For the past 30 years, helium nano-droplets have been of particular interest to experimentalists.Indeed, this is a cold dense finite liquid environment which is an excellent matrix forspectroscopy applications, in atomic and molecular collision physics as well as in ultra coldchemistry with ability of isolating interesting reactions intermediates like HOCO in OH + CO→ CO2 + H or to synthesize new materials as metallic nano-wires. These phenomena areconsequences of the quantum collective behaviour of helium atoms at temperature T < 1 Kwhich classify helium nano-droplets as quantum liquids. In this thesis work we propose tomodel photo-dissociation [1] of immersed diatomic as molecular iodine, doping and rotationalexcitation of these droplets by using an home-made molecular dynamics developed by Pr.Marius Lewerenz, the CLUSTER code. To take the quantum nature of helium atoms intoaccount the methodology exploits the quantum effective potential technique [2] at experimentalwork temperature 0.37 K.With the photo-dissociation, an excitation above a molecular fragmentation limit leads to twopossible scenarios depending one the amortised energy by the helium droplets. The first one isthe fast recombination so-called ’cage effect’ [3] and the second is where photo-fragmentsreside in the helium bath. But with nano-meter scale of droplets a third scenario is possible withfragments leaving the cluster surrounded by a helium solvating shell. Results are shown forhelium nano-droplets containing thousands atoms (2500 to 9000 He) and statistics on size andvelocity of I@Hen photo-fragments have been computed and are similar to experimentaloutcomes for analogous system CH3I [4].According experiments using 1 fs X-ray flashes [5], the helium nano-droplets are geoids whichis a clue indicating a rotation on itself as the Earth. Our code can set precise angular momentumin order to study the pattern of distortion from fission to multiple splitting. To evaluate thenumbers of sub-cluster a Complete Clustering algorithm based on graph theory has beenprogrammed exhibiting a linear complexity.To conclude a study of xenon doping is presented where the recombination dynamics unveils ametastable state called Atkins’ snowball [6] and different patterns of aggregation as nano-crystals and nano-wires well known by experimentalists
For the past 30 years, helium nano-droplets have been of particular interest to experimentalists.Indeed, this is a cold dense finite liquid environment which is an excellent matrix forspectroscopy applications, in atomic and molecular collision physics as well as in ultra coldchemistry with ability of isolating interesting reactions intermediates like HOCO in OH + CO→ CO2 + H or to synthesize new materials as metallic nano-wires. These phenomena areconsequences of the quantum collective behaviour of helium atoms at temperature T < 1 Kwhich classify helium nano-droplets as quantum liquids. In this thesis work we propose tomodel photo-dissociation [1] of immersed diatomic as molecular iodine, doping and rotationalexcitation of these droplets by using an home-made molecular dynamics developed by Pr.Marius Lewerenz, the CLUSTER code. To take the quantum nature of helium atoms intoaccount the methodology exploits the quantum effective potential technique [2] at experimentalwork temperature 0.37 K.With the photo-dissociation, an excitation above a molecular fragmentation limit leads to twopossible scenarios depending one the amortised energy by the helium droplets. The first one isthe fast recombination so-called ’cage effect’ [3] and the second is where photo-fragmentsreside in the helium bath. But with nano-meter scale of droplets a third scenario is possible withfragments leaving the cluster surrounded by a helium solvating shell. Results are shown forhelium nano-droplets containing thousands atoms (2500 to 9000 He) and statistics on size andvelocity of I@Hen photo-fragments have been computed and are similar to experimentaloutcomes for analogous system CH3I [4].According experiments using 1 fs X-ray flashes [5], the helium nano-droplets are geoids whichis a clue indicating a rotation on itself as the Earth. Our code can set precise angular momentumin order to study the pattern of distortion from fission to multiple splitting. To evaluate thenumbers of sub-cluster a Complete Clustering algorithm based on graph theory has beenprogrammed exhibiting a linear complexity.To conclude a study of xenon doping is presented where the recombination dynamics unveils ametastable state called Atkins’ snowball [6] and different patterns of aggregation as nano-crystals and nano-wires well known by experimentalists
Superfluid helium droplets represent a unique state of matter, which are large clusters of helium typically containing approximately 103-1011 helium atoms and exhibit remarkable properties such as superfluidity, a very low temperature (0.37 K) and high thermal conductivity. This PhD project investigates two novel aspects of superfluid helium droplets: the use of superfluid helium nanodroplets as the nanoreactors to grow magnetic nanoparticles and the generation and exploration of quantum vortices in a controlled manner. In the first part, we exploit the very low temperature and rapid cooling to develop a new approach for fabricating magnetic nanoparticles. For the very low temperature and the ultrahigh thermal conductivity, superfluid helium can suppress thermal effects during the atom-by-atom growth of magnetic nanoparticles, making the relatively weak exchange interactions (compared with metallic bonding) the driving force. As a result, the atomic spins align for ferromagnetic elements and thus the magnetic moments of nanoparticles are maximized. In particular, we focus on iron nanoparticles coated by a gold shell and investigate their properties by electron microscopy (for structural investigation) and x-ray circular dichroism (XMCD), for magnetic property measurement) at the Diamond Light Source. We first study mass spectrometry of small iron clusters and observed abnormal behaviours. Unlike other molecular clusters formed in helium droplets such as water, gold and silver, which typically follow a Poisson distribution, Fe+ channel was found to be far greater than that of FeN+ (N = 2-8) clusters. We postulate this as an indicator for the formation of high-spin iron clusters inside superfluid helium and attempt to provide an interpretation based on DFT calculations. However, XMCD showed an expected low magnetisation for Fe/Au core-shell nanoparticles which is even lower than iron oxide nanoparticles, indicating that the neutral Fe atoms are oxidized into Fe2+ within the nanoparticles which is magnetically inert. This is accounted by the very high electron negativity of Au atoms and the alloying effect during the growth of nanoparticles, which dismisses the magnetic properties. Our work shows that the choice of protective shell is important to maintain the magnetic properties of iron nanoparticles and points the direction for the next-step research. The second part presents a breakthrough in quantum vortex research. We demonstrate a novel method for generating controlled vortex arrays in superfluid helium droplets through collisions with cesium ions. Subsequential addition of metal atoms (Ag and Au) to helium droplets and the formation of nanodroplets allow the vortex lattices to be imaged after the nanoparticles are deposited onto a solid surface. By this approach we have revealed a record-high vortex density of 5.6×10¹⁴ m⁻², exceeding previous observations in bulk superfluid helium by more than six orders of magnitude. This unprecedented vortex density opens new possibilities for studying quantum hydrodynamics at extreme angular momenta and investigating quantum turbulence in previously inaccessible regimes. Through detailed theoretical analysis and experimental characterization, this work establishes superfluid helium droplets as a versatile platform for both materials synthesis and fundamental research. Our findings not only advance the understanding of superfluidity but also provide a new pathway for developing high-performance magnetic nanomaterials that can potentially revolutionize biomedical science and technologies.
Helium nanodroplets are considered ideal model systems to explore quantum hydrodynamics in self-contained, isolated superfluids. However, exploring the dynamic properties of individual droplets is experimentally challenging. In this work, we used single-shot femtosecond x-ray coherent diffractive imaging to investigate the rotation of single, isolated superfluid helium-4 droplets containing ~10(8) to 10(11) atoms. The formation of quantum vortex lattices inside the droplets is confirmed by observing characteristic Bragg patterns from xenon clusters trapped in the vortex cores. The vortex densities are up to five orders of magnitude larger than those observed in bulk liquid helium. The droplets exhibit large centrifugal deformations but retain axially symmetric shapes at angular velocities well beyond the stability range of viscous classical droplets.
Free superfluid helium droplets constitute a versatile medium for a diverse range of experiments in physics and chemistry that extend from studies of the fundamental laws of superfluid motion to the synthesis of novel nanomaterials. In particular, the emergence of quantum vortices in rotating helium droplets is one of the most dramatic hallmarks of superfluidity and gives detailed access to the wave function describing the quantum liquid. This review provides an introduction to quantum vorticity in helium droplets, followed by a historical account of experiments on vortex visualization in bulk superfluid helium and a more detailed discussion of recent advances in the study of the rotational motion of isolated, nano- to micrometer-scale superfluid helium droplets. Ultrafast X-ray and extreme ultraviolet scattering techniques enabled by X-ray free-electron lasers and high-order harmonic generation in particular have facilitated the in situ detection of droplet shapes and the imaging of vortex structures inside individual, isolated droplets. New applications of helium droplets ranging from studies of quantum phase separations to mechanisms of low-temperature aggregation are discussed.
Spectroscopy of doped helium nanodroplets has become, in recent years, a popular tool for the study of bothfinite size samples of the helium quantum fluid and molecules isolated in this sub Kelvin environment. Whilemany dopants migrate to the center of the droplet, alkali (Ak) atoms in their ground electronic state, becauseof their so weak interaction with He, remain at the surface, the latter being in this way slightly distortedexhibiting a dimple. However, when in their first excited states, Ak atoms are forming exciplexes. These areanisotropic with the central atom surrounded by a ring of He atoms located in the nodal plane of the valenceelectron pz orbital. Structural properties, obtained by DMC and PIMC, are presented here for some Ak -Hen exciplexes.Ak2 dimers in helium environment have also gained interest in this last decade, in connexion with the generationof ultracold molecules. When attached to helium droplets, Ak atoms can float on the surface andform molecules in cold collisions. DMC and PIMC methods are used to compute energetics and structuralinformations for Rb2 in helium. In particular, the orientation of the dimer relative to the droplet surface isexamined.
Below Tλ = 2.17 K, bulk 4He is a superfluid and has a non-zero Bose-Einstein condensate fraction. This work will focus primarily on how phenomena such as superfluidity, Bose condensation and superfluid vortices are manifested in microscopic, inhomogeneous helium systems. Path Integral Monte Carlo is a powerful method for calculating the equilibrium properties of quantum systems at finite temperature. We have achieved linear scaling of computer time with number of particles through the use of neighbor lists, allowing us to simulate systems of several thousand atoms. We have derived a local superfluid estimator and used it to examine the microscopic superfluid response around a molecule rotating in a helium nanodroplet. We found that the first solvation layer is well-described by a two dimensional superfluid, with thermal excitations occuring at a lower temperature than in bulk helium. The effective moment of inertia of a linear impurity in a helium droplet is calculated, and compared with experimental scattering results. In addition, we calculated the vortex formation energy for both pure droplets and droplets doped with linear impurities, and found that the linear impurities had a negligible impact on the formation energy. A possible spectroscopic signature of vortices in doped helium droplets was suggested. After deriving a local estimator, we calculated the condensate fraction throughout the free helium surface of a semi-infinite slab. These results, along with densitydensity correlation functions, were used to characterize the surface excitations and calculate the extent to which ripplons are present. In addition, the ripplon dispersion relation was calculated using imaginary-time correlation functions, and found to be lll in good agreement with experimental results. Finally, we have calculated the Dey be-Waller factor in solid helium for a range of temperatures and densities, and compared the scaling behavior with the predictions of harmonic theory. The first non-Gaussian contribution to the density distribution was calculated.
Abstract In this introductory chapter, we begin by informing the reader about the fascinating history of superfluidity in bulk liquid helium. This is followed by relating attempts in using liquid helium as a low temperature matrix for spectroscopy. After a brief review of the thermodynamic properties of helium in Sect. 1.2, the different types of free jet expansions used in experiments to produce clusters and nanodroplets of different sizes are described in Sect. 1.3. First it is shown how they depend on the nature and location in the phase diagram of the isentropes which determine the course of the expansion. Depending on the four regimes of isentropes, different number sizes and distributions are expected. Next in Sect. 1.4, the results of theoretical and, where available, experimental results on the total energies, excited states, radial density distributions, and temperatures of clusters and droplets are discussed. Finally, in Sect. 1.5 the theoretical and experimental evidence for the superfluidity of nanodroplets is briefly reviewed. For more information on the production and characteristics of nanodroplets, the reader is referred to the chapters in this book and to the reviews in Appendix.