Quantized Vortices in MixedH3e−H4

Abstract

Using density functional theory, we investigate the structure of mixed 3 He N3 -4 He N4 droplets with an embedded impurity (Xe atom or HCN molecule) which pins a quantized vortex line. We find that the dopant 1 vortex 1 4 He N4 complex, which in a previous work [F. Dalfovo et al., Phys. Rev. Lett. 85, 1028] was found to be energetically stable below a critical size N cr , is robust against the addition of 3 He. While 3 He atoms are distributed along the vortex line and on the surface of the 4 He drop, the impurity is mostly coated by 4 He atoms. Results for N 4 500 and a number of 3 He atoms ranging from 0 to 100 are presented, and the binding energy of the dopant to the vortex line is determined. DOI: 10.1103/PhysRevLett.87.145301 PACS numbers: 67.60. -g Helium nanodroplets have recently attracted considerable interest. A major reason is the possibility of using them as an inert, ultracold matrix for molecular spectroscopy studies [1]. They also allow one to address superfluid phenomena at a microscopic scale [2], and constitute an ideal testing ground for quantum many-body theories. An interesting perspective in this direction is the investigation of quantized vortices in finite systems. Key experiments have been carried out in the past two years on vortices in Bose-Einstein condensed gases of rubidium and sodium atoms confined in magnetic traps [3], where vortical states are created by acting with external perturbations in different ways. These states turn out to be more robust than expected on the basis of qualitative arguments. In principle, analogous vortical configurations are also possible in superfluid 4 He droplets, where the external perturbation could be a moving and/or rotating impurity. Although the presence of vortices in superfluid 4 He drops is not energetically favorable [4], we have argued that they can be stabilized by molecules hosted in the bulk of the drop [5], and that their existence could be inferred from the changes they induce in the molecular spectrum [6].The aim of this paper is to extend our previous analysis [5] to the case of mixed 3 He-4 He droplets. The addition of 3 He atoms to doped 4 He droplets has significant consequences in current experiments, since it lowers the temperature of the droplet from about 0.4 to 0.15 K, and their presence can be used as another source of information for characterizing the interaction of the dopant with the superfluid environment [7]. In this context, an accurate description of the first solvation layers of 4 He and/or 3 He around the impurity is important. The presence of 3 He in a droplet hosting a quantized vortex would display several interesting features, since (i) 3 He atoms behave as a normal component in the superfluid, providing a friction mechanism for the motion of vortex lines; (ii) 3 He atoms occupy surface states, known as Andreev states, which are energetically favored by the lighter mass and the larger zero point motion of 3 He compared to 4 He; (iii) some 3 He atoms will be attached to the vortex core, where they are expe...

Interaction of ions, atoms, and small molecules with quantized vortex lines in superfluid 4He

“…Unfortunately, neither of these effects can be easily modeled with the methods employed here because, at present, the suitable functionals for describing such mixed systems at finite temperatures have not yet been developed. 53,65 The OT-DFT results for both positive and negative ion binding towards rectilinear vortex lines appear to be in good agreement with the experimentally observed values, demonstrating that the present theoretical method can reliably model such interactions. An overview of the calculated model parameters R and a F at 0 K and saturated vapor pressure for Ag, Ag 2 , Cu, Cu 2 , H 2 , Li, He * , and He * 2 are given in Table I and the full interaction potential curves for selected species are plotted in Fig.…”

Vortices in quantum droplets: Analogies between boson and fermion systems

“…Grisenti and Toennies (2003) indicate that anomalies in their cluster beam experiments could be caused by vortex formation. However, no clear experimental evidence of vortex formation in small helium droplets has yet emerged, while theoretical studies suggest that vortices form in 4 He nanodroplets (Lehmann and Schmied, 2003;Mayol et al, 2001;Sola et al, 2007). The properties of helium nanodroplets have been recently reviewed by Barranco et al (2006).…”

The Structure and Energetics of 3He and 4He Nanodroplets Doped with Alkaline Earth Atoms

“…For 4 He we have used the Orsay-Trento functional, 27 and for 3 He the one described in Ref. 28 and references therein. These functionals have been used in our previous work on helium drops doped with alkali atoms 8,9 as well as in many other theoretical works.…”