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arXiv:1302.4710 · Physical Review Letters

Excimers He 2 * as Tracers of Quantum Turbulence in He 4 in the T = 0 Limit

D. E. Zmeev, Fatemeh Pakpour, Paul M. Walmsley, Andrei I. Golov, Wei Guo, Daniel N. McKinsey, G. G. Ihas, P. V. E. McClintock, S. N. Fisher, William Frank Vinen

Published Apr 26, 2013• 53 citations
arXivHTMLPDF

Abstract

We have studied the interaction of metastable $^{4}\mathrm{He}_{2}^{*}$ excimer molecules with quantized vortices in superfluid $^{4}\mathrm{He}$ in the zero temperature limit. The vortices were generated by either rotation or ion injection. The trapping diameter of the molecules on quantized vortices was found to be $96\ifmmode\pm\else\textpm\fi{}6\text{ }\text{ }\mathrm{nm}$ at a pressure of 0.1 bar and $27\ifmmode\pm\else\textpm\fi{}5\text{ }\text{ }\mathrm{nm}$ at 5.0 bar. We have also demonstrated that a moving tangle of vortices can carry the molecules through the superfluid helium.

DOI
10.1103/physrevlett.110.175303

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We have studied the interaction of metastable 4He2∗^{4}\mathrm{He}_{2}^{*}4He2∗​ excimer molecules with quantized vortices in superfluid 4He^{4}\mathrm{He}4He in the zero temperature limit. The vortices were generated by either rotation or ion injection. The trapping diameter of the molecules on quantized vortices was found to be 96\ifmmode±\else\textpm\fi6  nm96\ifmmode\pm\else\textpm\fi{}6\text{ }\text{ }\mathrm{nm}96\ifmmode±\else\textpm\fi6  nm at a pressure of 0.1 bar and 27\ifmmode±\else\textpm\fi5  nm27\ifmmode\pm\else\textpm\fi{}5\text{ }\text{ }\mathrm{nm}27\ifmmode±\else\textpm\fi5  nm at 5.0 bar. We have also demonstrated that a moving tangle of vortices can carry the molecules through the superfluid helium.
The decay of quantum turbulence in superfluid (_^4)He in the zero temperature limit wasinvestigated. Quantum turbulence was created by impulsive spin-down from a specific angular velocity to rest. A measurement of the vortex line density was performed using the scattering of charged vortex rings. The vortex line density decayed as L ? t^(-3/2) which is the characteristic of quasiclassical turbulence forced at large length scales. The interaction of metastable spin-triplet ?He?_2^* molecules with quantized vortex lines in superfluid (_^4)He at temperatures below 200 mK was studied too. The molecules were generated during an injection of electrons from a sharp metal tip at high voltage. They were detected as a current into a metal collector after ionization upon colliding with the collector surface. The detected current was suppressed by even a small rotation indicating the trapping of the molecules on quantized vortices. The presence of (_^3)He impurities at the level of 0.3 ppb strongly suppressed the detected signal. The temperature dependence of the detected signal showed a sharp peak, most probably associated with the condensation of (_^3)He atoms on vortex cores. The time of flight of the molecules as a function of temperature was measured. It was observed that there are three regimes for ?He?_2^* molecules transportation in superfluid (_^4)He : ballistic regime for T 200 mK, and an intermediate regime between them. The vortex lines were created by either rotation or ion injection. The trapping diameter of the molecules on quantized vortices was found to be 96 � 6 nm at pressure of 0.1 bar and 27 � 5 nm at 5.0 bar. It was also demonstrated that a tangle of vortices moving in superfluid (_^4)He are capable of conveying the ?He?_2^* molecules through the drift region.
Metastable He2∗{\mathrm{He}}_{2}^{*}He2∗​ excimer molecules have been utilized as tracer particles of the normal component in superfluid 4He^{4}\mathrm{He}4He (He II) which can be imaged via laser-induced fluorescence. These excimer molecules form tiny bubbles in He II and can bind to quantized vortices at sufficiently low temperatures, thereby allowing for direct visualization of vortex dynamics in an inviscid superfluid. However, the ${a}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}\ensuremath{\rightarrow}{c}^{3}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}$ optical absorption line, which is responsible for the fluorescence imaging of the He2∗{\mathrm{He}}_{2}^{*}He2∗​ molecules, is controlled by fluctuations on the bubble shape, and its exact line profile is not known at low temperatures. In this paper, we present a bubble model for evaluating the surface fluctuation eigenmodes of the excimers in He II. The line profile of the ${a}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}\ensuremath{\rightarrow}{c}^{3}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}$ transition is calculated at different temperatures by considering both the zero-point and thermal fluctuations on the bubble shape. We show that as the temperature drops from 2 K to 20 mK, the peak absorption strength is enhanced by a factor of about five, accompanying a blueshift of the peak location by about 2 nm. A double-peak line profile due to the rotational levels of the molecular core can be resolved. This bubble model also allows us to evaluate the stiffness of the He2∗{\mathrm{He}}_{2}^{*}He2∗​ bubbles and hence their diffusion constant in He II due to scattering off thermal phonons. Our results will aid the design of future experiments on imaging quantized vortices in He II using He2∗{\mathrm{He}}_{2}^{*}He2∗​ tracers.
Recent experiments on quantum turbulence in superfluid helium made use of small tracer particles to track the motion of quantized vortices, determine velocity statistics and visualize vortex reconnections. A problem with this visualization technique is that it may change the turbulent flow which it visualizes. To address this problem, we derive and solve the equations of motion of a quantized vortex ring which contains a given number of particles trapped on the vortex core, hence derive a quantitative criterion to determine in which measure small particles trapped in quantized vortices affect vortex motion. Finally we apply the criterion to a recent experiment.
Recent experiments have shown that micron-size particles can be trapped in quantized vortices in superfluid helium. We present results of a dynamically self-consistent calculation of the nonlinear interaction of a sphere and a vortex. We find that, depending on the regime, the sphere can be trapped in the vortex or break free from it. We also find that, if trapped, the sphere can travel along the vortex. We analyze the role played by the various forces acting on the sphere during the interaction.
An oscillating object can stretch quantized vortices attached to it in superfluids due to the relative superflow, steadily generating quantum turbulence, even in the zero-temperature limit. We report the emission and propagation of quantized vortices from quantum turbulence generated in superfluid 4{}^{4}4He at low temperatures. A vortex-free vibrating wire enables us to detect the first collision of vortex rings and therefore to measure the time-of-flight of a vortex emitted from a generator to a detector. The detection times from the start of turbulence generation exhibit an exponential distribution, suggesting that the detection is a Poisson process. Vortices are emitted continuously, but each vortex has a random flight velocity and direction. We estimated the nondetection time and mean detection period from the distribution for two flight distances. By estimating the flight velocity, we find that only vortices with velocities lower than the detector velocity can be detected, even if the sizes of the emitted vortices are smaller than the wire thickness or the vibration amplitude. The ratio of the detection rate as a function of vortex velocity suggests anisotropic emission of vortices from the quantum turbulence.