On the dynamics of rotationally broad, spatially aligned wave packets

Laser-Induced Coulomb Explosion Imaging of Aligned Molecules and Molecular Dimers

We discuss how Coulomb explosion imaging (CEI), triggered by intense femtosecond laser pulses and combined with laser-induced alignment and covariance analysis of the angular distributions of the recoiling fragment ions, provides new opportunities for imaging the structures of molecules and molecular complexes. First, focusing on gas phase molecules, we show how the periodic torsional motion of halogenated biphenyl molecules can be measured in real time by timed CEI, and how CEI of one-dimensionally aligned difluoroiodobenzene molecules can uniquely identify four structural isomers. Next, focusing on molecular complexes formed inside He nanodroplets, we show that the conformations of noncovalently bound dimers or trimers, aligned in one or three dimensions, can be determined by CEI. Results presented for homodimers of CS₂, OCS, and bromobenzene pave the way for femtosecond time-resolved structure imaging of molecules undergoing bimolecular interactions and ultimately chemical reactions. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Time-resolved study of laser emission in nitrogen gas pumped by two near IR femtosecond laser pulses

The time profile of a lasing signal at 391.4 nm emitted by a weakly ionized gas of nitrogen molecules at low pressure is measured under double excitation with intense femtosecond laser pulses at 800 nm. An abrupt decrease in emission occurs at the time of arrival of the second pulse. It is explained by a transfer of population from ground to first excited ionic level and by a disruption of coherence, terminating the conditions for lasing in a V-scheme without population inversion.

Ionization induced dynamic alignment of water

Two-body dissociation resulting from strong-field double ionization of water is investigated. Two distinct features are seen in the alignment of the fragment momenta with respect to the laser polarization. One feature shows alignment of the H-OH axis with the laser polarization, while the other indicates polarization alignment normal to the H-OH axis. By analyzing kinematic differences between the OH⁺/D⁺ and OD⁺/H⁺ channels of HOD, these two alignment features are shown to result from dissociation from different states in the dication. Only dissociation from one of these states has an alignment dependence consistent with predictions of sequential strong-field tunneling ionization models. The alignment dependence of dissociation from the other state can only be explained by dynamic alignment launched by the unbending of the molecule during ionization.

The Effect of Nuclear-Quadrupole Coupling in the Laser-Induced Alignment of Molecules

We present a theoretical study of the time-dependent laser alignment of molecules taking into account the hyperfine coupling due to nuclear-quadrupole interactions. The coupling of nuclear spins to the overall angular momentum of molecules significantly influences their rotational dynamics. Here, we systematically analyze the impact of the nuclear-quadrupole coupling on the rotational dynamics of the linear and the asymmetric-top diiodobenzene molecule induced by external laser fields. We explore different regimes of pulse shapes and laser-pulse intensities and detail under which conditions the quadrupole coupling cannot be neglected in the description of the laser alignment of molecules.

Laser-Directed Assembly of Nanorods of 2D Materials

Herein, the previously unrealized ability to grow nanorods and nanotubes of 2D materials using femtosecond laser irradiation is demonstrated. In as short as 20 min, nanorods of tungsten disulfide, molybdenum disulfide, graphene, and boron nitride are grown in solutions. The technique fragments nanoparticles of the 2D materials from bulk flakes and leverages molecular scale alignment by nonresonant intense laser pulses to direct their assembly into nanorods up to several micrometers in length. The laser treatment process is found to induce phase transformations in some of the materials, and also results in the modification of the nanorods with functional groups from the solvent atoms. Notably, the WS₂ nanoparticles, which are ablated from semiconducting 2H WS₂ crystallographic phase flakes, reassemble into nanorods consisting of the 1T metallic phase. Due to this transition, and the 1D nature of the fabricated nanorods, the WS₂ nanorods display substantial improvements in electrical conductivity and optical transparency when employed as transparent conductors.

Impulsive alignment of 4He-CH3I: A theoretical study

We simulate the non-adiabatic laser alignment of the weakly bound ⁴He-CH₃I complex based on a quantum mechanical wave packet calculation for a model He-CH₃I interaction potential. Two different regimes are found depending on the laser intensity. At intensities typical of non-adiabatic alignment experiments, the rotational dynamics resembles that of the isolated molecule. This is attributed to the fact that after the initial prompt alignment peak the complex rapidly dissociates. The subsequent revival pattern is due to the free rotation of the molecule detached from the helium atom. It is superimposed to a flat background corresponding to ∼20% of the wave packet which remains bound, containing lower rotational excitation. At lower intensities, dissociation is avoided but the rotational excitation is not high enough to provide an efficient alignment and a broad non-regular structure is observed. Besides, the interaction of the He atom with the molecule quenches any possible alignment. These interpretations are based on the calculation of different observables related to the rotational motion. We compare our findings with recent experimental and theoretical results of non-adiabatic alignment of linear molecules solvated in helium nanodroplets or weakly interacting with one helium atom.

Rotational dissociation of impulsively aligned van der Waals complexes

The nonadiabatic alignment dynamics of weakly bound molecule-atom complexes, induced by a moderately intense 300 fs nonresonant laser pulse, is calculated by direct numerical solution of the time-dependent Schrödinger equation. Our method propagates the wave function according to the coupled channel equations for the complex, which can be done in a very efficient and stable manner out to large times. We present results for two van der Waal complexes, CS₂-He and HCCH-He, as respective examples of linear molecules with large and small moments of inertia. Our main result is that at intensities typical of nonadiabatic alignment experiments, these complexes rapidly dissociate. In the case of the CS₂-He complex, the ensuing rotational dynamics resembles that of isolated molecules, whereas for the HCCH-He complex, the detachment of the He atom severely perturbs and essentially quenches the subsequent rotational motion. At intensities of the laser pulse ≲2.0 × 10¹² W/cm², it is shown that the molecule-He complex can rotate and align without breaking apart. We discuss the implications of our findings for recent experiments on iodine molecules solvated in helium nanodroplets.

Energy deposition from focused terawatt laser pulses in air undergoing multifilamentation

Laser filamentation is responsible for the deposition of a significant part of the laser pulse energy in the propagation medium. We found that using terawatt laser pulses and moderately strong focusing conditions in air, more than 60 % of the pulses energy is transferred to the medium, eventually degrading into heat. This results in a strong hydrodynamic reaction of air with the generation of shock waves and associated underdense channels for each of the generated multiple filaments. In the focal zone, where filaments are close to each other, these discrete channels eventually merge to form a single cylindrical low-density tube over a ~ 1 µs timescale. We measured the maximum lineic deposited energy to be more than 1 J·m-¹.

Direct observation, study, and control of molecular superrotors

Extremely fast rotating molecules whose rotational energy is comparable with the molecular bond strength are known as "superrotors." It has been speculated that superrotors may exhibit a number of unique properties, yet only indirect evidence of these molecular objects has been reported to date. Here we demonstrate the first direct observation of molecular superrotors by detecting coherent unidirectional molecular rotation with extreme frequencies exceeding 10 THz. The technique of an "optical centrifuge" is used to control the degree of rotational excitation in an ultrabroad range of rotational quantum numbers, reaching as high as N = 95 in oxygen and N = 60 in nitrogen. State-resolved detection enables us to determine the shape of the excited rotational wave packet and quantify the effect of centrifugal distortion on the rotational spectrum. Femtosecond time resolution reveals coherent rotational dynamics with increasing coherence times at higher angular momentum. We demonstrate that molecular superrotors can be created and observed in dense samples under normal conditions where the effects of ultrafast rotation on many-body interactions, intermolecular collisions, and chemical reactions can be readily explored.

Computational studies of the x-ray scattering properties of laser aligned stilbene

The enhancement of the x-ray scattering signal from partially aligned molecular samples is investigated. The alignment properties of the studied molecular system are modeled based on the method of laser alignment. With the advances in the area of laser alignment of molecules, the application of this sample manipulation technique promises a great potential for x-ray scattering measurements. Preferential alignment of molecules in an otherwise amorphous sample leads to constructive interference and thus increases the scattering intensity. This enhances the structural information encoded in the scattering images and enables improved resolution in studies of reaction dynamics, as in this work is shown for the example of the photo-isomerization of stilbene. We demonstrate that the scattering signal is strongly influenced by the alignment axis. Even the most basic one-dimensional alignment offers significant improvement compared to the structural information provided by a randomly oriented sample. Although the signal is sensitive to the uncertainty in the alignment angle, it offers encouraging results even at realistic alignment uncertainties.

Molecular rotational excitation by strong femtosecond laser pulses

We study the rotational wave packet created by nonadiabatic rotational excitation of molecules with strong femtosecond laser pulses. The applicable condition of the Delta-Kick method is obtained by comparing the laser intensity and pulse duration dependences of the wave packet calculated with different methods. The wave packet evolution is traced analytically with the Delta-Kick method. The calculations demonstrate that the rotational populations can be controlled for the rotational wave packet created by two femtosecond laser pulses. The evolution of the rotational wave packet with controlled populations produces interference patterns with exotic spatial symmetries. These calculations are validated by comparing the theoretical calculations with our experimental measurements for the rotational wave packet created by thermal ensemble CO(2) and two strong femtosecond laser pulses. Potential applications in molecular science are also discussed for the rotational wave packet with controlled populations and spatial symmetries.

Field-free molecular alignment for studies using x-ray pulses from a synchrotron radiation source

A short, intense laser pulse may be employed to create a spatially aligned molecular sample that persists after the laser pulse is over. We theoretically investigate whether this impulsive molecular alignment technique may be exploited for experiments using x-ray pulses from a third-generation synchrotron radiation facility. Using a linear rigid rotor model, the alignment dynamics of model molecular systems with systematically increasing size is calculated utilizing both a quantum density matrix formalism and a classical ensemble method. For each system, the alignment dynamics obtained for a 95 ps laser is compared with that obtained for a 10 ps laser pulse. The average degree of alignment after the laser pulse, as calculated quantum mechanically, increases with the size of the molecule. This effect is quantitatively reproduced by the classical calculations. The average degree of impulsive alignment is high enough to induce a pronounced linear dichroism in resonant x-ray absorption using the intense 100 ps x-ray pulses currently available. However, for structural studies based on elastic x-ray scattering, bright x-ray pulses with a duration of 1 ps or shorter will be required in order to make full use of impulsive molecular alignment.

Coherent control of molecular alignment of homonuclear diatomic molecules by analytically designed laser pulses

We present an analytic scheme for designing laser pulses to manipulate the field-free molecular alignment of a homonuclear diatomic molecule. The scheme is based on the use of a generalized pulse-area theorem and makes use of pulses constructed around two-photon resonant frequencies. In the proposed scheme, the populations and relative phases of the rovibrational states of the molecule are independently controlled utilizing changes in the laser intensity and in the carrier-envelope phase difference, respectively. This allows us to create the correct coherent superposition of rovibrational states needed to achieve optimal molecular alignment. The validity and efficiency of the scheme are demonstrated by explicit application to the H(2) molecule. The analytically designed laser pulses are tested by exact numerical solutions of the time-dependent Schrodinger equation including laser-molecule interactions to all orders of the field strength. The design of a sequence of pulses to further enhance molecular alignment is also discussed and tested. It is found that the rotating wave approximation used in the analytic design of the laser pulses leads to small errors in the prediction of the relative phase of the rotational states. It is further shown how these errors may be easily corrected.

Coherent manipulations of atoms using laser light

The internal structure of a particle - an atom or other quantum system in which the excitation energies are discrete - undergoes change when exposed to pulses of near-resonant laser light. This tutorial review presents basic concepts of quantum states, of laser radiation and of the Hilbert-space statevector that provides the theoretical portrait of probability amplitudes - the tools for quantifying quantum properties not only of individual atoms and molecules but also of artificial atoms and other quantum systems. It discusses the equations of motion that describe the laser-induced changes (coherent excitation), and gives examples of laser-pulse effects, with particular emphasis on two-state and three-state adiabatic time evolution within the rotating-wave approximation. It provides pictorial descriptions of excitation based on the Bloch equations that allow visualization of two-state excitation as motion of a three-dimensional vector (the Bloch vector). Other visualization techniques allow portrayal of more elaborate systems, particularly the Hilbert-space motion of adiabatic states subject to various pulse sequences. Various more general multilevel systems receive treatment that includes degeneracies, chains and loop linkages. The concluding sections discuss techniques for creating arbitrary pre-assigned quantum states, for manipulating them into alternative coherent superpositions and for analyzing an unknown superposition. Appendices review some basic mathematical concepts and provide further details of the theoretical formalism, including photons, pulse propagation, statistical averages, analytic solutions to the equations of motion, exact solutions of periodic Hamiltonians, and population-trapping "dark" states.

Measurement of the field-free alignment of diatomic molecules

An apparatus was constructed to experimentally quantify the field-free alignment of diatomic molecules irradiated by strong femtosecond laser pulses. In this apparatus, both homodyne and pure heterodyne detections were realized. The alignment signal is proportional to [<cos(2)theta> - 1/3](2) for homodyne detection and (<cos(2)theta> - 1/3) for pure heterodyne detection, where theta is the polar angle between the molecular axis and the laser polarization direction. Fourier transform spectra of the homodyne signal and the pure heterodyne signal were also studied. By comparing the alignment signal and its Fourier transform spectrum with the numerical calculation of the time-dependent Schrödinger equation, we demonstrated that the pure heterodyne signal directly reproduced the alignment parameter <cos(2)theta>, and its Fourier transform spectrum provided information regarding the populations of different J states in the rotational wavepacket.

Vibrationally selective optimal control of alignment and orientation using infrared laser pulses: application to carbon monoxide

Optimal control methods are used to study molecular alignment and orientation using infrared laser pulses. High order molecule-field interactions are taken into account through the use of the electric-nuclear Born-Oppenheimer approximation [G. G. Balint-Kurti et al., J. Chem. Phys. 122, 084110 (2005)]. High degrees of alignment and orientation are achieved by optimized infrared laser pulses of duration on the order of one rotational period of the molecule. It is shown that, through the incorporation of a vibrational projection operator into the optimization procedure, it is possible not only to maximize the alignment and orientation but also to bring the whole system into a single prescribed vibrational manifold. Numerical calculations are performed for carbon monoxide using ab initio potential energies computed in the presence of external electric fields.

Characterization of intensity-dependent optical rotation phenomena in chiral molecules in solution

The rotation of the plane of polarization of linearly polarized light by chiral molecules in solution is due to a forward scattering event. Ordinary optical rotation, a single-photon effect, is independent of intensity. As the light intensity is increased, other effects can appear, such as two-photon scattering or alignment of the molecule by one photon and scattering with a change of polarization by another. Both of these effects result in intensity-dependent (or nonlinear) optical rotation. A polarimeter was used to measure the nonlinear optical rotation of solutions in a heterodyne experiment. No nonlinear optical rotation was found in molecules lacking an absorption band near the laser frequency. In the three pyrimidine nucleosides studied, which do have such an absorption band, a nonlinear optical rotation was identified that was cumulative with each laser pulse. The effect persisted with a time constant that was on the order of seconds and characteristic of the molecule.

Optimal control of molecular alignment in dissipative media

We explore the controllability of nonadiabatic alignment in dissipative media, and the information content of control experiments regarding the bath properties and the bath system interactions. Our approach is based on a solution of the quantum Liouville equation within the multilevel Bloch formalism, assuming Markovian dynamics. We find that the time and energy characteristics of the laser fields that produce desired alignment characteristics at a predetermined instant respond in distinct manners to decoherence and to population relaxation, and are sensitive to both time scales. In particular, the time-evolving spectral composition of the optimal pulse mirrors the time-evolving rotational composition of the wave packet, and points to different mechanisms of rotational excitation in isolated systems, in systems subject to a decoherering bath, and in ones subject to a population relaxing bath.

Enhanced alignment and orientation of polar molecules by vibrational resonant adiabatic passage

The authors show that polar molecules can be adiabatically aligned and oriented by laser pulses more efficiently when the laser frequencies are vibrationally resonant. The aligned molecules are found in a superposition of vibrational pendular states, each associated with the alignment of the rotor in one vibrational state. The authors construct the dressed potential associated with this mechanism. Values of detunings and field amplitudes are given to optimize the degree of alignment and orientation for the CO molecule.

Role of rotational temperature in adiabatic molecular alignment

One-dimensional alignment of molecules in the adiabatic limit, where the pulse duration greatly exceeds the molecular rotational periods, is studied experimentally. Four different asymmetric top molecules (iodobenzene, p-diiodobenzene, 3,4-dibromothiophene, and 4,4'-dibromobiphenyl), rotationally cooled through a high pressure supersonic pulsed valve, are aligned by a 9-ns-long pulse. Their orientations are measured through Coulomb explosion, induced by a 130-fs-long pulse, and by recording the direction of the recoiling ions. The paper focuses on the crucial role of the initial rotational temperature for the degree of alignment. In particular, we show that at molecular temperatures in the 1 K range very strong alignment is obtained already at intensities of a few times 10(11) W/cm2 for all four molecules. At the highest intensities (approximately 10(12) W/cm2) the molecules can tolerate without ionizing <cos2 theta> >or=0.92 in the case of iodobenzene. This is the strongest degree of alignment ever reported for any molecule.

Time-dependent alignment of molecules trapped in octahedral crystal fields

The hindered rotational states of molecules confined in crystal fields of octahedral symmetry, and their time-dependent alignment obtained by pulsed nonresonant laser fields, are studied computationally. The control over the molecular axis direction is discussed based on the evolution of the rotational wave packet generated in the cubic crystal-field potential. The alignment degree obtained in a cooperative case, where the alignment field is applied in a favorable crystal-field direction, or in a competitive direction, where the crystal field has a saddle point, is presented. The investigation is divided into two time regimes where the pulse duration is either ultrashort, leading to nonadiabatic dynamics, or long with respect to period of molecular libration, which leads to synchronous alignment due to nearly adiabatic following. The results are contrasted to existing gas phase studies. In particular, the irregularity of the crystal-field energies leads to persistent interference patterns in the alignment signals. The use of nonadiabatic alignment for interrogation of crystal-field energetics and the use of adiabatic alignment for directional control of molecular dynamics in solids are proposed as practical applications.

Dissipative dynamics of laser induced nonadiabatic molecular alignment

Nonadiabatic alignment induced by short, moderately intense laser pulses in molecules coupled to dissipative environments is studied within a nonperturbative density matrix theory. We focus primarily on exploring and extending a recently proposed approach [Phys. Rev. Lett. 95, 113001 (2005)], wherein nonadiabatic laser alignment is used as a coherence spectroscopy that probes the dissipative properties of the solvent. To that end we apply the method to several molecular collision systems that exhibit sufficiently varied behavior to represent a broad variety of chemical environments. These include molecules in low temperature gas jets, in room temperature gas cells, and in dense liquids. We examine also the possibility of prolonging the duration of the field free (post-pulse) alignment in dissipative media by a proper choice of the system parameters.

Damped and thermal motion of laser-aligned hydrated macromolecule beams for diffraction

We consider a monodispersed Rayleigh droplet beam of water droplets doped with proteins. An intense infrared laser is used to align these droplets. The arrangement has been proposed for electron- and x-ray-diffraction studies of proteins which are difficult to crystallize. This paper considers the effect of thermal fluctuations on the angular spread of alignment in thermal equilibrium, and relaxation phenomena, particularly the damping of oscillations excited as the molecules enter the field. The possibility of adiabatic alignment is also considered. We find that damping times in a high-pressure gas cell as used in x-ray-diffraction experiments are short compared with the time taken for molecules to traverse the beam and that a suitably shaped field might be used for electron-diffraction experiments in vacuum to provide adiabatic alignment, thus obviating the need for a damping gas cell.

Field-free alignment of molecules observed with high-order harmonic generation

High-order harmonic generation is demonstrated to provide a sensitive way for an extensive study of dynamic processes in the field-free alignment of strong-field-induced molecular rotational wave packets. The time-dependent harmonic signal observed from field-free-aligned N2, O2, and CO2 has been found to include two sets of beat frequency for pairs of coherently populated rotational states. One of them is the well-known frequency component characterizing the field-free alignment of molecules, and the other is ascribed to the beat that arises from coherence embedded in the wave packet. We discuss the effect of each frequency component on the revival signal observed with the harmonic generation.

Optimal molecular alignment and orientation through rotational ladder climbing

We study the control by electromagnetic fields of molecular alignment and orientation in a linear, rigid-rotor model. With the help of a monotonically convergent algorithm, we find that the optimal field is in the microwave part of the spectrum and acts by resonantly exciting the rotation of the molecule progressively from the ground state, i.e., by rotational ladder climbing. This mechanism is present not only when maximizing orientation or alignment, but also when using prescribed target states that simultaneously optimize the efficiency of orientation/alignment and its duration. The extension of the optimization method to consider a finite rotational temperature is also presented.

Intense laser alignment in dissipative media as a route to solvent dynamics

We extend the concept of alignment by short intense pulses to dissipative environments within a density matrix formalism and illustrate the application of this method as a probe of the dissipative properties of dense media. In particular, we propose a means of disentangling rotational population relaxation from decoherence effects via strong laser alignment. We illustrate also the possibility of suppressing rotational relaxation to prolong the alignment lifetime through choice of the field parameters. Implications to several disciplines and a number of potential applications are proposed.

Mapping rotational coherences onto time-resolved photoelectron imaging observables

We explore the information content of time-resolved photoelectron imaging, a potentially powerful pump-probe technique whose popularity has been rapidly growing in recent years. To that end, we identify a mapping of the alignment properties of time-evolving wave packets onto the moments of the photoelectron images and investigate its origin and consequences theoretically and numerically.

Electron diffraction from laser-aligned beams of large hydrated molecules

We consider X-ray or electron diffraction from a molecular beam of hydrated proteins. These are aligned by the polarized field of a powerful continuous infrared laser. The laser power, temperature and molecular size needed to obtain sufficient alignment accuracy for sharp diffraction patterns is estimated using a thermal average, and the resulting Dawson integral compared with the estimate based on equipartition used in our previous work. The conditions determined allow sub-nanometer resolution charge-density maps to be reconstructed from phased diffraction patterns, so that the secondary structure of the proteins can be observed.

Intense-field alignment of molecules confined in octahedral fields

The combined effect of static octahedral potential and anisotropic interactions with intense linearly polarized light on the rotational motion of linear molecules is investigated. Avoided crossings of quantized energy levels corresponding to pendular states with different degrees of alignment are found by varying the strength parameters for the light and static fields. High alignment is achieved for both cooperative and competitive choices of the relative directionality of the two fields, thus presenting means for controlling the dynamics of impurity centers with respect to the surrounding media.

Nonadiabatic alignment of asymmetric top molecules: Rotational revivals

The rotational revival structure of asymmetric top molecules, following irradiation by an intense picosecond laser pulse, is explored theoretically and experimentally. Numerically we solve nonperturbatively for the rotational dynamics of a general asymmetric top subject to a linearly polarized intense pulse, and analyze the dependence of the dynamical alignment on the field and system parameters. Experimentally we use time-resolved photofragment imaging to measure the alignment of two molecules with different asymmetry, iodobenzene, and iodopentafluorobenzene. Our numerical results explain the experimental observations and generalize them to other molecules. The rotational revival structure of asymmetric tops differs qualitatively from the intensively studied linear top case. Potentially it provides valuable structural information about molecules.

Observation of enhanced field-free molecular alignment by two laser pulses

We show experimentally that field-free alignment of iodobenzene molecules, induced by a single, intense, linearly polarized 1.4-ps-long laser pulse, can be strongly enhanced by dividing the pulse into two optimally synchronized pulses of the same duration. For a given total energy of the two-pulse sequence the degree of alignment is maximized with an intensity ratio of 1:3 and by sending the second pulse near the time where the alignment created by the first pulse peaks.

Alignment of molecules in pulsed resonant laser fields

We investigate by numerical simulations the dynamics of alignment of linear molecules in resonant pulsed laser fields and its dependence on pulse length, field strength, and molecular parameters. We propose an analytical short-time approximation for the time-dependent wave packets. We provide a theoretical basis for the occurrence of saturation in the rotational pumping. We present a formula to predict the time at which the maximum alignment occurs. We discuss the magnitude of the laser-induced alignment and we relate it to a theoretical upper limit.

Nonadiabatic alignment of asymmetric top molecules: field-free alignment of iodobenzene

Nonadiabatic laser alignment of an asymmetric top molecule is studied using the combination of a quantum dynamical theory and time-resolved photofragment imaging experiments. In particular, the degree of alignment of iodobenzene, induced by an intense, linearly polarized picosecond laser pulse, is calculated and measured. Pronounced alignment is obtained under field-free conditions.