-diaza-s-indacene molecule (meso-tert-butyl-BODIPY) as a showcase of how strong and ultrastrong coupling might help in the development of organic solar cells. The meso-tert-butyl-BODIPY is known for its low fluorescence yield caused by the non-radiative decay through a conical intersection. However, we show here that, by considering this system within a cavity, the strong coupling can lead to significant changes in the multidimensional landscape of the potential energy surfaces of meso-tert-butyl-BODIPY, suppressing almost completely the decay of the excited state wave packet back to the ground state. By means of multi configuration electronic structure calculations and nuclear wave packet dynamics, the coupling with the cavity is analyzed in-depth to provide further insight of the interaction. By fine-tuning the cavity field strength and resonance frequency, we show that one can change the nuclear dynamics in the excited state, and control the non-radiative decay. This may lead to a faster and more efficient population transfer or the suppression of it.

Direct Transition from Triplet Excitons to Hybrid Light-Matter States via Triplet-Triplet Annihilation.

Strong light-matter coupling generates hybrid states that inherit properties of both light and matter, effectively allowing the modification of the molecular potential energy landscape. This phenomenon opens up a plethora of options for manipulating the properties of molecules, with a broad range of applications in photochemistry and photophysics. In this article, we use strong light-matter coupling to transform an endothermic triplet-triplet annihilation process into an exothermic one. The resulting gradual on-off photon upconversion experiment demonstrates a direct conversion between molecular states and hybrid light-matter states. Our study provides a direct evidence that energy can relax from nonresonant low energy molecular states directly into hybrid light-matter states and lays the groundwork for tunable photon upconversion systems that modify molecular properties in situ by optical cavities rather than with chemical modifications.

Multi-wave mixing in the high harmonic regime: monitoring electronic dynamics.

It has been demonstrated that electronic coherences across many eV can be detected in pump-probe experiments involving high harmonic sources. An additional degree of control over the phase matching can be employed by investigating a more general class of multi-wave mixing. Non-collinear multi-wave mixing of high harmonics with energy (q1ω1 + q2ω2) can be selectively detected along the direction of (q1k1 + q2k2). Simulations based on a recently developed semi-perturbative approach show that only the specific harmonic signals with q1ω1 close to the energy difference between ground state and excited states are observable when the two input pulses are well separated in time. The coherent dynamics between different states can be selectively tracked by detecting the time-delay dependent signals with different q1k1, which can overcome the potential spectral congestion in real experiments. Additionally, such non-collinear geometry can be used to separate the dephasing induced decay and collision induced recovery behaviors of pump-probe high harmonic signal typically observed in the time-resolved high harmonic pump-probe signals.

Controlling the Photostability of Pyrrole with Optical Nanocavities.

Strong light-matter coupling provides a new strategy to manipulate the non-adiabatic dynamics of molecules by modifying potential energy surfaces. The vacuum field of nanocavities can couple strongly with the molecular degrees of freedom and form hybrid light-matter states, termed as polaritons or dressed states. The photochemistry of molecules possessing intrinsic conical intersections can be significantly altered by introducing cavity couplings to create new conical intersections or avoided crossings. Here, we explore the effects of optical cavities on the photo-induced hydrogen elimination reaction of pyrrole. Wave packet dynamics simulations have been performed on the two-state, two-mode model of pyrrole, combined with the cavity photon mode. Our results show how the optical cavities assist in controlling the photostability of pyrrole and influence the reaction mechanism by providing alternative dissociation pathways. The cavity effects have been found to be intensely dependent on the resonance frequency. We further demonstrate the importance of the vibrational cavity couplings and dipole-self interaction terms in describing the cavity-modified non-adiabatic dynamics.

Multiscale wavelet decomposition of time-resolved X-ray diffraction signals in cyclohexadiene.

We demonstrate how the wavelet transform, which is a powerful tool for compression, filtering, and scaling analysis of signals, may be used to separate large- and short-scale electron density features in X-ray diffraction patterns. Wavelets can isolate the electron density associated with delocalized bonds from the much stronger background of highly localized core electrons. The wavelet-processed signals clearly reveal the bond formation and breaking in the early steps of the photoinduced pericyclic ring opening reaction of 1,3-cyclohexadiene, which are not resolved in the bare signal.

Monitoring molecular nonadiabatic dynamics with femtosecond X-ray diffraction.

Ultrafast time-resolved X-ray scattering, made possible by free-electron laser sources, provides a wealth of information about electronic and nuclear dynamical processes in molecules. The technique provides stroboscopic snapshots of the time-dependent electronic charge density traditionally used in structure determination and reflects the interplay of elastic and inelastic processes, nonadiabatic dynamics, and electronic populations and coherences. The various contributions to ultrafast off-resonant diffraction from populations and coherences of molecules in crystals, in the gas phase, or from single molecules are surveyed for core-resonant and off-resonant diffraction. Single-molecule [Formula: see text] scaling and two-molecule [Formula: see text] scaling contributions, where N is the number of active molecules, are compared. Simulations are presented for the excited-state nonadiabatic dynamics of the electron harpooning at the avoided crossing in NaF. We show how a class of multiple diffraction signals from a single molecule can reveal charge-density fluctuations through multidimensional correlation functions of the charge density.

Atom Assisted Photochemistry in Optical Cavities.

Strong light-matter coupling can modify the photochemistry of molecular systems. The collective dynamics of an ensemble of molecules coupled to the light field plays a crucial role in experimental observations. However, the theory of polaritonic chemistry is primarily understood in terms of single molecules, since even in small molecular ensembles the collective dynamics becomes difficult to disentangle. Understanding of the underlying ensemble mechanisms is key to a conceptual understanding and interpretation of experiments. We present a model system that simplifies the problem by mixing two-level Mg atoms with a single MgH+ molecule and investigate its collective dynamics. Our focus is on the modified chemical properties of a single diatomic molecule in the presence of an ensemble of resonant atoms as well as the structure of the major and intermediate polariton states. We present quantum dynamics simulations of the coupled vibronic-photonic system for a variable size of the atomic ensemble. Special attention is given to dissociative the dynamics of the MgH+ molecule.

Simulating photodissociation reactions in bad cavities with the Lindblad equation.

Optical cavities, e.g., as used in organic polariton experiments, often employ low finesse mirrors or plasmonic structures. The photon lifetime in these setups is comparable to the timescale of the nuclear dynamics governing the photochemistry. This highlights the need for including the effect of dissipation in the molecular simulations. In this study, we perform wave packet dynamics with the Lindblad master equation to study the effect of a finite photon lifetime on the dissociation of the MgH+ molecule model system. Photon lifetimes of several different orders of magnitude are considered to encompass an ample range of effects inherent to lossy cavities.

Simulating Coherent Multidimensional Spectroscopy of Nonadiabatic Molecular Processes: From the Infrared to the X-ray Regime.

Crossings of electronic potential energy surfaces in nuclear configuration space, known as conical intersections, determine the rates and outcomes of a large class of photochemical molecular processes. Much theoretical progress has been made in computing strongly coupled electronic and nuclear motions at different levels, but how to incorporate them in different spectroscopic signals and the approximations involved are less established. This will be the focus of the present review. We survey a wide range of time-resolved spectroscopic techniques which span from the infrared to the X-ray regimes and can be used for probing the nonadiabatic dynamics in the vicinity of conical intersections. Transient electronic and vibrational probes and their theoretical signal calculations are classified by their information content. This includes transient vibrational spectroscopic methods (transient infrared and femtosecond off-resonant stimulated Raman), resonant electronic probes (transient absorption and photoelectron spectroscopy), and novel stimulated X-ray Raman techniques. Along with the precise definition of what to calculate for predicting the various signals, we outline a toolbox of protocols for their simulation.

Imaging of transition charge densities involving carbon core excitations by all X-ray sum-frequency generation.

X-ray diffraction signals from the time-evolving molecular charge density induced by selective core excitation of chemically inequivalent carbon atoms are calculated. A narrowband X-ray pulse selectively excites the carbon K-edge of the -CH3 or -CH2F groups in fluoroethane (CH3-CH2F). Each excitation creates a distinct core coherence which depends on the character of the electronic transition. Direct propagation of the reduced single-electron density matrix, using real-time time-dependent density functional theory, provides the time-evolving charge density following interactions with external fields. The interplay between partially filled valence molecular orbitals upon core excitation induces characteristic femtosecond charge migration which depends on the core-valence coherence, and is monitored by the sum-frequency generation diffraction signal. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

X-Ray Sum Frequency Diffraction for Direct Imaging of Ultrafast Electron Dynamics.

X-ray diffraction from molecules in the ground state produces an image of their charge density, and time-resolved x-ray diffraction can thus monitor the motion of the nuclei. However, the density change of excited valence electrons upon optical excitation can barely be monitored with regular diffraction techniques due to the overwhelming background contribution of the core electrons. We present a nonlinear x-ray technique made possible by novel free electron laser sources, which provides a spatial electron density image of valence electron excitations. The technique, sum frequency generation carried out with a visible pump and a broadband x-ray diffraction pulse, yields snapshots of the transition charge densities, which represent the electron density variations upon optical excitation. The technique is illustrated by ab initio simulations of transition charge density imaging for the optically induced electronic dynamics in a donor or acceptor substituted stilbene.

Monitoring Nonadiabatic Electron-Nuclear Dynamics in Molecules by Attosecond Streaking of Photoelectrons.

Streaking of photoelectrons has long been used for the temporal characterization of attosecond extreme ultraviolet pulses. When the time-resolved photoelectrons originate from a coherent superposition of electronic states, they carry additional phase information, which can be retrieved by the streaking technique. In this contribution we extend the streaking formalism to include coupled electron and nuclear dynamics in molecules as well as initial coherences. We demonstrate how streaked photoelectrons offer a novel tool for monitoring nonadiabatic dynamics as it occurs in the vicinity of conical intersections and avoided crossings. Streaking can provide high time resolution direct signatures of electronic coherences, which affect many primary photochemical and biological events.

Novel photochemistry of molecular polaritons in optical cavities.

Violations of the Born-Oppenheimer approximation (BOA) and the consequent nonadiabatic dynamics have long been an object of intense study. Recently, such dynamics have been induced via strong coupling of the molecule to a high-amplitude (spatially confined) mode of the electromagnetic field in optical cavities. However, the effects of a cavity on a pre-existing avoided crossing or conical intersection are relatively unexplored. The dynamics of molecules dressed by cavity modes are usually calculated by invoking the rotating wave approximation (RWA), which greatly simplifies the calculation but breaks down when the cavity mode frequency is higher than the relevant material frequencies. We develop a protocol for computing curve crossing dynamics in an optical cavity by exploiting a recently-developed method of solving the quantum Rabi model without invoking the RWA. The method is demonstrated for sodium iodide.