Laser-induced Molecular Alignment Research Articles

Eliminating molecular-alignment dephasing with a phase-modulated femtosecond laser pulse

Alignment dephasing caused by centrifugal distortion is a significant effect accompanying laser-induced field-free molecular alignment. Centrifugal distortion is the manifestation of the intrinsic nonrigidity of molecules, which is especially prominent when molecules are excited to high angular velocities. In this work, we show that this type of dephasing can be almost completely eliminated by modulating the phase of the femtosecond laser pulse. Nearly perfect molecular alignment can be achieved as if the molecules were ideal rigid rotors. The dephasing effect can be cancelled in various time windows by tuning the modulation strength parameter. The dephasing cancellation mechanism is explained by considering the relative phases of the eigenstates forming the rotational wave packet. This work is of great significance to the experiment and dynamics studies of molecular alignment.

Non-Markovian collisional dynamics probed with laser-aligned molecules

The Markov, as well as the secular, approximations are key assumptions that have been widely used to model decoherence in a large variety of open quantum systems, but, as far as intermolecular collisions are considered, very little has been done in the time domain. In order to probe the limits of both approximations, we here study the influence of pressure on the alignment revivals (echoes) created in properly chosen gas mixtures (HCl and ${\mathrm{CO}}_{2}$, pure and diluted in He) by one (two) intense and short laser pulse(s). Experiments and direct predictions using molecular-dynamics simulations consistently demonstrate, through analyses at very short times $(<15 \mathrm{ps})$ after the laser kick(s), the breakdown of these approximations in some of the selected systems. We show that the nonadiabatic laser-induced molecular alignment technique and model used in this paper directly provide detailed information on the physical mechanisms involved in the collisional dissipation. Besides this ``fundamental'' interest, our findings also have potential practical applications for radiative heat transfer in planetary atmospheres and climate studies. Indeed, short time delays in the dipole autocorrelation function monitoring the light absorption spectrum correspond to large detunings from the optical resonances in the frequency domain, thus influencing the atmospheric transparency windows. Furthermore, the fact that the approach tested here for linear rotors can potentially be applied to almost any gas mixture (including, for instance, nonlinear and/or reacting molecules) further strengthens and broadens the perspectives that it opens.

Laser-induced dynamic alignment of the HD molecule without the Born-Oppenheimer approximation.

Laser-induced molecular alignment is well understood within the framework of the Born-Oppenheimer (BO) approximation. Without the BO approximation, however, the concept of molecular structure is lost, making it hard to precisely define alignment. In this work, we demonstrate the emergence of alignment from the first-ever non-BO quantum dynamics simulations, using the HD molecule exposed to ultrashort laser pulses as a few-body test case. We extract the degree of alignment from the non-BO wave function by means of an operator expressed in terms of pseudo-proton coordinates that mimics the BO-based definition of alignment. The only essential approximation, in addition to the semiclassical electric-dipole approximation for the matter-field interaction, is the choice of time-independent explicitly correlated Gaussian basis functions. We use a variational, electric-field-dependent basis-set construction procedure, which allows us to keep the basis-set dimension low while capturing the main effects of electric polarization on the nuclear and electronic degrees of freedom. The basis-set construction procedure is validated by comparing with virtually exact grid-based simulations for two one-dimensional model systems: laser-driven electron dynamics in a soft attractive Coulomb potential and nuclear rovibrational dynamics in a Morse potential.

Gradient-based reconstruction of molecular Hamiltonians and density matrices from time-dependent quantum observables

We consider a quantum system with a time-independent Hamiltonian parametrized by a set of unknown parameters $\alpha$. The system is prepared in a general quantum state by an evolution operator that depends on a set of unknown parameters $P$. After the preparation, the system evolves in time, and it is characterized by a time-dependent observable ${\cal O}(t)$. We show that it is possible to obtain closed-form expressions for the gradients of the distance between ${\cal O}(t)$ and a calculated observable with respect to $\alpha$, $P$ and all elements of the system density matrix, whether for pure or mixed states. These gradients can be used in projected gradient descent to infer $\alpha$, $P$ and the relevant density matrix from dynamical observables. We combine this approach with random phase wave function approximation to obtain closed-form expressions for gradients that can be used to infer population distributions from averaged time-dependent observables in problems with a large number of quantum states participating in dynamics. The approach is illustrated by determining the temperature of molecular gas (initially, in thermal equilibrium at room temperature) from the laser-induced time-dependent molecular alignment.

Trends in angle-resolved molecular photoelectron spectroscopy.

The field of angle-resolved molecular photoelectron spectroscopy is reviewed, with emphasis on foundations and most recent applications in different regimes of light-matter interaction. The basic formalism underlying one-photon electron angular distributions is presented, from the primary molecular frame (MF) photoemission i.e. emission from fully oriented molecules to laboratory frame (LF) observables produced from randomly oriented targets, extensions to multiphoton and strong field processes being briefly described, followed by a survey of current quantum mechanical computational approaches. The description of experimental developments is focused on the advancements in two major instrumentation fields for angle-resolved PES of molecules in the last two decades, namely charged-particle imaging spectrometers and adiabatically or impulsively laser-induced molecular alignment, together with their interplay with the remarkable characteristics achieved nowadays by the ionizing light sources and the challenging control of complex molecules in the gas phase. Aspects and applications of LF angular observables from unoriented targets are presented, with contemporary applications, especially as probes of the target electronic structure, including higher angular observables, in particular photoelectron circular dichroism (PECD) from chiral molecules, which is confirmed as a powerful chiral technique, and higher terms arising from multiphoton or non-dipole terms. Molecular frame photoelectron angular distributions (MFPADs), which stand out as the most complete observables of molecular photoionization stereodynamics in different excitation regimes, now broadly extended to characterize molecular structure and dynamics, are then discussed stemming from fully oriented molecules tackled by electron-ion momentum coincidence techniques, or from laser aligned samples. Finally, novel developments and challenging perspectives, notably the implementation of PAD in time-resolved schemes at ultrashort time scales, high energy, and high intensity regimes are drawn.

Excited rotational states of molecules in a superfluid

We combine experimental and theoretical approaches to explore excited rotational states of molecules embedded in helium nanodroplets using CS$_2$ and I$_2$ as examples. Laser-induced nonadiabatic molecular alignment is employed to measure spectral lines for rotational states extending beyond those initially populated at the 0.37 K droplet temperature. We construct a simple quantum mechanical model, based on a linear rotor coupled to a single-mode bosonic bath, to determine the rotational energy structure in its entirety. The calculated and measured spectral lines are in good agreement. We show that the effect of the surrounding superfluid on molecular rotation can be rationalized by a single quantity -- the angular momentum, transferred from the molecule to the droplet.

Measuring the rotational temperature and pump intensity in molecular alignment experiments via high harmonic generation.

We demonstrate a method to simultaneously measure the rotational temperature and pump intensity in laser-induced molecular alignment by the time-resolved high harmonic spectroscopy (HHS). It relies on the sensitive dependence of the arising times of the local minima and maxima of the harmonic yields at the rotational revivals on the pump intensity and rotational temperature. By measuring the arising times of these local extrema from the time-resolved harmonic signals, the rotational temperature and pump intensity can be accurately measured. We have demonstrated our method using N2 molecules. The validity and robustness of our method are tested with different harmonic orders and by changing the gas pressures as well as the distance between the gas exit and the optical axis. Moreover, we have also demonstrated the versatility of our method by applying it to CO2 molecules.

Intrinsic calibration of laser-induced molecular alignment using rotational echoes

We propose and experimentally validate the use of rotational echo responses for obtaining the degree of molecular alignment induced in a gas. The method is independent of various parameters that are hardly accessible in most experimental configurations such as the effective length of interaction and the gas density as it relies on the intrinsic, self-contained dynamics of the rotational echo response.

All-optical field-free three-dimensional orientation of asymmetric-top molecules

Orientation and alignment of molecules by ultrashort laser pulses is crucial for a variety of applications and has long been of interest in physics and chemistry, with the special emphasis on stereodynamics in chemical reactions and molecular orbitals imaging. As compared to the laser-induced molecular alignment, which has been extensively studied and demonstrated, achieving molecular orientation is a much more challenging task, especially in the case of asymmetric-top molecules. Here, we report the experimental demonstration of all-optical field-free three-dimensional orientation of asymmetric-top molecules by means of phase-locked cross-polarized two-color laser pulse. This approach is based on nonlinear optical mixing process caused by the off-diagonal elements of the molecular hyperpolarizability tensor. It is demonstrated on SO2 molecules and is applicable to a variety of complex nonlinear molecules.

Control of laser-induced nonadiabatic molecular alignment in dissipative media

Laser-induced nonadiabatic alignment in nitrogen and mixtures of nitrogen with Ar gas was investigated using the ultrafast optical Kerr effect in the collinear pump-probe setup. We find that dissipative media produce desired alignment characteristics in distinct manners to decoherence and to population relaxation. The results show that the intense laser alignment can be used as a control tool of molecular dynamics in dissipative environments.

LIMAO: Cross-platform software for simulating laser-induced alignment and orientation dynamics of linear-, symmetric- and asymmetric tops

A user-friendly and cross-platform software called Laser-Induced Molecular Alignment and Orientation simulator (LIMAO) has been developed. The program can be used to simulate within the rigid rotor approximation the rotational dynamics of gas phase molecules induced by linearly polarized intense laser fields at a given temperature. The software is implemented in the Java and Mathematica programming languages. The primary aim of LIMAO is to aid experimental scientists in predicting and analyzing experimental data representing laser-induced spatial alignment and orientation of molecules. Program summaryProgram title: LIMAOProgram Files doi: http://dx.doi.org/10.17632/x7h287gc9p.1Licensing provisions: GNU General Public License 3 (GPL)Programming languages: JAVA, MathematicaSupplementary material: LIMAO_SM.pdfNature of problem: LIMAO is a user-friendly software, which can be used to compute the temporal evolution of the laser-induced alignment and orientation [1-3] of gas phase molecules at a given temperature within the rigid rotor approximation. The user is asked to provide (i) molecular parameters such as rotational constant(s), a dipole moment, polarizabilities, and nuclear spin-statistical weights for the rotational levels, (ii) external field parameters such as time when the laser pulse becomes maximum, the pulse width, the intensity and carrier frequency of laser pulse(s), and (iii) temperature as input data. As an output, LIMAO generates the temporal evolution of the expectation values of physical quantities of molecules representing the spatial alignment and orientation.Solution method: LIMAO solves numerically the time-dependent Schrödinger equation of a rigid rotor molecule interacting with a time-dependent external field. The time-dependent rotational wave packet is expanded by the field-free stationary rotational eigenstates of the system. The solution is obtained by the following four steps: (i) the rotational eigenstates are derived and their symmetries within the corresponding molecular rotation group are assigned, (ii) the matrix representation of the time-dependent Hamiltonian, containing the interaction terms with an external light field as well as the matrix representations of physical quantities to be observed are constructed using the rotational eigenstates, (iii) the initial populations in the respective rotational eigenstates are determined by the Boltzmann distribution at a given temperature, and (iv) the wave packets are propagated in time and the expectation values of the relevant physical quantities are computed as a function of time.Additional comments including Restrictions and Unusual features: Simulations with the LIMAO software are limited to the rotational degrees of freedom. Light-induced vibrational excitations are neglected and light-induced electronic excitations are only accounted for in a perturbative manner through molecular polarizabilities. Therefore, the results obtained by LIMAO simulations should be treated with caution when dynamical processes such as light-induced deformation of geometrical structure, resonant vibrational excitation, and electronic excitation beyond the perturbative regime need to be considered.

Rotational Echoes: Rephasing of Centrifugal Distortion in Laser-Induced Molecular Alignment.

We study and demonstrate the rephasing property of the echo response in a multilevel rotational system of iodomethane via long time-resolved optical birefringence measurements. The strong centrifugal distortion of iodomethane is utilized as a dephasing mechanism imprinted on the echo signal and is shown to rephase throughout its evolution. The dependence of the echo signal amplitude on the driving pulses' intensities is theoretically and experimentally explored. The analogy to Hahn's spin echoes is discussed, and a quantum-mechanical version of Hahn's track runners is provided for the case of multilevel rotational system.

Coherent Radiative Decay of Molecular Rotations: A Comparative Study of Terahertz-Oriented versus Optically Aligned Molecular Ensembles.

The decay of field-free rotational dynamics is experimentally studied by two complementary methods: laser-induced molecular alignment and terahertz-field-induced molecular orientation. A comparison between the decay rates of different molecular species at various gas pressures reveals that oriented molecular ensembles decay faster than aligned ensembles. The discrepancy in decay rates is attributed to the coherent radiation emitted by the transiently oriented ensembles and is absent from aligned molecules. The experimental results reveal the dramatic contribution of coherent radiative emission to the observed decay of rotational dynamics and underline a general phenomenon expected whenever field-free coherent dipole oscillations are induced.

Laser-induced molecular alignment in the presence of chaotic rotational dynamics.

Coherent control of chaotic molecular systems, using laser-assisted alignment of sulphur dioxide (SO2) molecules in the presence of a static electric field as an example, is considered. Conditions for which the classical version of this system is chaotic are established, and the quantum and classical analogs are shown to be in very good correspondence. It is found that the chaos present in the classical system does not impede the alignment, neither in the classical nor in the quantum system. Using the results of numerical calculations, we suggest that laser-assisted alignment is stable against rotational chaos for all asymmetric top molecules.

Laser-induced Coulomb explosion of 1,4–diiodobenzene molecules: Studies of isolated molecules and molecules in helium nanodroplets

Coulomb explosion of 1,4--diiodobenzene molecules, isolated or embedded in helium nanodroplets, is induced by irradiation with an intense femtosecond laser pulse. The recoiling ion fragments are probed by time-of-flight measurements and two-dimensional velocity map imaging. Correlation analysis of the emission directions of ${\mathrm{I}}^{+}$ ions recoiling from each end of the molecules reveals significant deviation from axial recoil, i.e., where the ${\mathrm{I}}^{+}$ ions leave strictly along the I-I symmetry axis. For isolated molecules, the relative angular distribution of the ${\mathrm{I}}^{+}$ ions is centered at ${180}^{\ensuremath{\circ}}$, corresponding to perfect axial recoil, but with a full width at half maximum of ${30}^{\ensuremath{\circ}}$. For molecules inside He droplets, the width of the distribution increases to ${45}^{\ensuremath{\circ}}$. These results provide a direct measure of the accuracy of Coulomb explosion as a probe of the spatial orientation of molecules, which is particularly relevant in connection with laser-induced molecular alignment and orientation. In addition, our studies show how it is possible to identify fragmentation pathways of the Coulomb explosion for the isolated 1,4--diiodobenzene molecules. Finally, for the 1,4--diiodobenzene molecules in He droplets, it is shown that the angular correlation between fragments from the Coulomb explosion is preserved after they have interacted with the He environment.

Molecular alignment and filamentation: Comparison between weak- and strong-field models

The impact of nonadiabatic laser-induced molecular alignment on filamentation is numerically studied. Weak and strong field model of impulsive molecular alignment are compared in the context of nonlinear pulse propagation. It is shown that the widely used weak field model describing the refractive index modification induced by impulsive molecular alignment accurately reproduces the propagation dynamics providing that only a single pulse is involved during the experiment. On the contrary, it fails at reproducing the nonlinear propagation experienced by an intense laser pulse traveling in the wake of a second strong laser pulse. The discrepancy depends on the relative delay between the two pulses and is maximal for delays corresponding to half the rotational period of the molecule.

Molecular alignment allows low-order harmonic generation by circular light in a gas

We experimentally investigate odd-order harmonic generation in molecular gases produced by circularly polarized laser fields. While forbidden in isotropic medium, this effect is allowed by symmetry breaking resulting from nonadiabatic laser-induced molecular alignment. The demonstration is provided by generating the third harmonic in CO${}_{2}$ molecules. Attractive properties and challenging potential applications are discussed in the context of higher-order harmonic generation.

The quantitative determination of laser-induced molecular axis alignment

Experiments in the gas phase usually involve averaging observables over a random molecular axis alignment distribution. This deleterious averaging limits insights gained by probes of molecular dynamics, but can be overcome by prealigning molecular axes using laser-alignment methods. However, the transformation from the laboratory frame to the molecular frame of reference requires quantitative knowledge of the axis alignment distribution. The latter is often hard to obtain directly from experimental data, particularly for polyatomic molecules. Here we describe a general maximum-likelihood classification procedure for non-adiabatic numerical alignment simulations with free parameters that employs experimental data from an alignment-dependent probe. This method delivers (i) the most probable molecular frame angular dependence of the probe, and (ii) the most likely laboratory frame axis alignment distribution of the sample, each with a confidence interval. This procedure was recently used for studies of angle- and channel-resolved strong field ionization of 1,3-butadiene in the molecular frame [Mikosch et al., Phys. Rev. Lett. 110, 023004 (2013)], used here as an illustrative example.

Modifying molecular scattering from rough solid surfaces using ultrashort laser pulses

We consider solid surface scattering of molecules that were subject to strong non-resonant ultrashort laser pulses just before hitting the surface. The pulses modify the rotational state of the molecules, causing their field-free alignment, or a rotation with a preferred sense. We show that field-free laser-induced molecular alignment leads to correlation between the scattering angle and the sense of rotation of the scattered molecules. Moreover, by controlling the sense of laser-induced unidirectional molecular rotation, one may affect the scattering angle of the molecules. This provides a new means for separation of mixtures of molecules (such as isotopes and nuclear-spin isomers) by laser-controlled surface scattering.

Mechanisms of Two-Color Laser-Induced Field-Free Molecular Orientation

Two mechanisms of two-color (ω+2ω) laser-induced field-free molecular orientation, based on the hyperpolarizability and ionization depletion, are explored and compared. The CO molecule is used as a computational example. While the hyperpolarizability mechanism generates small amounts of orientation at intensities below the ionization threshold, ionization depletion quickly becomes the dominant mechanism as soon as ionizing intensities are reached. Only the ionization mechanism leads to substantial orientation (e.g., on the order of <cosθ> ≳0.1). For intensities typical of laser-induced molecular alignment and orientation experiments, the two mechanisms lead to robust, characteristic timings of the field-free orientation wave-packet revivals relative to the alignment revivals and the revival time. The revival timings can be used to detect the active orientation mechanism experimentally.