The density of states and other thermodynamic functions of helium nanodroplets are calculated for a microcanonical ensemble with both energy and total angular momentum treated as conserved quantum numbers. These functions allow angular momentum conserving evaporative cooling simulations.
As part of this project, a recursion relationship is derived for the reduction to irreducible representations of the n'th symmetric power of the irreducible representations of the rotation group. These give the distribution of total angular momentum states generated by putting multiple quanta into a ripplon or phonon mode of the droplet, each of which is characterized by a angular momentum quantum number.
This article provides a review of recent work in the field of helium nanodroplet spectroscopy with emphasis on the dynamical aspects of the interactions between molecules in helium as well as their interaction with this unique quantum solvent. Emphasis is placed on experimental methods and studies introducing recent new approaches, in particular including time-resolved techniques. Corresponding theoretical results on the energetics and dynamics of helium droplets are also discussed.
The dynamics of vibrational wave packets excited in Na2 dimers in the triplet ground and excited states is investigated by means of helium nanodroplet isolation (HENDI) combined with femtosecond pump-probe spectroscopy. Different pathways in the employed resonant multi-photon ionization scheme are identified. Within the precision of the method, the wave packet dynamics appears to be unperturbed by the helium droplet environment.
Deuterated imidazole (IM) molecules, dimers and trimers formed in liquid helium nanodroplets are studied by the electrostatic beam deflection method. Monitoring the deflection profile of (IM)D+ provides a direct way to establish that it is the primary product of the ionization-induced fragmentation both of (IM)2 and (IM)3. The magnitude of the deflection determines the electric dipole moments of the parent clusters: nearly 9 D for the dimer and 14.5 D for the trimer. These very large dipole values confirm theoretical predictions and derive from a polar chain bonding arrangement of the heterocy…
Long-range intermolecular forces are able to steer polar molecules submerged in superfluid helium nanodroplets into highly polar metastable configurations. We demonstrate that the presence of such special structures can be identified, in a direct and determinative way, by electrostatic deflection of the doped nanodroplet beam. The measurement also establishes the structures' electric dipole moments. In consequence, the introduced approach is complementary to spectroscopic studies of low-temperature molecular assembly reactions. It is enabled by the fact that within the cold superfluid matrix t…
Rotationally resolved infrared spectra are reported for halogen atom - HF free radical complexes formed in helium nanodroplets. An effusive pyrolysis source is used to dope helium droplets with Cl, Br and I atoms, formed by thermal dissociation of Cl$_2$, Br$_2$ and I$_2$. A single hydrogen fluoride molecule is then added to the droplets, resulting in the formation of the X-HF complexes of interest. Analysis of the resulting spectra confirms that the observed species have $^2Π_{3/2}$ ground electronic states, consistent with the linear hydrogen bound structures predicted from theory. Stark spe…
We report spectra of various benzene isotopomers and their dimers in helium nanodroplets in the region of the first Herzberg-Teller allowed vibronic transition 610 1B2u<-1A1g (the A00 transition) at ~260 nm. Excitation spectra have been recorded using both beam depletion detection and laser-induced fluorescence. Unlike for many larger aromatic molecules, the monomer spectra consist of a single "zero-phonon" line, blueshifted by ~30 cm-1 from the gas phase position. Rotational band simulations show that the moments of inertia of C6H6 in the nanodroplets are at least 6 times larger than in the g…
We have studied complexes of gold atoms and imidazole (C$_3$N$_2$H$_4$, abbreviated Im) produced in helium nanodroplets. Following the ionization of the doped droplets we detect a broad range of different Au$_m$Im$_n^+$ complexes, however we find that for specific values of $m$ certain $n$ are "magic" and thus particularly abundant. Our density functional theory calculations indicate that these abundant clusters sizes are partially the result of particularly stable complexes, e.g. AuIm$_2^+$, and partially due to a transition in fragmentation patterns from the loss of neutral imidazole molecul…
Doubly-excited Rydberg states of helium (He) nanodroplets have been studied using synchrotron radiation. We observed Fano resonances related to the atomic N = 2,0 series as a function of droplet size. Although similar qualitatively to their atomic counterparts, the resonance lines are broader and exhibit a shift in energy which increases for the higher excited states. Furthermore, additional resonances are observed which are not seen in atomic systems. We discuss these features in terms of delocalized atomic states perturbed by the surrounding He atoms and compare to singly excited droplets.
Dimers of tetracene molecules are formed inside helium nanodroplets and identified through covariance analysis of the emission directions of kinetic tetracene cations stemming from femtosecond laser-induced Coulomb explosion. Next, the dimers are aligned in either one or three dimensions under field-free conditions by a nonresonant, moderately intense laser pulse. The experimental angular covariance maps of the tetracene ions are compared to calculated covariance maps for seven different dimer conformations and found to be consistent with four of these. Additional measurements of the alignment…
Here, we report the observation of electron transfer mediated decay (ETMD) involving Mg clusters embedded in helium nanodroplets which is initiated by the ionization of helium followed by removal of two electrons from the Mg clusters of which one is transferred to the He environment neutralizing it while the other electron is emitted into the continuum. The process is shown to be the dominant ionization mechanism for embedded clusters for photon energies above the ionization potential of He. The photoelectron spectrum reveals a low energy ETMD peak. For Mg clusters larger than 5 atoms we obser…
An effusive pyrolysis source is described for generating a continuous beam of radicals under conditions appropriate for the helium droplet pick-up method. Rotationally resolved spectra are reported for the $ν_1$ vibrational mode of the propargyl radical in helium droplets at 3322.15 cm$^{-1}$. Stark spectra are also recorded that allow for the first experimental determination of the permanent electric dipole moment of propargyl, namely -0.150 D and -0.148 D for ground and excited state, respectively, in good agreement with previously reported ab initio results of -0.14 D [1]. The infrared spec…
Helium nanodroplets doped with polar molecules are studied by electrostatic deflection. This broadly applicable method allows even polyatomic molecules to attain sub-Kelvin temperatures and nearly full orientation in the field. The resulting intense force from the field gradient strongly deflects even droplets with tens of thousands of atoms, the most massive neutral systems studied by beam "deflectometry." We use the deflections to extract droplet size distributions. Moreover, since each host droplet deflects according to its mass, spatial filtering of the deflected beam translates into size …
Molecules with their axes sharply confined in space, available through laser-induced alignment methods, are essential for many current experiments, including ultrafast molecular imaging. Most of these applications require both that the aligning laser field is turned-off, to avoid undesired perturbations, and that the molecules remain aligned sufficiently long 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 nanodropl…
We show that a 450 fs nonresonant, moderately intense, linearly polarized laser pulse can induce field-free molecular axis alignment of methyliodide molecules dissolved in a helium nanodroplet. Time-resolved measurements reveal rotational dynamics much slower than that of isolated molecules and, surprisingly, complete absence of the sharp transient alignment recurrences characteristic of gas phase molecules. Our results presage a range of new opportunities for exploring both molecular dynamics in a dissipative environment and the properties of He nanodroplets.
In this article, recent developments in HElium NanoDroplet Isolation (HENDI) spectroscopy are reviewed, with an emphasis on the infrared region of the spectrum. Topics discussed include experimental details, comparison of radiation sources, symmetry issues of the helium solvation structure, sources of line broadening, changes in spectroscopic constants upon solvation, and applications including formation of novel chemical structures.
Metal-fullerene compounds are characterized by significant electron transfer to the fullerene cage, giving rise to an electric dipole moment. We use the method of electrostatic beam deflection to verify whether such reactions take place within superfluid helium nanodroplets between an embedded C$_{60}$ molecule and either alkali (heliophobic) or rare-earth (heliophilic) atoms. The two cases lead to distinctly different outcomes: C$_{60}$Na$_n$ ($n$=1-4) display no discernible dipole moment, while C$_{60}$Yb is strongly polar. This suggests that the fullerene and small alkali clusters fail to f…
We investigate the solvent shift of phthalocyanine (Pc) doped into superfluid helium droplets and probed by optical spectroscopy at the electronic origin. Our present work complements extant studies and provides results that in part contradict previous conclusions. In particular, the solvent shift does not increase monotonously with droplet radius all the way up to the bulk limit, but exhibits a turnaround instead. Moreover, a substructure is resolved, whose characteristics depend on the droplet size. This behavior can hardly be reconciled with that of a freely rotating Pc-helium complex.
Evaporative cooling of helium nanodroplets is studied with a statistical rate model that includes, for the first time, angular momentum conservation as a constraint on the accessible droplet states. It is found that while the final temperature of the droplets is almost identical to that previously predicted and later observed, the distribution of total droplet energy and angular momentum states is vastly more excited than a canonical distribution at the same temperature. It is found that the final angular momentum of the droplets is highly correlated with the initial direction, and that a sign…
The ro--vibrational spectra of molecules dissolved in liquid $^4$He nanodroplets display rotational structure. Where resolved, this structure has been used to determine a temperature that has been assumed to equal that of the intrinsic excitations of the helium droplets containing the molecules. Consideration of the density of states as a function of energy and total angular momentum demonstrates that there is a small but significant bias of the rotor populations that make the temperature extracted from a fit to its rotational level populations slightly higher than the temperature of the rippl…
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 corresponding covariance maps reveal the pr…
Helium tagging in action spectroscopy is an efficient method for measuring the absorption spectrum of complex molecular ions with minimal perturbations to the gas phase spectrum. We have used superfluid helium nanodroplets doped with corannulene to prepare cations of these molecules complexed with different numbers of He atoms. In total we identify 13 different absorption bands from corannulene cations between 5500 Å and 6000 Å. The He atoms cause a small, chemically induced redshift to the band positions of the corannulene ion. By studying this effect as a function of the number of solvating …
Rubidium dimers residing on the surface of He nanodroplets are doubly ionized by an intense fs laser pulse leading to fragmentation into a pair of $\mathrm{Rb^+}$ ions. We show that the kinetic energy of the $\mathrm{Rb^+}$ fragment ions can be used to identify dimers formed in either the X $^1Σ_{\mathrm{g}}^+$ ground state or in the lowest-lying triplet state, a $^3Σ_{\mathrm{u}}^+$. From the experiment, we estimate the abundance ratio of dimers in the a and X states as a function of the mean droplet size and find values between 4:1 and 5:1. Our technique applies generally to dimers and trime…
The energy and angular momentum of both straight and curved vortex states of a helium nanodroplet are examined as a function of droplet size. For droplets in the size range of many experiments, it is found that during the pickup of heavy solutes, a significant fraction of events deposit sufficient energy and angular momentum to form a straight vortex line. Curved vortex lines exist down to nearly zero angular momentum and energy, and thus could in principle form in almost any collision. Further, the coalescence of smaller droplets during the cooling by expansion could also deposit sufficient a…
Much of our knowledge about dynamics and functionality of molecular systems has been achieved with femtosecond time-resolved spectroscopy. Despite extensive technical developments over the past decades, some classes of systems have eluded dynamical studies so far. Here, we demonstrate that superfluid helium nanodroplets, acting as thermal bath of 0.4 K temperature to stabilize weakly bound or reactive systems, are well suited for time-resolved studies of single molecules solvated in the droplet interior. By observing vibrational wavepacket motion of indium dimers (In$_2$) for over 50 ps, we de…
We have deduced the structure of the \ce{bromobenzene}--\ce{I2} heterodimer and the \ce{(bromobenzene)2} homodimer inside helium droplets using a combination of laser-induced alignment, Coulomb explosion imaging, and three-dimensional ion imaging. The complexes were fixed in a variety of orientations in the laboratory frame, then in each case multiply ionized by an intense laser pulse. A three dimensional ion imaging detector, including a Timepix3 detector allowed us to measure the correlations between velocity vectors of different fragments and, in conjunction with classical simulations, work…
The increase in moment of inertia of SF$_6$ in helium nanodroplets is calculated using the quantum hydrodynamic approach. This required an extension of the numerical solution to the hydrodynamic equation to three explicit dimensions. Based upon an expansion of the density in terms of the lowest four Octahedral spherical harmonics, the predicted increase in moment of inertia is $170 {\rm u Å^2}$, compared to an experimentally determined value of $310(10) {\rm u Å^2}$, i.e., 55% of the observed value. The difference is likely in at least part due to lack of convergence with respect to the angula…
We thoroughly investigate vibrational quantum dynamics of dimers attached to He droplets motivated by recent measurements with K-2 [1]. For those femtosecond pump-probe experiments, crucial observed features are not reproduced by gas phase calculations but agreement is found using a description based on dissipative quantum dynamics, as briefly shown in [2]. Here we present a detailed study of the influence of possible effects induced by the droplet. The helium droplet causes electronic decoherence, shifts of potential surfaces, and relaxation of wave packets in attached dimers. Moreover, a rea…
Valence Ionization Of Water Clusters Formed Inside Helium Nanodroplets
Indian Institute of Technology Madras（印度马德拉斯理工学院）；Aarhus University（奥胡斯大学）；Université Grenoble Alpes, CNRS, LIPhy（格勒诺布尔阿尔卑斯大学，法国国家科学研究中心，LIPhy）；Elettra-Sincrotrone Trieste（的里雅斯特电子同步加速器）
Oligomers of the organic semiconductor PTCDA are studied by means of helium nanodroplet isolation (HENDI) spectroscopy. In contrast to the monomer absorption spectrum, which exhibits clearly separated, very sharp absorption lines, it is found that the oligomer spectrum consists of three main peaks having an apparent width orders of magnitude larger than the width of the monomer lines. Using a simple theoretical model for the oligomer, in which a Frenkel exciton couples to internal vibrational modes of the monomers, these experimental findings are nicely reproduced. The three peaks present in t…
During the last decade, density function theory (DFT) in its static and dynamic time dependent forms, has emerged as a powerful tool to describe the structure and dynamics of doped liquid helium and droplets. In this review, we summarize the activity carried out in this field within the DFT framework since the publication of the previous review article on this subject [M. Barranco et al., J. Low Temp. Phys. 142, 1 (2006)]. Furthermore, a comprehensive presentation of the actual implementations of helium DFT is given, which have not been discussed in the individual articles or are scattered in …
Alkali metal dimers attached to the surface of helium nanodroplets are found to be efficiently doubly ionized by electron transfer-mediated decay (ETMD) when photoionizing the helium droplets. This process is evidenced by detecting in coincidence two energetic ions created by Coulomb explosion and one low-kinetic energy electron. The kinetic energy spectra of ions and electrons are reproduced by simple model calculations based on diatomic potential energy curves, and are in agreement with ab initio calculations for the He-Na_2 and He-KRb systems. This work demonstrates that ETMD is an importan…
This paper presents an analysis of a model problem, consisting of two interacting rigid rings, for the rotation of molecules in liquid $^4$He. Due to Bose symmetry, the excitation of the rotor corresponding to a ring of N helium atoms is restricted to states with integer multiples of N quanta of angular momentum. This minimal model shares many of the same features of the rotational spectra that have been observed for molecules in nanodroplets of $\approx 10^3 - 10^4$ helium atoms. In particular, this model predicts, for the first time, the very large enhancement of the centrifugal distortion c…
We use laser-induced rotation of single molecules embedded in superfluid helium nanodroplets to reveal angular momentum dynamics and transfer in a controlled setting, under far-from-equilibrium conditions. As an unexpected result, we observe pronounced oscillations of time-dependent molecular alignment that have no counterpart in gas-phase molecules. Angulon theory reveals that these oscillations originate from the unique rotational structure of molecules in He droplets and quantum-state-specific transfer of rotational angular momentum to the many-body He environment on picosecond timescales. …
The formation of vortices is usually considered to be the main mechanism of angular momentum disposal in superfluids. Recently, it was predicted that a superfluid can acquire angular momentum via an alternative, microscopic route -- namely, through interaction with rotating impurities, forming so-called `angulon quasiparticles' [Phys. Rev. Lett. 114, 203001 (2015)]. The angulon instabilities correspond to transfer of a small number of angular momentum quanta from the impurity to the superfluid, as opposed to vortex instabilities, where angular momentum is quantized in units of $\hbar$ per atom…
We present a simple quantum mechanical model describing excited rotational states of molecules in superfluid helium nanodroplets, as recently studied in non-adiabatic molecular alignment experiments [Cherepanov et al., Phys. Rev. A 104, L061303 (2021)]. We show that a linear molecule immersed in a superfluid can be seen as an effective symmetric top, similar to the rotational structure of radicals, such as OH or NO, but with the angular momentum of the superfluid playing the role of the electronic angular momentum in free molecules. The model allows to evaluate the effective rotational and cen…
