Abstract
We studied a novel cooling method, in which ^{3}hbox {He} and ^{4}hbox {He} are mixed at the ^{4}hbox {He} crystallization pressure at temperatures below 0.5,mathrm {mK}. We describe the experimental setup in detail and present an analysis of its performance under varying isotope contents, temperatures, and operational modes. Further, we developed a computational model of the system, which was required to determine the lowest temperatures obtained, since our mechanical oscillator thermometers already became insensitive at the low end of the temperature range, extending down to left( 90pm 20right) ,upmu {mathrm {K}}approx frac{T_{c}}{left( 29pm 5right) } (T_{c} of pure ^{3}hbox {He}). We did not observe any indication of superfluidity of the ^{3}hbox {He} component in the isotope mixture. The performance of the setup was limited by the background heat leak of the order of 30,mathrm {pW} at low melting rates, and by the heat leak caused by the flow of ^{4}hbox {He} in the superleak line at high melting rates up to 500,upmu mathrm {mol/s}. The optimal mixing rate between ^{3}hbox {He} and ^{4}hbox {He}, with the heat leak taken into account, was found to be about 100..150,upmu mathrm {mol/s}. We suggest improvements to the experimental design to reduce the ultimate achievable temperature further.
Highlights
Strong motivation for pursuing ever lower temperatures in helium fluids is the anticipated superfluid transition of the 3He component in dilute 3He–4He mixtures
The requirement for the BCS pairing is an attractive interaction between the particles, and since a very weak attraction is still present in the mixture systems, the 3He component superfluid transition is expected to occur at some ultra-low temperature [2,3,4,5,6]
We studied a novel cooling method that operates with mixture of 3He and 4He, at the 4He crystallization pressure 2.564 MPa [26] at the 3He saturation molar concentration 8.1% [30] motivated by the search for the coveted superfluid transition of 3He in dilute 3He–4He mixture [6]
Summary
Strong motivation for pursuing ever lower temperatures in helium fluids is the anticipated superfluid transition of the 3He component in dilute 3He–4He mixtures. Oh et al [20] used a two-stage nuclear demagnetization refrigerator to cool a small mixture sample, with a 4000 m2 heat-exchanger surface area, to 97 μK at 1 MPa. The major problem with an external cooling method, such as that, is the rapidly increasing thermal boundary resistance, or Kapitza resistance, between liquid helium and metallic coolant. The adiabatic melting method [22,23,24,25] overcomes the Kapitza bottleneck by relying on internal cooling that takes place directly in helium fluid In this setup, the nuclear demagnetization refrigerator provides only precooling conditions, and the surface area of the cell will no longer be the ultimate limiting factor. We will suggest improvements for the iteration of the experiment
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