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Register a new userRotating mixed $^3$He-$^4$He nanodroplets
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Added by
Francesco Ancilotto
Publication date
2020
fields
Physics
and research's language is
English
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Mixed $^3$He-$^4$He droplets created by hydrodynamic instability of a cryogenic fluid-jet may acquire angular momentum during their passage through the nozzle of the experimental apparatus. These free-standing droplets cool down to very low temperatures undergoing isotopic segregation, developing a nearly pure $^3$He crust surrounding a very $^4$He-rich superfluid core. Here, the stability and appearance of rotating mixed helium droplets are investigated using Density Functional Theory for an isotopic composition that highlights, with some marked exceptions related to the existence of the superfluid inner core, the analogies with viscous rotating droplets.
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Helium atoms in the metastable $2^3{S_{1}}$ state (He$^*$) have unique advantages for ultracold atomic experiments. However, there is no known accessible Feshbach resonance in He$^*$, which could be used to manipulate the scattering length and hence unlock several new experimental possiblities. Previous experimental and theoretical studies for He$^*$ have produced contradictory results. We aimed to resolve this discrepancy with a theoretical search for Feshbach resonances, using a new close-coupled model of He$^*$ collisions in the presence of an external magnetic field. Several resonances were detected and the existing literature discrepancy was resolved. Although none of the resonances identified are readily experimentally useable, an interesting non-Feshbach scattering length variation with magnetic field was observed in heteronuclear collisions, at field strengths that are experimentally accessible.
We present systematic results, based on density functional calculations, for the structure and energetics of $^3$He and $^4$He nanodroplets doped with alkaline earth atoms. We predict that alkaline earth atoms from Mg to Ba go to the center of $^3$He drops, whereas Ca, Sr, and Ba reside in a deep dimple at the surface of $^4$He drops, and Mg is at their center. For Ca and Sr, the structure of the dimples is shown to be very sensitive to the He-alkaline earth pair potentials used in the calculations. The $5s5pleftarrow5s^2$ transition of strontium atoms attached to helium nanodroplets of either isotope has been probed in absorption experiments. The spectra show that strontium is solvated inside $^3$He nanodroplets, supporting the calculations. In the light of our findings, we emphasize the relevance of the heavier alkaline earth atoms for analyzing mixed $^3$He-$^4$He nanodroplets, and in particular, we suggest their use to experimentally probe the $^3$He-$^4$He interface.
Motivated by recent experiments, we study normal-phase rotating He-3 droplets within Density Functional Theory in a semi-classical approach. The sequence of rotating droplet shapes as a function of angular momentum are found to agree with those of rotating classical droplets, evolving from axisymmetric oblate to triaxial prolate to two-lobed shapes as the angular momentum of the droplet increases. Our results, which are obtained for droplets of nanoscopic size, are rescaled to the mesoscopic size characterizing ongoing experimental measurements, allowing for a direct comparison of shapes. The stability curve in the angular velocity-angular momentum plane shows small deviations from the classical rotating drop model predictions, whose magnitude increases with angular momentum. We attribute these deviations to effects not included in the simplified classical model description of a rotating fluid held together by surface tension, i.e. to surface diffuseness, curvature and finite compressibility, and to quantum effects associated with deformation of the He-3 Fermi surface. The influence of all these effects is expected to diminish as the droplet size increases, making the classical rotating droplet model a quite accurate representation of He-3 rotation.
Within density functional theory, we have obtained the structure of $^4$He droplets doped with neutral calcium atoms. These results have been used, in conjunction with newly determined {it ab-initio} $^1Sigma$ and $^1Pi$ Ca-He pair potentials, to address the $4s4p$ $^1$P$_1 leftarrow 4s^2$ $^1$S$_0$ transition of the attached Ca atom, finding a fairly good agreement with absorption experimental data. We have studied the drop structure as a function of the position of the Ca atom with respect of the center of mass of the helium moiety. The interplay between the density oscillations arising from the helium intrinsic structure and the density oscillations produced by the impurity in its neighborhood plays a role in the determination of the equilibrium state, and hence in the solvation properties of alkaline earth atoms. In a case of study, the thermal motion of the impurity within the drop surface region has been analyzed in a semi-quantitative way. We have found that, although the atomic shift shows a sizeable dependence on the impurity location, the thermal effect is statistically small, contributing by about a 10% to the line broadening. The structure of vortices attached to the calcium atom has been also addressed, and its effect on the calcium absorption spectrum discussed. At variance with previous theoretical predictions, we conclude that spectroscopic experiments on Ca atoms attached to $^4$He drops will be likely unable to detect the presence of quantized vortices in helium nanodrops.
We develop a first principles, microscopic theory of impurity atom scattering from inhomogeneous quantum liquids such as adsorbed films, slabs, or clusters of He-4. The theory is built upon a quantitative, microscopic description of the ground state of both the host liquid as well as the impurity atom. Dynamic effects are treated by allowing all ground-state correlation functions to be time-dependent. Our description includes both the elastic and inelastic coupling of impurity motion to the excitations of the host liquid. As a specific example, we study the scattering of He-3 atoms from adsorbed He-4 films. We examine the dependence of ``quantum reflection on the substrate, and the consequences of impurity bound states, resonances, and background excitations for scattering properties. A thorough analysis of the theoretical approach and the physical circumstances point towards the essential role played by inelastic processes which determine almost exclusively the reflection probabilities. The coupling to impurity resonances within the film leads to a visible dependence of the reflection coefficient on the direction of the impinging particle.
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