Moderately intense, nonresonant laser pulses can be used to accurately control how gas phase molecules are oriented in space. This topic, driven by intense experimental and theoretical efforts, has been ever growing and developed for more than 20 years, and laser-induced alignment methods are used routinely in a number of applications in physics and chemistry. Starting in 2013, we have demonstrated that laser-induced alignment also applies to molecules dissolved in helium nanodroplets. Here we present an overview of this newwork discussing alignment in both the nonadiabatic (short-pulse) and adiabatic (long-pulse) limit. We show how femtosecond or picosecond pulses can set molecules into coherent rotation that lasts for a long time and reflects the rotational structure of the helium-solvated molecules, provided the pulses are weak or, conversely, results in desolvation of the molecules when the pulses are strong. For long pulses we show that the 0.4 K temperature of the droplets, shared with the molecules or molecular complexes, leads to exceptionally high degrees of alignment. Upon rapid truncation of the laser pulse, the strong alignment can be made effectively field-free, lasting for about 10 ps thanks to slowing of molecular rotation by the helium environment. Finally, we discuss how the combination of strongly aligned molecular dimers and laser-induced Coulomb explosion imaging enables determination of the structure of the dimers. As a background and reference point, the first third of the article introduces some of the central concepts of laser-induced alignment for isolated molecules, illustrated by numerical and experimental examples.

Alignment of OCS, CS_{2}, and I_{2} molecules embedded in helium nanodroplets is measured as a function of time following rotational excitation by a nonresonant, comparatively weak ps laser pulse. The distinct peaks in the power spectra, obtained by Fourier analysis, are used to determine the rotational, B, and centrifugal distortion, D, constants. For OCS, B and D match the values known from IR spectroscopy. For CS_{2} and I_{2}, they are the first experimental results reported. The alignment dynamics calculated from the gas-phase rotational Schrödinger equation, using the experimental in-droplet B and D values, agree in detail with the measurement for all three molecules. The rotational spectroscopy technique for molecules in helium droplets introduced here should apply to a range of molecules and complexes.

Molecules with their axes sharply confined in space, available through laser-induced alignment methods, are essential for many current experiments, including ultrafast molecular imaging. For these applications the aligning laser field should ideally be turned-off, to avoid undesired perturbations, and the strong alignment should last long enough that reactions and dynamics can be mapped out. Presently, this is only possible for small, linear molecules and for times less than 1 picosecond. Here, we demonstrate strong, field-free alignment of large molecules inside helium nanodroplets, lasting >10 picoseconds. One-dimensional or three-dimensional alignment is created by a slowly switched-on laser pulse, made field-free through rapid pulse truncation, and retained thanks to the impeding effect of the helium environment on molecular rotation. The opportunities field-free aligned molecules open are illustrated by measuring the alignment-dependent strong-field ionization yield of dibromothiophene oligomers. Our technique will enable molecular frame experiments, including ultrafast excited state dynamics, on a variety of large molecules and complexes.

Dimers of carbon disulfide (CS$_2$) molecules embedded in helium nanodroplets are aligned using a moderately intense, 160ps, non-resonant, circularly polarized laser pulse. It is shown that the intermolecular carbon-carbon (C-C) axis aligns along the axis perpendicular to the polarization plane of the alignment laser pulse. The degree of alignment, quantified by $\langle \cos^2(\theta_\text{2D}) \rangle$, is determined from the emission directions of recoiling CS$_2$$^+$ fragment ions, created when an intense 40fs probe laser pulse doubly ionizes the dimers. Here, $\theta_\text{2D}$ is the projection of the angle between the C-C axis on the 2D ion detector and the normal to the polarization plane. $\langle \cos^2(\theta_\text{2D}) \rangle$ is measured as a function of the alignment laser intensity and the results agree well with $\langle \cos^2(\theta_\text{2D}) \rangle$ calculated for gas-phase CS$_2$ dimers with a rotational temperature of 0.4K.

A moderately intense 450 fs laser pulse is used to create rotational wave packets in gas phase I_{2} molecules. The ensuing time-dependent alignment, measured by Coulomb explosion imaging with a delayed probe pulse, exhibits the characteristic revival structures expected for rotational wave packets but also a complex nonperiodic substructure and decreasing mean alignment not observed before. A quantum mechanical model attributes the phenomena to coupling between the rotational angular momenta and the nuclear spins through the electric quadrupole interaction. The calculated alignment trace agrees very well with the experimental results.

A160-ps near-Gaussian, linearly polarized laser pulse is used to align iodine (I-2) molecules embedded in helium nanodroplets. The rise time of the laser pulse is sufficiently long and smooth that the alignment, characterized by < cos(2) theta(2D)>, behaves adiabatically during the pulse turnon. However, after the laser pulse has turned off < cos(2) theta(2D)> stays above 0.50 and a recurrence structure occurs similar to 650 ps later. Measurements on isolated (I-2) molecules with identical laser pulses are used to identify, through analysis of the observed half-and full-rotational revivals, that the nonadiabatic postpulse alignment dynamics results from a mild truncation of the trailing edge of the laser pulse. This truncation establishes a well-defined starting time for coherent rotation, which leads to the revival structures observed both for isolated molecules and molecules in He droplets. In the latter case the time-dependent < cos(2) theta(2D)> trace recorded here is compared to that obtained previously for a 450-fs alignment pulse. It is found that the observed revivals are very similar.

We use 10 ps long moderately intense laser pulses to initiate rotation of molecules embedded in helium nanodroplets and measure the time-dependent molecular alignment by femtosecond-laser-pulse-induced Coulomb explosion imaging. Our studies carried out on I2, OCS and CS2 and C2HI molecules show pronounced yet decreasing oscillations in the degree of alignment for the first 200 ps after the alignment pulse. These oscillations have a period of 40-50 ps – depending on the molecule. For each molecule the period decreases as the intensity of the alignment pulse is increased but, strikingly, saturates at a certain value that does not change even when the alignment pulse intensity is more than doubled. The observations stand in stark contrast to results for gas phase molecules measured under identical laser conditions where no oscillations are observed.

The carbon disulphide (CS_{2}) dimer is formed inside He nanodroplets and identified using fs laser-induced Coulomb explosion, by observing the CS_{2}^{+} ion recoil velocity. It is then shown that a 160 ps moderately intense laser pulse can align the dimer in advantageous spatial orientations which allow us to determine the cross-shaped structure of the dimer by analysis of the correlations between the emission angles of the nascent CS_{2}^{+} and S^{+} ions, following the explosion process. Our method will enable fs time-resolved structural imaging of weakly bound molecular complexes during conformational isomerization, including formation of exciplexes.

Dimers and trimers of carbonyl sulfide (OCS) molecules embedded in helium nanodroplets are aligned by a linearly polarized 160 ps long moderately intense laser pulse and Coulomb exploded with an intense 40 fs long probe pulse in order to determine their structures. For the dimer, recording of 2D images of OCS+ and S+ ions and covariance analysis of the emission directions of the ions allow us to conclude that the structure is a slipped-parallel shape similar to the structure found for gas phase dimers. For the trimer, the OCS+ ion images and the corresponding covariance maps reveal the presence of a barrel-shaped structure (as in the gas phase) but also other structures not present in the gas phase, most notably a linear chain structure.

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Rotation of molecules embedded in helium nanodroplets is explored by a combination of fs laser-induced alignment experiments and angulon quasiparticle theory. We demonstrate that at low fluence of the fs alignment pulse, the molecule and its solvation shell can be set into coherent collective rotation lasting long enough to form revivals. With increasing fluence, however, the revivals disappear-instead, rotational dynamics as rapid as for an isolated molecule is observed during the first few picoseconds. Classical calculations trace this phenomenon to transient decoupling of the molecule from its helium shell. Our results open novel opportunities for studying nonequilibrium solute-solvent dynamics and quantum thermalization.

Iodine (I2) molecules embedded in He nanodroplets are aligned by a 160 ps long laser pulse. The highest degree of alignment, occurring at the peak of the pulse and quantified by ⟨cos2𝜃2D⟩, is measured as a function of the laser intensity. The results are well described by ⟨cos2𝜃2D⟩ calculated for a gas of isolated molecules each with an effective rotational constant of 0.6 times the gas-phase value and at a temperature of 0.4 K. Theoretical analysis using the angulon quasiparticle to describe rotating molecules in superfluid helium rationalizes why the alignment mechanism is similar to that of isolated molecules with an effective rotational constant. A major advantage of molecules in He droplets is that their 0.4 K temperature leads to stronger alignment than what can generally be achieved for gas phase molecules-here demonstrated by a direct comparison of the droplet results to measurements on a ∼1 K supersonic beam of isolated molecules. This point is further illustrated for a more complex system by measurements on 1,4-diiodobenzene and 1,4-dibromobenzene. For all three molecular species studied, the highest values of ⟨cos2𝜃2D⟩ achieved in He droplets exceed 0.96.

We present an efficient, noise-robust method based on Fourier analysis for reconstructing the three-dimensional measure of the alignment degree, ⟨cos2θ⟩, directly from its two-dimensional counterpart, ⟨cos2θ2D⟩. The method applies to nonadiabatic alignment of linear molecules induced by a linearly polarized, nonresonant laser pulse. Our theoretical analysis shows that the Fourier transform of the time-dependent ⟨cos2θ2D⟩ trace over one molecular rotational period contains additional frequency components compared to the Fourier transform of ⟨cos2θ⟩. These additional frequency components can be identified and removed from the Fourier spectrum of ⟨cos2θ2D⟩. By rescaling of the remaining frequency components, the Fourier spectrum of ⟨cos2θ⟩ is obtained and, finally, ⟨cos2θ⟩ is reconstructed through inverse Fourier transformation. The method allows the reconstruction of the ⟨cos2θ⟩ trace from a measured ⟨cos2θ2D⟩ trace, which is the typical observable of many experiments, and thereby provides direct comparison to calculated ⟨cos2θ⟩ traces, which is the commonly used alignment metric in theoretical descriptions. We illustrate our method by applying it to the measurement of nonadiabatic alignment of I2 molecules. In addition, we present an efficient algorithm for calculating the matrix elements of cos2θ2D and any other observable in the symmetric top basis. These matrix elements are required in the rescaling step, and they allow for highly efficient numerical calculation of ⟨cos2θ2D⟩ and ⟨cos2θ⟩ in general.

We demonstrate 3D spatial alignment of 3,5-dichloroiodobenzene molecules embedded in helium nanodroplets using nonresonant elliptically polarized 160 ps laser pulses at a 1 kHz repetition rate. Through Coulomb explosion imaging and ion-ion covariance mapping, the 3D alignment is characterized and found to be stronger than that of isolated molecules. The 3D alignment follows the intensity profile of the alignment laser pulse almost adiabatically, except for a delayed response in the helium droplets, which could be exploited for field-free 3D alignment. Our results pave the way for next-generation molecular dynamics and diffraction experiments, performed within a cold helium solvent.

We report a quantitative study of the effect of nonaxial recoil during Coulomb explosion of laser-aligned molecules and introduce a method to remove the blurring caused by nonaxial recoil in the fragment-ion angular distributions. Simulations show that nonaxial recoil affects correlations between the emission directions of fragment ions differently from the effect caused by imperfect molecular alignment. The method, based on analysis of the correlation between the emission directions of the fragment ions from Coulomb explosion, is used to deconvolute the effect of nonaxial recoil from experimental fragment angular distributions. The deconvolution method is then applied to a number of experimental data sets to correct the degree of alignment for nonaxial recoil, to select optimal Coulomb explosion channels for probing molecular alignment, and to estimate the highest degree of alignment that can be observed from selected Coulomb explosion channels.

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 I+ ions recoiling from each end of the molecules reveals significant deviation from axial recoil, i.e., where the I+ ions leave strictly along the I-I symmetry axis. For isolated molecules, the relative angular distribution of the I+ ions is centered at 180 degrees, corresponding to perfect axial recoil, but with a full width at half maximum of 30.. For molecules inside He droplets, the width of the distribution increases to 45 degrees. 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.

The torsional motion of a molecule composed of two substituted benzene rings, linked by a single bond, is coherently controlled by a pair of strong (3×10^{13}  W cm^{-2}), nonresonant (800 nm) 200-fs-long laser pulses-both linearly polarized perpendicular to the single-bond axis. If the second pulse is sent at the time when the two benzene rings rotate toward (away from) each other the amplitude of the torsion is strongly enhanced (reduced). The torsional motion persists for more than 150 ps corresponding to approximately 120 torsional oscillations. Our calculations show that the key to control is the strong transient modification of the natural torsional potential by the laser-induced dynamic Stark effect.

Optical excitation of toluene to the S1 electronic state in helium nanodroplets is found to alter the rate of production of the fragment ions C7H7(+) and C5H5(+) when the droplets are subjected to subsequent electron ionization. The optical excitation process reduces the abundance of C7H7(+) ions delivered into the gas phase, whereas C5H5(+) ions become more abundant beyond a minimum droplet size. This process contrasts with normal optical depletion spectroscopy, where the optical absorption of a molecular dopant in a helium nanodroplet shrinks the helium droplet, and thus, the electron impact cross-sections because of dissipation of the absorbed energy by evaporative loss of helium atoms. The observations here are interpreted in terms of formation of an excited state in the neutral molecule, which survives for several hundred μs. This long-lived excited state, which is assumed to be the lowest triplet electronic state, shows different cross-sections for production of C7H7(+) and C5H5(+) relative to the S0 state.

In a recent experiment (H(2)O)(n)∕X(m) binary clusters (where X = Ar, N(2), CO, CO(2), and several other molecules) were formed in superfluid helium nanodroplets and investigated by electron impact mass spectrometry [Liu et al., Phys. Chem. Chem. Phys. 13, 13920 (2011)]. The addition of dopant X was found to affect the branching ratio between H(3)O(+)(H(2)O)(n) and (H(2)O)(+)(n+2) formation. Specifically, the addition of CO increased the proportion of protonated water cluster ions, whereas dopants such as Ar, N(2), and CO(2), had the opposite effect. In this work ab initio calculations have been performed on [X(H(2)O)(2)](+) ions, where X = Ar, N(2), CO, and CO(2), to try and explain this distinct behavior. CO is found to be unique in that it forms a HOCO-H(3)O(+) unit in the most stable cationic complexes where the binding between HO and CO is stronger than that between H(3)O(+) and OH. Thus, on purely energetic grounds, loss of HOCO rather than CO should be the preferred fragmentation process. No comparable chemistry occurs when X = Ar, N(2), or CO(2) and so the co-dopant requires less energy to depart than OH. The calculations therefore account for the experimental observations and provide evidence that HOCO formation is induced in helium droplets containing (H(2)O)(n) clusters and co-doped with CO when subject to electron impact ionization.

Author Institution: Department of Chemistry, University of Leicester; University Road, Leicester, LE1 7RH, UK