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Physical Review Letters

Cryogenic Microjet Source for Orthotropic Beams of Ultralarge Superfluid Helium Droplets

R. E. Grisenti, Jan Peter Toennies

Published Jun 9, 2003• 63 citations

Abstract

Liquid $^{4}\mathrm{H}\mathrm{e}$ at pressures ${P}_{0}=0.5--30\text{ }\text{ }\mathrm{\text{bars}}$ and temperatures ${T}_{0}=1.5--4.2\text{ }\text{ }\mathrm{K}$ is discharged into vacuum through two different $2\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ nozzles. The velocities of the beam of particles obey the Bernoulli equation down to $15\text{ }\text{ }\mathrm{m}\mathrm{/}\mathrm{s}\mathrm{e}\mathrm{c}$. With decreasing ${T}_{0}$ and increasing ${P}_{0}$ the velocity and angular distributions become exceedingly narrow with $\ensuremath{\Delta}v/v\ensuremath{\lesssim}1%$ and $\ensuremath{\Delta}\ensuremath{\vartheta}\ensuremath{\lesssim}1\text{ }\text{ }\mathrm{m}\mathrm{r}\mathrm{a}\mathrm{d}$. Optical observations indicate that the beam consists of micron-sized droplets ($N\ensuremath{\gtrsim}{10}^{9}\text{ }\text{ }\mathrm{\text{atoms}}$). This new droplet source provides opportunities for novel experimental studies of superfluid behavior.

DOI: 10.1103/physrevlett.90.234501

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Liquid

^{4}\mathrm{H}\mathrm{e}

at pressures

{P}_{0}=0.5--30\text{ }\text{ }\mathrm{\text{bars}}

and temperatures

{T}_{0}=1.5--4.2\text{ }\text{ }\mathrm{K}

is discharged into vacuum through two different

2\text{ }\text{ }\ensuremath{\mu}\mathrm{m}

nozzles. The velocities of the beam of particles obey the Bernoulli equation down to

15\text{ }\text{ }\mathrm{m}\mathrm{/}\mathrm{s}\mathrm{e}\mathrm{c}

. With decreasing

{T}_{0}

and increasing

{P}_{0}

the velocity and angular distributions become exceedingly narrow with

\ensuremath{\Delta}v/v\ensuremath{\lesssim}1%

and

\ensuremath{\Delta}\ensuremath{\vartheta}\ensuremath{\lesssim}1\text{ }\text{ }\mathrm{m}\mathrm{r}\mathrm{a}\mathrm{d}

. Optical observations indicate that the beam consists of micron-sized droplets (

N\ensuremath{\gtrsim}{10}^{9}\text{ }\text{ }\mathrm{\text{atoms}}

). This new droplet source provides opportunities for novel experimental studies of superfluid behavior.

Factors affecting the size of liquid-helium droplets produced by a pulsed nozzle are described. The shape of the nozzle orifice is found to be important in allowing control of the size of the droplets. With an appropriate choice of nozzle geometry, the average droplet size is shown to be continuously variable over nearly two orders of magnitude by adjustment of the helium gas stagnation pressure and/or temperature. A scaling law similar to, but not identical with, that found for helium droplets produced by continuous supersonic expansion sources is found for the pulsed source. The pulsed nozzle described in this article has been used to make helium droplets ranging in size from a few thousand atoms up to nearly 105 helium atoms.

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.

Helium droplets spanning a wide size range, N(He) = 10(3)-10(10), were formed in a continuous-nozzle beam expansion at different nozzle temperatures and a constant stagnation pressure of 20 bars. The average sizes of the droplets have been obtained by attenuation of the droplet beam through collisions with argon and helium gases at room temperature. The results obtained are in good agreement with previous measurements in the size range N(He) = 10(5)-10(7). Moreover, the measurements give the average sizes in the previously uncharacterized range of very large droplets of 10(7)-10(10) atoms. The droplet sizes and beam flux increase rapidly at nozzle temperatures below 6 K, which is ascribed to the formation of droplets within the nozzle interior. The mass spectra of the droplet beam upon electron impact ionization have also been obtained. The spectra show a large increase in the intensity of the He(4) (+) signal upon increase of the droplet size, an effect which can be used as a secondary size standard in the droplet size range N(He) = 10(4)-10(9) atoms.

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.