FEMTOSECOND LASER PHOTOELECTRON SPECTROSCOPY ON ATOMS AND SMALL MOLECULES: Prototype Studies in Quantum Control

Absolute control over the quantum yield of a photodissociation reaction mediated by nonadiabatic couplings

Control of molecular reaction dynamics with laser pulses has been developed in the last decades. Among the different magnitudes whose control has been actively pursued, the branching ratio between different product channels constitutes the clearest signature of quantum control. In polyatomic molecules, the dynamics in the excited state is quagmired by non-adiabatic couplings, which are not directly affected by the laser, making control over the branching ratio a very demanding challenge. Here we present a control scheme for the CH3I photodissociation in the A band, that modifies the quantum yield of the two fragmentation channels of the process. The scheme relies on the optimized preparation of an initial superposition of vibrational states in the ground potential, which further interfere upon the excitation with a broad pump pulse. This interference can suppress any of the channels, regardless of its dominance, and can be achieved over the whole spectral range of the A band. Furthermore, it can be accomplished without strong fields or direct intervention during the dynamics in the excited states: the whole control is predetermined from the outset. The present work thus opens the possibility of extensive and universal control of the channel branching ratio in complex photodissociation processes.

Three-state coherent control using narrowband and passband sequences

In this work, we propose a comprehensive design for narrowband and passband composite pulse sequences by involving the dynamics of all states in the three-state system. The design is quite universal as all pulse parameters can be freely employed to modify the coefficients of error terms. Two modulation techniques, the strength and phase modulations, are used to achieve arbitrary population transfer with a desired excitation profile, while the system keeps minimal leakage to the third state. Furthermore, the current sequences are capable of tolerating inaccurate waveforms, detuning errors, and work well when rotating wave approximation is not strictly justified. Therefore, this work provides versatile adaptability for shaping various excitation profiles in both narrowband and passband sequences.

Ultrafast X-Ray Probes of Elementary Molecular Events

Elementary events that determine photochemical outcomes and molecular functionalities happen on the femtosecond and subfemtosecond timescales. Among the most ubiquitous events are the nonadiabatic dynamics taking place at conical intersections. These facilitate ultrafast, nonradiative transitions between electronic states in molecules that can outcompete slower relaxation mechanisms such as fluorescence. The rise of ultrafast X-ray sources, which provide intense light pulses with ever-shorter durations and larger observation bandwidths, has fundamentally revolutionized our spectroscopic capabilities to detect conical intersections. Recent theoretical studies have demonstrated an entirely new signature emerging once a molecule traverses a conical intersection, giving detailed insights into the coupled nuclear and electronic motions that underlie, facilitate, and ultimately determine the ultrafast molecular dynamics. Following a summary of current sources and experiments, we survey these techniques and provide a unified overview of their capabilities. We discuss their potential to dramatically increase our understanding of ultrafast photochemistry.

Multiphoton Ionization Reduction of Atoms in Two-Color Femtosecond Laser Fields

We report the ionization reduction of atoms in two-color femtosecond laser fields in this joint theoretical-experimental study. For the multiphoton ionization of atoms using a 400 nm laser pulse, the ionization probability is reduced if another relatively weak 800 nm laser pulse is overlapped. Such ionization reduction consistently occurs regardless of the relative phase between the two pulses. The time-dependent Schrödinger equation simulation results indicate that with the assisted 800 nm photons the electron can be launched to Rydberg states with large angular quantum numbers, which stand off the nuclei and thus are hard to be freed in the multiphoton regime. This mechanism works for hydrogen, helium, and probably some other atoms if two-color laser fields are properly tuned.

Molecular Free Electron Vortices in Photoionization by Polarization-Tailored Ultrashort Laser Pulses

Atomic and molecular free electron vortices (FEVs), characterized by their spiral-shaped momentum distribution, have recently attracted a great deal of attention due to their varied shapes and their unusual topological properties. Shortly after their theoretical prediction by the single-photon ionization (SPI) of He atoms using pairs of counterrotating circularly polarized attosecond pulses, FEVs have been demonstrated experimentally by the multiphoton ionization (MPI) of alkali atoms using single-color and bichromatic circularly polarized femtosecond pulse sequences. Recently, we reported on the analysis of the experimental results employing a numerical model based on the ab initio solution of the time-dependent Schrödinger equation (TDSE) for a two-dimensional (2D) atom interacting with a polarization-shaped ultrashort laser field. Here, we apply the 2D TDSE model to study molecular FEVs created by SPI and MPI of a diatomic molecule using polarization-tailored single-color and bichromatic femtosecond pulse sequences. We investigate the influence of the coupled electron-nuclear dynamics on the vortex formation dynamics and discuss the effect of CEP- and rotational averaging on the photoelectron momentum distribution. By analyzing how the molecular structure and dynamics is imprinted in the photoelectron spirals, we explore the potential of molecular FEVs for ultrafast spectroscopy.

Electronic coherences in nonadiabatic molecular photophysics revealed by time-resolved photoelectron spectroscopy

Time-resolved photoelectron spectroscopy (TRPES) is a promising technique for the study of ultrafast molecular processes, such as the nonadiabatic dynamics taking place at conical intersections. Directly accessing the evolution of the coherences generated at the conical intersection should provide most valuable dynamical information. However, the signals are dominated by background contributions due to state populations, and most theoretical treatments completely neglect the role of the coherences. Here we show that distinguishable signatures of molecular coherences appear in TRPES. These can be recorded using currently available ultrashort pulses and unambiguously extracted at the postprocessing stage. The technique thus provides direct access to nonadiabatic coherence dynamics.

The influence of molecular alignment and orientation in the ground state and excited state on the resonance-enhanced multi-photon ionization dynamics

We explore the influence of molecular alignment and orientation in the ground and excited states on the ionization probability, photoelectron angular distribution (PAD), energy-resolved photoelectron energy spectrum (PES) and two-dimensional momentum spectrum in the resonance-enhanced multiphoton ionization (REMPI) process. The calculated results for the LiH molecule show that molecular pre-alignment and -orientation have different effects on molecular photoionization. The ionization probability and energy-resolved photoelectron spectrum are associated with molecular pre-alignment. The angular distribution of photoelectrons and angular distribution of the momentum spectra are closely dependent on molecular pre-orientation. The ionization probability is also related to the center time and overlap area of the pump and probe pulses.

Investigation of photoassociation with full-dimensional thermal-random-phase wavefunctions

By taking the femtosecond two-photon photoassociation (PA) of magnesium atoms as an example, we propose a method to calculate the thermally averaged population, which is transferred from the ground X¹Σ_g ⁺ state to the target (1)¹Π_g state, based on the solution of full-dimensional time-dependent Schrödinger equation. In this method, named as method A, we use thermal-random-phase wavefunctions with the random phases expanded in both the vibrational and rotational degrees of freedom to model the thermal ensemble of the initial eigenstates. This method is compared with the other two methods (B and C) at different temperatures. Method B is also based on thermal-random-phase wavefunctions, except that the random-phase expansion is merely used for the vibrational degree of freedom. Method C is based on the independent propagation of every initial eigenstate, instead of the thermal-random-phase wavefunctions. Taking the (1)¹Π_g state as the target state, it is found that although these three methods can present the same population on the (1)¹Π_g state, the computation efficiency of method A increases dramatically with the increase in temperature. With this efficient method A, we find that the PA process at 1000 K can also induce rotational coherence, i.e., the molecular field-free alignment in the excited electronic states.

Self-referencing circular dichroism ion yield measurements for improved statistics using femtosecond laser pulses

The combination of circular dichroism with laser mass spectrometry via the measurement of ion yields is a powerful tool in chiral recognition, but the measured anisotropies are generally weak. The method presented in this contribution reduces the measurement error significantly. A common path optical setup generates a pair of counter-rotating laser foci in the interaction region of a time-of-flight spectrometer. As the space focus condition is fulfilled for both foci individually, this becomes a twin-peak ion source with well separated and sufficiently resolved mass peaks. The individual control of polarization allows for in situ correction of experimental fluctuations measuring circular dichroism. Our robust optical setup produces reliable and reproducible results and is applicable for dispersion sensitive femtosecond laser pulses. In this contribution, we use 3-methyl-cyclopentanone as a prototype molecule to illustrate the evaluation procedure and the measurement principle.

Weak-field coherent control of photodissociation in polyatomic molecules

A coherent control scheme is suggested to modify the output of photodissociation in a polyatomic system. The performance of the scheme is illustrated by applying it to the ultrafast photodissociation of CH₃I in the A-band. The control scheme uses a pump laser weak field that combines two pulses of a few femtoseconds delayed in time. By varying the time delay between the pulses, the shape of the laser field spectral profile is modulated, which causes a change in the initial relative populations excited by the pump laser to the different electronic states involved in the photodissociation. Such a change in the relative populations produces different photodissociation outputs, which is the basis of the control achieved. The degree of control obtained over different photodissociation observables, like the branching ratio between the two dissociation channels of CH₃I yielding I(²P_3/2) and I*(²P_1/2) and the fragment angular distributions associated with each channel, is investigated. These magnitudes are found to oscillate strongly with the time delay, with the branching ratio changing by factors between two and three. Substantial variations of the angular distributions also indicate that the scheme provides a high degree of control. Experimental application of the scheme to general polyatomic photodissociation processes should be straightforward.

Time-resolved radiation chemistry: femtosecond photoelectron spectroscopy of electron attachment and photodissociation dynamics in iodide-nucleobase clusters

Iodide-nucleobase (I-·N) clusters studied by time-resolved photoelectron spectroscopy (TRPES) are an opportune model system for examining radiative damage of DNA induced by low-energy electrons. By initiating charge transfer from iodide to the nucleobase and following the dynamics of the resulting transient negative ions (TNIs) with femtosecond time resolution, TRPES provides a novel window into the chemistry triggered by the attachment of low-energy electrons to nucleobases. In this Perspective, we examine and compare the dynamics of electron attachment, autodetachment, and photodissociation in a variety of I-·N clusters, including iodide-uracil (I-·U), iodide-thymine (I-·T), iodide-uracil-water (I-·U·H2O), and iodide-adenine (I-·A), to develop a more unified representation of our understanding of nucleobase TNIs. The experiments probe whether dipole-bound or valence-bound TNIs are formed initially and the subsequent time evolution of these species. We also provide an outlook for forthcoming applications of TRPES to larger iodide-containing complexes to enable the further investigation of microhydration dynamics in nucleobases, as well as electron attachment and photodissociation in more complex nucleic acid constituents.

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.

Ultrafast imaging of laser-controlled non-adiabatic dynamics in NO2 from time-resolved photoelectron emission

Imaging and controlling the ultrafast conical intersection dynamics in NO₂ using the latest advances in attosecond and light-synthesizer technology.

Na2 Vibrating in the Double-Well Potential of State 2 1Σu+ (JM = 00): A Pulsating "Quantum Bubble" with Antagonistic Electronic Flux

The theory of concerted electronic and nuclear flux densities associated with the vibration and dissociation of a multielectron nonrotating homonuclear diatomic molecule (or ion) in an electronic state ^2S+1Σ_g,u⁺ (JM = 00) is presented. The electronic population density, nuclear probability density, and nuclear flux density are isotropic. A theorem of Barth , presented in this issue, shows that the electronic flux density (EFD) is also isotropic. Hence, the evolving system appears as a pulsating, or exploding, "quantum bubble". Application of the theory to Na₂ vibrating in the double-minimum potential of the 2  ¹Σ_u⁺ (JM = 00) excited state reveals that the EFD consists of two antagonistic components. One arises from electrons that flow essentially coherently with the nuclei. The other, which is oppositely directed (i.e., antagonistic) and more intense, is due to the transition in electronic structure from "Rydberg" to "ionic" type as the nuclei traverse the potential barrier between inner and outer potential wells. This "transition" component of the EFD rises and falls sharply as the nuclei cross the barrier.

Revealing Deactivation Pathways Hidden in Time-Resolved Photoelectron Spectra

Time-resolved photoelectron spectroscopy is commonly employed with the intention to monitor electronic excited-state dynamics occurring in a neutral molecule. With the help of theory, we show that when excited-state processes occur on similar time scales the different relaxation pathways are completely obscured in the total photoionization signal recorded in the experiment. Using non-adiabatic molecular dynamics and Dyson norms, we calculate the photoionization signal of cytosine and disentangle the transient contributions originating from the different deactivation pathways of its tautomers. In the simulations, the total signal from the relevant keto and enol tautomers can be decomposed into contributions either from the neutral electronic state populations or from the distinct mechanistic pathways across the multiple potential surfaces. The lifetimes corresponding to these contributions cannot be extracted from the experiment, thereby illustrating that new experimental setups are necessary to unravel the intricate non-adiabatic pathways occurring in polyatomic molecules after irradiation by light.

Time-dependent quantum simulation of coronene photoemission spectra

Photoelectron spectroscopy is usually described by a simple equation that relates the binding energy of the photoemitted electron, Ebinding, its kinetic energy, Ekinetic, the energy of the ionizing photon, Ephoton, and the work function of the spectrometer, ϕ, Ebinding = Ephoton - Ekinetic - ϕ. Behind this equation there is an extremely rich physics, which we describe here using as an example a relatively simple conjugated molecule, namely coronene. The theoretical analysis of valence band and C1s core level photoemission spectra showed that multiple excitations play an important role in determining the intensities of the final spectrum. An explicit, time-evolving model is applied, which is able to count all possible photo-excitations occurring during the photoemission process, showing that they evolve on a short time-scale, of about 10 fs. The method reveals itself to be a valid approach to reproduce photoemission spectra of polycyclic aromatic hydrocarbons (PAHs).

A proposed new scheme for vibronically resolved time-dependent photoelectron spectroscopy: pump-repump-continuous wave-photoelectron spectroscopy (prp-cw-pes)

We propose a new scheme for time-resolved photoelectron spectroscopy denoted as pump-repump-continuous wave-photoelectron spectroscopy (prp-cw-pes). This scheme is comprised of two femtosecond laser (pump) pulses under cw illumination (probe). By changing the time-delay between pump and repump lasers one can manipulate the populations of vibronic levels in electronic excited states. The cw laser acts on for a long time and establishes resonance between excited states and the continuum photo-ionized states. Sharp spectra can be obtained from the resonance condition [formula: see text]. The intensities in the spectra are sensitive to the time-delay between the pump-repump pulses, but only depend on the populations of excited states, not the phase relations (coherence). As a result, each time-delayed snapshot spectrum is a weighted sum of so-called fingerprints, where a fingerprint is the vibrationally resolved photoelectron spectrum for a single vibronic excited state. The latter information can potentially be simulated reliably using vibronic models and wave packet propagation methods. In the easiest application of the experiment, different time-delays produce different spectra, for a single molecular system. This wealth of experimental data can be fitted to an, ideally small, set of theoretical fingerprints by adjusting the populations as fitting parameters. This technique might be able to distinguish between closely related molecular species. Adopting a different viewpoint, the proposed scheme can also be employed to monitor the time-dependent dynamics by changing the phase relationship between the pump and repump laser that can be viewed as a "control mechanism" employed in wave packet interferometry. Simplifications arise as the change in the spectra is due to the changing populations, not because of the coherence. In this paper, we outline the ideas behind the scheme and illustrate the ideas theoretically using simple model systems.

Weak-field laser phase modulation coherent control of asymptotic photofragment distributions

Coherent control of the asymptotic photofragment state-resolved distributions by means of laser phase modulation in the weak-field limit is demonstrated computationally for a polyatomic molecule. The control scheme proposed applies a pump laser field consisting of two pulses delayed in time. Phase modulation of the spectral bandwidth profile of the laser field is achieved by varying the time delay between the pulses. The underlying equations show that such a phase modulation is effective in order to produce control effects on the asymptotic, long-time limit photofragment distributions only when the bandwidths of the two pulses overlap in a frequency range. The frequency overlap of the pulses gives rise to an interference term which is responsible for the modulation of the spectral profile shape. The magnitude of the range of spectral overlap between the pulses becomes an additional control parameter. The control scheme is illustrated computationally for the asymptotic photofragment state distributions produced from different scenarios of the Ne-Br2 predissociation. An experimental application of the control scheme is found to be straightforward.

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.

Robust quantum control by a single-shot shaped pulse

Considering the problem of the control of a two-state quantum system by an external field, we establish a general and versatile method allowing the derivation of smooth pulses which feature the properties of high fidelity, robustness, and low area. Such shaped pulses can be interpreted as a single-shot generalization of the composite pulse-sequence technique with a time-dependent phase.

Fingerprints of Adiabatic versus Diabatic Vibronic Dynamics in the Asymmetry of Photoelectron Momentum Distributions

When the Born-Oppenheimer approximation is valid, electrons adiabatically follow the nuclear motion in molecules. For strong nonadiabatic coupling between electronic states, one encounters a diabatic motion where the electrons remain local and do not adapt to molecular geometry changes. We show that the mentioned limiting cases are reflected differently in the asymmetry of time-resolved photoelectron momentum distributions. Whereas for adiabatic dynamics, the asymmetry directly maps the time-dependent average nuclear momentum, in the diabatic case, the asymmetry is determined by a nonclassical interference effect arising from the mixing of wave function components in different electronic states, which is present at times nonadiabatic transitions take place.

CONTROLLING ABOVE-THRESHOLD DISSOCIATION BRANCHING RATIOS OF HD+ WITH FEMTOSECOND LASER PULSE TRAIN

Above-threshold dissociation (ATD) process of the molecular ions HD+ steered by a femtosecond laser pulse train (LPT) is investigated theoretically using the time-dependent quantum wave packet method. Energy-dependent distributions of ATD fragments are analyzed by using an asymptotic-flow expression in the momentum space. It is found that fragment kinetic energy spectra shift to low energy region with increasing pulse number of LPT. The photofragment branching ratio between the 1sσg and 2pσu dissociation channels is sensitive to the pulse number of LPT. The momentum distribution of the ATD fragments is discussed in detail.

Generating molecular rovibrational coherence by two-photon femtosecond photoassociation of thermally hot atoms

The formation of diatomic molecules with rotational and vibrational coherence is demonstrated experimentally in free-to-bound two-photon femtosecond photoassociation of hot atoms. In a thermal gas at a temperature of 1000 K, pairs of magnesium atoms, colliding in their electronic ground state, are excited into coherent superpositions of bound rovibrational levels in an electronically excited state. The rovibrational coherence is probed by a time-delayed third photon, resulting in quantum beats in the UV fluorescence. A comprehensive theoretical model based on ab initio calculations rationalizes the generation of coherence by Franck-Condon filtering of collision energies and partial waves, quantifying it in terms of an increase in quantum purity of the thermal ensemble. Our results open the way to coherent control of a binary reaction.

Excited-state dynamics of CS2 studied by photoelectron imaging with a time resolution of 22 fs

The ultrafast dynamics of CS(2) in the (1)B(2)((1)Σ(u)(+)) state was studied by photoelectron imaging with a time resolution of 22 fs. The photoelectron signal intensity exhibited clear vibrational quantum beats due to wave packet motion. The signal intensity decayed with a lifetime of about 400 fs. This decay was preceded by a lag of around 30 fs, which was considered to correspond to the time for a vibrational wave packet to propagate from the Franck-Condon region to the region where predissociation occurred. The photoelectron angular distribution remained constant when the pump-probe delay time was varied. Consequently, variation of the electronic character caused by the vibrational wave packet motion was not identified within the accuracy of our measurements.

Time-resolved photoelectron spectroscopy: from wavepackets to observables

Time-resolved photoelectron spectroscopy (TRPES) is a powerful tool for the study of intramolecular dynamics, particularly excited state non-adiabatic dynamics in polyatomic molecules. Depending on the problem at hand, different levels of TRPES measurements can be performed: time-resolved photoelectron yield; time- and energy-resolved photoelectron yield; time-, energy-, and angle-resolved photoelectron yield. In this pedagogical overview, a conceptual framework for time-resolved photoionization measurements is presented, together with discussion of relevant theory for the different aspects of TRPES. Simple models are used to illustrate the theory, and key concepts are further amplified by experimental examples. These examples are chosen to show the application of TRPES to the investigation of a range of problems in the excited state dynamics of molecules: from the simplest vibrational wavepacket on a single potential energy surface; to disentangling intrinsically coupled electronic and nuclear motions; to identifying the electronic character of the intermediate states involved in non-adiabatic dynamics by angle-resolved measurements in the molecular frame, the most complete measurement.

Time-resolved photoelectron imaging of S2 → S1 internal conversion in benzene and toluene

Ultrafast internal conversion of benzene and toluene from the S(2) states was studied by time-resolved photoelectron imaging with a time resolution of 22 fs. Time-energy maps of the photoelectron intensity and the angular anisotropy were generated from a series of photoelectron images. The photoelectron kinetic energy distribution exhibits a rapid energy shift and intensity revival, which indicates nuclear motion on the S(2) adiabatic surface, while the ultrafast evolution of the angular anisotropy revealed a change in the electronic character of the S(2) adiabatic surface. From their decay profiles of the total photoelectron intensity, the time constants of 48 ± 4 and 62 ± 4 fs were determined for the population decay from the S(2) states in benzene and toluene, respectively.

Zeptosecond precision pulse shaping

We investigate the temporal precision in the generation of ultrashort laser pulse pairs by pulse shaping techniques. To this end, we combine a femtosecond polarization pulse shaper with a polarizer and employ two linear spectral phase masks to mimic an ultrastable common-path interferometer. In an all-optical experiment we study the interference signal resulting from two temporally delayed pulses. Our results show a 2σ-precision of 300 zs = 300 × 10(-21) s in pulse-to-pulse delay. The standard deviation of the mean is 11 zs. The obtained precision corresponds to a variation of the arm's length in conventional delay stage based interferometers of 0.45 Å. We apply these precisely generated pulse pairs to a strong-field quantum control experiment. Coherent control of ultrafast electron dynamics via photon locking by temporal phase discontinuities on a few attosecond timescale is demonstrated.