Unraveling the Absorption Spectra of Alkali Metal Atoms Attached to Helium Nanodroplets

Time-resolved solvation of alkali ions in superfluid helium nanodroplets

The sinking of alkali cations in superfluid 4He nanodroplets is investigated theoretically using liquid 4He time-dependent density functional theory at zero temperature. The simulations illustrate the dynamics of the buildup of the first solvation shell around the ions. The number of helium atoms in this shell is found to linearly increase with time during the first stages of the dynamics. This points to a Poissonian capture process, as concluded in the work of Albrechtsen et al. on the primary steps of Na+ solvation in helium droplets [Albrechtsen et al., Nature 623, 319 (2023)]. The energy dissipation rate by helium atom ejection is found to be quite similar between all alkalis, the main difference being a larger energy dissipated per atom for the lighter alkalis at the beginning of the dynamics. In addition, the number of helium atoms in the first solvation shell is found to be lower at the end of the dynamics than at equilibrium for both Li+ and Na+, pointing to a kinetic rather than thermodynamical control of the snowball size for small and strongly attractive ions.

Time-Resolved Ultrafast Interatomic Coulombic Decay in Superexcited Sodium-Doped Helium Nanodroplets

The autoionization dynamics of superexcited superfluid He nanodroplets doped with Na atoms is studied by extreme-ultraviolet (XUV) time-resolved electron spectroscopy. Following excitation into the higher-lying droplet absorption band, the droplet relaxes into the lowest metastable atomic 1s2s ^1,3S states from which interatomic Coulombic decay (ICD) takes place either between two excited He atoms or between an excited He atom and a Na atom attached to the droplet surface. Four main ICD channels are identified, and their decay times are determined by varying the delay between the XUV pulse and a UV pulse that ionizes the initial excited state and thereby quenches ICD. The decay times for the different channels all fall in the range of ∼1 ps, indicating that the ICD dynamics are mainly determined by the droplet environment. A periodic modulation of the transient ICD signals is tentatively attributed to the oscillation of the bubble forming around the localized He excitation.

Dynamics of Photoexcited Cs Atoms Attached to Helium Nanodroplets

We present an experimental study of the dynamics following the photoexcitation and subsequent photoionization of single Cs atoms on the surface of helium nanodroplets. The dynamics of excited Cs atom desorption and readsorption as well as CsHe exciplex formation are measured by using femtosecond pump-probe velocity map imaging spectroscopy and ion time-of-flight spectrometry. The time scales for the desorption of excited Cs atoms off helium nanodroplets as well as the time scales for CsHe exciplex formation are experimentally determined for the 6p states of Cs. For the 6p ²Π_1/2 state, our results confirm that the excited Cs atoms only desorb from the nanodroplet when the excitation wavenumber is blue-shifted from the 6p ²Π_1/2 ← 6s ²Σ_1/2 resonance. Our results suggest that the dynamics following excitation to the 6p ²Π_3/2 state can be described by an evaporation-like desorption mechanism, whereas the dynamics arising from excitation to the 6p ²Σ_1/2 state is indicative for a more impulsive desorption process. Furthermore, our results suggest a helium-induced spin-orbit relaxation from the 6p ²Σ_1/2 state to the 6p ²Π_1/2 state. Our findings largely agree with the results of time-dependent ⁴He density functional theory (DFT) simulations published earlier [Eur. Phys. J. D 2019, 73, 94].

Alkali atoms attached to vortex-hosting helium nanodroplets

Light absorption or fluorescence excitation spectroscopy of alkali atoms attached to ⁴He droplets is investigated as a possible way for detecting the presence of vortices. To this end, we have calculated the equilibrium configuration and energetics of alkali atoms attached to a ⁴He₁₀₀₀ droplet hosting a vortex line using ⁴He density functional theory. We use them to study how the dipole absorption spectrum of the alkali atom is modified when the impurity is attached to a vortex line. Spectra are found to be blue-shifted (higher frequencies) and broadened compared to vortex-free droplets because the dimple in which the alkali atom sits at the intersection of the vortex line and the droplet surface is deeper. This effect is smaller for lighter alkali atoms and all the more so when using a quantum description since, in this case, they sit further away from the droplet surface on average due to their zero-point motion. Spectral modifications due to the presence of a vortex line are minor for np ← ns excitation and therefore insufficient for vortex detection. In the case of higher n'p ← ns or n's ← ns (n' > n) excitations, the shifts are larger as the excited state orbital is more extended and therefore more sensitive to changes in the surrounding helium density.

4s to 5s and 4p photoexcitation dynamics of K atoms from the surface of helium nanodroplets: a theoretical study

We study the photodissociation of the potassium atom from a superfluid helium nanodroplet upon 5s ²S or 4p ²P excitation using the time-dependent helium density functional method (He-TDDFT). The results show possible K spin–orbit relaxation.

Coherent multidimensional spectroscopy of dilute gas-phase nanosystems

Two-dimensional electronic spectroscopy (2DES) is one of the most powerful spectroscopic techniques with unique sensitivity to couplings, coherence properties and real-time dynamics of a quantum system. While successfully applied to a variety of condensed phase samples, high precision experiments on isolated systems in the gas phase have been so far precluded by insufficient sensitivity. However, such experiments are essential for a precise understanding of fundamental mechanisms and to avoid misinterpretations. Here, we solve this issue by extending 2DES to isolated nanosystems in the gas phase prepared by helium nanodroplet isolation in a molecular beam-type experiment. This approach uniquely provides high flexibility in synthesizing tailored, quantum state-selected model systems of single and many-body character. In a model study of weakly-bound Rb₂ and Rb₃ molecules we demonstrate the method's unique capacity to elucidate interactions and dynamics in tailored quantum systems, thereby also bridging the gap to experiments in ultracold quantum science.

Spectroscopy of gold atoms and gold oligomers in helium nanodroplets

The 6p ²P_1/2 ← 6s ²S_1/2 and 6p ²P_3/2 ← 6s ²S_1/2 transitions (D lines) of gold atoms embedded in superfluid helium nanodroplets have been investigated using resonant two-photon ionization spectroscopy. Both transitions are strongly blue-shifted and broadened due to the repulsive interaction between the Au valence electron and the surrounding helium. The in-droplet D lines are superimposed by the spectral signature of Au atoms relaxed into the metastable ²D states. These features are narrower than the in-droplet D lines and exhibit sharp rising edges that coincide with bare atom transitions. It is concluded that they originate from metastable ²D state AuHe_n exciplexes that have been ejected from the helium droplets during a relaxation process. Interestingly, the mechanism that leads to the formation of these complexes is suppressed for very large helium droplets consisting of about 2 × 10⁶ He atoms, corresponding to a droplet diameter on the order of 50 nm. The assignment of the observed spectral features is supported by ab initio calculations employing a multiconfigurational self-consistent field method and a multi-reference configuration interaction calculation. For large helium droplets doped with Au oligomers, excitation spectra for mass channels corresponding to Au_n with n = 2, 3, 4, 5, 7, and 9 are presented. The mass spectrum reveals even-odd oscillations in the number of Au atoms that constitute the oligomer, which is characteristic for coinage metal clusters. Resonances are observed close by the in-droplet D1 and D2 transitions, and the corresponding peak forms are very similar for different oligomer sizes.

Lithium atoms on helium nanodroplets: Rydberg series and ionization dynamics

The electronic excitation spectrum of lithium atoms residing on the surface of helium nanodroplets is presented and analyzed employing a Rydberg-Ritz approach. Utilizing resonant two-photon ionization spectroscopy, two different Rydberg series have been identified: one assigned to the nS(Σ) series and the other with predominantly nP(Π) character. For high Rydberg states, which have been resolved up to n = 13, the surrounding helium effectively screens the valence electron from the Li ion core, as indicated by the apparent red-shift of Li transitions and lowered quantum defects on the droplet with respect to their free atom counterparts. For low n states, the screening effect is weakened and the prevailing repulsive interaction gives rise to strongly broadened and blue-shifted transitions. The red-shifts originate from the polarization of nearby He atoms by the positive Li ion core. As a consequence of this effect, the ionization threshold is lowered by 116 ± 10 cm^-1 for Li on helium droplets with a radius of about 40 Å. Upon single-photon ionization, heavy complexes corresponding to Li ions attached to intact helium droplets are detected. We conclude that ionization close to the on-droplet ionization threshold triggers a dynamic process in which the Li ion core undergoes a transition from a surface site into the droplet.

Desorption dynamics of RbHe exciplexes off He nanodroplets induced by spin-relaxation

Doped He nanodroplets are ideal model systems to study elementary photophysical processes in hetero-nanostructures. Here we study the formation of free RbHe exciplexes from laser-excited Rb-doped He nanodroplets.

Rydberg states of alkali atoms on superfluid helium nanodroplets: inside or outside?

Electronic excitations of an electron bound to an alkali metal ion inside a droplet of superfluid 4He are computed via a combination of helium density functional theory and the numerical integration of the Schrödinger equation for a single electron in a modified, He density dependent atomic pseudopotential. The application of a spectral method to the radial part of the valence electron wavefunction allows the computation of highly excited Rydberg states. For low principal quantum numbers, the energy required to push the electron outward is larger than the solvation energy of the ion. However, for higher principal quantum numbers the situation is reversed, which suggests the stability of a system where the ion sits inside the droplet while the valence electron orbits the nanodroplet.

Imaging Excited-State Dynamics of Doped He Nanodroplets in Real-Time

The real-time dynamics of excited alkali metal atoms (Rb) attached to quantum fluid He nanodroplets is investigated using femtosecond imaging spectroscopy and time-dependent density functional theory. We disentangle the competing dynamics of desorption of excited Rb atoms off the He droplet surface and solvation inside the droplet interior as the Rb atom is ionized. For Rb excited to the 5p and 6p states, desorption occurs on starkly differing time scales (∼100 versus ∼1 ps, respectively). The comparison between theory and experiment indicates that desorption proceeds either impulsively (6p) or in a transition regime between impulsive dissociation and complex desorption (5p).

Spatial quenching of a molecular charge-transfer process in a quantum fluid: the Csx-C60 reaction in superfluid helium nanodroplets

A recent experimental study [Renzler et al., J. Chem. Phys., 2016, 145, 181101] on superfluid helium nanodroplets reported different reactivities for Cs atoms and Cs₂ dimers with C₆₀ fullerenes inside helium droplets. Alkali metal atoms and clusters are heliophobic, therefore typically residing on the droplet surface, while fullerenes are fully immersed into the droplet. In this theoretical study, which combines standard methods of computational chemistry with orbital-free helium density functional theory, we show that the experimental findings can be interpreted in the light of a quenched electron-transfer reaction between the fullerene and the alkali dopant, which is additionally hindered by a reaction barrier stemming from the necessary extrusion of helium upon approach of the two reactants.

Desorption Dynamics of Rb2 Molecules Off the Surface of Helium Nanodroplets

The desorption dynamics of rubidium dimers (Rb₂) off the surface of helium nanodroplets induced by laser excitation is studied by employing both nanosecond and femtosecond ion imaging spectroscopy. Similarly to alkali metal atoms, we find that the Rb₂ desorption process resembles the dissociation of a diatomic molecule. However, both angular and energy distributions of detected Rb₂⁺ ions appear to be most crucially determined by the Rb₂ intramolecular degrees of freedom rather than by those of the Rb₂He_N complex. The pump-probe dynamics of Rb₂⁺ is found to be slower than that of Rb⁺, pointing at a weaker effective guest-host repulsion for excited molecules than for single atoms.

Doping He droplets by laser ablation with a pulsed supersonic jet source

Laser ablation offers the possibility to study a rich number of atoms, molecules, and clusters in the gas phase. By attaching laser ablated materials to helium nanodroplets, one can gain highly resolved spectra of isolated species in a cold, weakly perturbed system. Here, we present a new setup for doping pulsed helium nanodroplet beams by means of laser ablation. In comparison to more well-established techniques using a continuous nozzle, pulsed nozzles show significant differences in the doping efficiency depending on certain experimental parameters (e.g., position of the ablation plume with respect to the droplet formation, nozzle design, and expansion conditions). In particular, we demonstrate that when the ablation region overlaps with the droplet formation region, one also creates a supersonic beam of helium atoms seeded with the sample material. The processes are characterized using a surface ionization detector. The overall doping signal is compared to that of conventional oven cell doping showing very similar dependence on helium stagnation conditions, indicating a comparable doping process. Finally, the ablated material was spectroscopically studied via laser induced fluorescence.

Solvation and spectral line shifts of chromium atoms in helium droplets based on a density functional theory approach

The interaction of an electronically excited, single chromium (Cr) atom with superfluid helium nanodroplets of various size (10 to 2000 helium (He) atoms) is studied with helium density functional theory. Solvation energies and pseudo-diatomic potential energy surfaces are determined for Cr in its ground state as well as in the y⁷P, a⁵S, and y⁵P excited states. The necessary Cr–He pair potentials are calculated by standard methods of molecular orbital-based electronic structure theory. In its electronic ground state the Cr atom is found to be fully submerged in the droplet. A solvation shell structure is derived from fluctuations in the radial helium density. Electronic excitations of an embedded Cr atom are simulated by confronting the relaxed helium density (ρ_He), obtained for Cr in the ground state, with interaction pair potentials of excited states. The resulting energy shifts for the transitions z⁷P ← a⁷S, y⁷P ← a⁷S, z⁵P ← a⁵S, and y⁵P ← a⁵S are compared to recent fluorescence and photoionization experiments.

Capture of heliophobic atoms by 4He nanodroplets: the case of cesium

Within Density Functional Theory (DFT), we address the capture of a Cs atom by a superfluid helium nanodroplet using models of different complexity.

Growing metal nanoparticles in superfluid helium

Helium droplets provide a cold and confined environment where atomic and/or molecular dopants can aggregate into clusters and nanoparticles. In particular, the sequential addition of different materials to helium droplets can lead to the formation of a wide range of nanoparticles, including core-shell nanoparticles, which can then be deposited onto a surface. Here we briefly discuss the fundamental properties of helium droplets and then address their implications for the formation of clusters and nanoparticles. Several key experiments on atomic and molecular clusters will be highlighted and new results obtained for nanoparticles formed in this way will be presented. Finally, the versatility, the limitations and new possibilities provided by superfluid helium droplets in nanoscience and nanotechnology will be addressed.

Helium droplets: a new route to nanoparticles

Helium droplets are large helium clusters that are capable of picking up individual atoms and molecules and show promise as nano-reactors for the synthesis of unique nanoparticles. In particular, the sequential addition of materials of different types offers opportunities for the fabrication of novel core-shell nanoparticles that cannot be synthesised by other methods. To exploit this potential, here we have carried out a mass spectrometry investigation on metal clusters in order to establish how to control the doping conditions for the fabrication of nanoparticles in superfluid helium droplets, and in particular to develop a recipe to control core and shell ratios in the case of core-shell nanoparticles. Several types of metal nanoparticles, including pure Ag, Au and Ni nanoparticles, and Ag/Au and Ni/Au core-shell systems, have been synthesised and then removed from the helium droplets by deposition on substrates for ex situ investigations using high-resolution transmission electron microscopy (TEM) and X-ray photoelectron spectroscopy (XPS). The TEM imaging has been used to estimate the sizes of nanoparticles, which show a bimodel distribution under the conditions employed. We also present the first evidence that crystalline metal nanoparticles are formed by self-assembly of metal atoms in helium droplets. The XPS investigation of Ni/Au core-shell nanoparticles shows an absence of any Au 4f core-level shift that would occur on alloying of Au and Ni, which provides the first direct evidence for the successful formation of core-shell nanoparticles using superfluid helium droplets.

Spectroscopy of lithium atoms and molecules on helium nanodroplets

We report on the spectroscopic investigation of lithium atoms and lithium dimers in their triplet manifold on the surface of helium nanodroplets (He_N). We present the excitation spectrum of the 3p ← 2s and 3d ← 2s two-photon transitions for single Li atoms on He_N. The atoms are excited from the 2S(Σ) ground state into Δ, Π, and Σ pseudodiatomic molecular substates. Excitation spectra are recorded by resonance enhanced multiphoton ionization time-of-flight (REMPI-TOF) mass spectroscopy, which allows an investigation of the exciplex (Li*–He_m, m = 1–3) formation process in the Li–He_N system. Electronic states are shifted and broadened with respect to free atom states, which is explained within the pseudodiatomic model. The assignment is assisted by theoretical calculations, which are based on the Orsay–Trento density functional where the interaction between the helium droplet and the lithium atom is introduced by a pairwise additive approach. When a droplet is doped with more than one alkali atom, the fragility of the alkali–He_N systems leads preferably to the formation of high-spin molecules on the droplets. We use this property of helium nanodroplets for the preparation of Li dimers in their triplet ground state (1³Σ_u⁺). The excitation spectrum of the 2³Π_g(ν′ = 0–11) ← 1³Σ_u⁺(ν″ = 0) transition is presented. The interaction between the molecule and the droplet manifests in a broadening of the transitions with a characteristic asymmetric form. The broadening extends to the blue side of each vibronic level, which is caused by the simultaneous excitation of the molecule and vibrations of the droplet (phonons). The two isotopes of Li form ⁶Li₂ and ⁷Li₂ as well as isotope mixed ⁶Li⁷Li molecules on the droplet surface. By using REMPI-TOF mass spectroscopy, isotope-dependent effects could be studied.

Shifts in the ESR spectra of alkali-metal atoms (Li, Na, K, Rb) on helium nanodroplets

He-droplet-induced changes of the hyperfine structure constants of alkali-metal atoms are investigated by a combination of relativistically corrected ab initio methods with a simulation of the helium density distribution based on He density functional theory. Starting from an accurate description of the variation of the hyperfine structure constant in the M-He diatomic systems (M=Li, Na, K, Rb) as a function of the interatomic distance we simulate the shifts induced by droplets of up to 10,000 (4)He atoms. All theoretical predictions for the relative shifts in the isotropic hyperfine coupling constants of the alkali-metal atoms attached to helium droplets of different size are then tied to a single, experimentally derived parameter of Rb.

Fluorescence emission of Ca-atom from photodissociated Ca2 in Ar doped helium droplets. II. Theoretical

The stability of the ground or excited state calcium atom in an argon-doped helium droplet has been investigated using an extension of the helium density functional method to treat clusters. This work was motivated by the experimental study presented in a companion paper, hereafter called Paper I [A. Masson, M. Briant, J. M. Mestdagh, M. A. Gaveau, A. Hernando, and N. Halberstadt, J. Chem. Phys. 137, 184310 (2012)], which investigated Ca(2) photodissociation in an argon-doped helium droplet and the nature of the fluorescent species. It is found that one single argon atom is sufficient to bring the calcium atom inside the droplet, for droplets of over 200 helium atoms. The absorption and emission spectra of CaAr(M) (M = 0-7) clusters have been simulated using the recently developed density sampling method to describe the influence of the helium environment. Absorption spectra exhibit broad, double bands that are significantly blueshifted with respect to the calcium atomic line. The emission spectra are less broad and redshifted with respect to the calcium resonance line. The shifts are found to be additive only for M ≤ 2, because only the first two argon atoms are located in equivalent positions around the calcium p orbital. This finding gives a justification for the fit presented in the companion paper, which uses the observed shifts in the emission spectra as a function of argon pressure to deduce the shifts as a function of the number of argon atoms present in the cluster. An analysis of this fit is presented here, based on the calculated shifts. It is concluded that the emitting species following Ca(2) photodissociation in an argon-doped droplet in Paper I could be Ca∗Ar(M) in a partly evaporated droplet where less than 200 helium atoms remain.

Rubidium on Helium Droplets: Analysis of an Exotic Rydberg Complex for n* < 20 and 0 ≤ l ≤ 3

Rubidium atom Rydberg states perturbed by helium droplets of different sizes provide insight into the role of a nanosized dielectric on the Coulomb potential. The observation of droplet size-dependent shifts of excited states with respect to bare atom states is explained by a decreased quantum defect and a lowered ionization threshold. Within the scope of a Rydberg model, we demonstrate that quantum defects and ionization potentials are constant for each specific Rydberg series, which confirms the Rydberg character of excited Rubidium states on helium droplets. A set of six Rydberg series could be identified. Individual Rydberg states are observed with effective principal quantum numbers up to n* ≈ 19 and l ≤ 3, for which the expectation value of the electron orbital radius is about 10 times larger than the droplet radius.

Homo- and heteronuclear alkali metal trimers formed on helium nanodroplets. Part II. Femtosecond spectroscopy and spectra assignments

Homo- and heteronuclear alkali quartet trimers of type K(3-n)Rb(n) (n = 0,1,2,3) formed on helium nanodroplets are probed by one-color femtosecond (fs) photoionization (PI) spectroscopy. The obtained frequencies are assigned to vibrations in different electronic states in comparison to high level ab initio calculations of the involved potentials including pronounced Jahn-Teller and spin-orbit couplings. Despite the fact that the resulting complex vibronic structure of the heavy alkali molecules complicates the comparison of experiment and theory we find good agreement for many of the observed lines for all species.

Vibrational relaxation and dephasing of Rb2 attached to helium nanodroplets

The vibrational wave-packet dynamics of diatomic rubidium molecules (Rb(2)) in triplet states formed on the surface of superfluid helium nanodroplets is investigated both experimentally and theoretically. Detailed comparison of experimental femtosecond pump-probe spectra with dissipative quantum dynamics simulations reveals that vibrational relaxation is the main source of dephasing. The rate constant for vibrational relaxation in the first excited triplet state 1(3)Σ(g)+ is found to be constant γ ≈ 0.5 ns(-1) for the lowest vibrational levels v ≲ 15 and to increase sharply when exciting to higher energies.

Unusual Rydberg system consisting of a positively charged helium nanodroplet with an orbiting electron

Evidence is presented of an unusual Rydberg system consisting of a helium nanodroplet containing a positively charged sodium ion and an orbiting electron. Rydberg states of this system with principal quantum number n<20 are found to be unstable on a nanosecond time scale. In contrast, Rydberg states with n≳100 are found to have a lifetime of 1.1 μs. In addition, it is found that the ionization threshold of sodium-doped helium is broadened and redshifted with respect to that of the free atom. These observations are successfully reproduced using a pseudodiatomic description of the system in which the interactions of the sodium and its ion with the helium are calculated as the sum of pair potentials.

Alkali-helium snowball complexes formed on helium nanodroplets

We systematically investigate the formation and stability of snowballs formed by femtosecond photoionization of small alkali clusters bound to helium nanodroplets. For all studied alkali species Ak = (Na,K,Rb,Cs) we observe the formation of snowballs Ak(+)He(N) when multiply doping the droplets. Fragmentation of clusters Ak(N) upon ionization appears to enhance snowball formation. In the case of Na and Cs we also detect snowballs Ak(2) (+)He(N) formed around Ak dimer ions. While the snowball progression for Na and K is limited to less than 11 helium atoms, the heavier atoms Rb and Cs feature wide distributions at least up to Ak(+)He(41). Characteristic steps in the mass spectra of Cs-doped helium droplets are found at positions consistent with predictions on the closure of the first shell of helium atoms around the Ak(+) ion based on variational Monte Carlo simulations.

Electron spin pumping of Rb atoms on He nanodroplets via nondestructive optical excitation

We measured laser-induced-fluorescence (LIF) and beam-depletion (BD) spectra of rubidium atoms (5S-5P transition) on the surface of superfluid helium nanodroplets (M-He_{N} with M=Rb). It is known that when M is a lighter alkali atom electronic excitation always leads to detachment of the excited atom (M;{*}). The dissociation energy, few tens cm;{-1}, comes either as photon excess energy or from the barrierless formation of a M;{*}-He exciplex. We observe that this picture does not hold when M=Rb and the photon excess energy is small: we are able to excite atoms without detaching them from the droplet, thanks to a barrier preventing formation of the exciplex. This system is ideally suited for optical spin pumping in a He nanodroplet, whose achievement we explicitly demonstrate in a pump-probe magnetic circular dichroism experiment.