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Journal of Physics Conference Series

Fabricating nanoscale aperture arrays for superfluid helium-4 weak link experiments

Aditya Joshi, Yuki Sato, R. E. Packard

Published Feb 1, 2009• 4 citations
Publisher

Abstract

Arrays of nanoscale apertures have been found to exhibit fascinating quantum phenomena such as the Josephson effect and collective quantized phase-slippage. To be in the Josephson regime, the aperture size must be comparable to the healing length of the 4He order parameter. For 50nm apertures this regime is attained ∼mK below T λ . Collective phase slippage occurs at considerably lower temperatures. Fabricating aperture arrays with appropriate properties (strength, temporal stability and reproducibility) at these length scales has been a long-standing goal for our group. Here, we present the techniques used thus far, based on recent work performed at the Cornell Nanoscale Facility. We discuss some issues that arise and their possible solutions.

DOI
10.1088/1742-6596/150/1/012018

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Arrays of nanoscale apertures have been found to exhibit fascinating quantum phenomena such as the Josephson effect and collective quantized phase-slippage. To be in the Josephson regime, the aperture size must be comparable to the healing length of the 4He order parameter. For 50nm apertures this regime is attained ∼mK below T λ . Collective phase slippage occurs at considerably lower temperatures. Fabricating aperture arrays with appropriate properties (strength, temporal stability and reproducibility) at these length scales has been a long-standing goal for our group. Here, we present the techniques used thus far, based on recent work performed at the Cornell Nanoscale Facility. We discuss some issues that arise and their possible solutions.
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Numerical simulation of 4^{4}4He superfluid weak link formation in nanoaperture arrays
We present a path integral Monte Carlo study of the global superfluid fraction and local superfluid density in cylindrically-symmetric reservoirs of liquid 4^{4}4He separated by nanoaperture arrays. The superfluid response to both translations along the axis of symmetry (longitudinal response) and rotations about the cylinder axis (transverse response) are computed, together with radial and axial density distributions that reveal the microscopic inhomogeneity arising from the combined effects of the confining external potential and the 4^44He-4^44He interatomic potentials. We make a microscopic determination of the length-scale of decay of superfluidity at the radial boundaries of the system by analyzing the local superfluid density distribution to extract a displacement length that quantifies the superfluid mass displacement away from the boundary. We find that the longitudinal superfluid response is reduced in reservoirs separated by a septum containing sufficiently small apertures compared to a cylinder with no intervening aperture array, for all temperatures below TλT_{\lambda}Tλ​. For a single aperture in the septum, a significant drop in the longitudinal superfluid response is seen when the aperture diameter is made smaller than twice the empirical temperature-dependent 4^44He healing length, consistent with the formation of a weak link between the reservoirs. Increasing the diameter of a single aperture or the number of apertures in the array results in an increase of the superfluid density toward the expected bulk value.
We describe the operation of a hydromechanical resonator immersed in 4He^{4}\mathrm{He}4He and 3B^{3}\mathit{B}3B superfluids and opened on the main bath by two holes, a micro-orifice acting as a weak link and a long parallel channel. Transitions between adjacent quantum states differing by one hydrodynamic circulation quantum can be induced coherently, yielding a succession of steps arranged in a staircase pattern. In 3He^{3}\mathrm{He}3He at about 0.8 mK and 0 bar, a nearly ideal, nondissipative hydrodynamic Josephson effect can be observed.
We find that a temperature differential can drive superfluid oscillations in 4He. The oscillations are excited by a heater which causes a time dependent temperature differential across an array of 70 nm apertures. By measuring the oscillation frequency and simultaneously determining both temperature and pressure differentials we prove the validity of the most general form of the Josephson frequency relation. These observations were made near saturated vapor pressure, within a few mK of the superfluid transition temperature.