Performance of Adiabatic Melting as a Method to Pursue the Lowest Possible Temperature in $$^{3}\hbox {He}$$ and $$^{3}\hbox {He}$$–$$^{4}\hbox {He}$$ Mixture at the $$^{4}\hbox {He}$$ Crystallization Pressure

Abstract

AbstractWe studied a novel cooling method, in which $$^{3}\hbox {He}$$3He and $$^{4}\hbox {He}$$4He are mixed at the $$^{4}\hbox {He}$$4He crystallization pressure at temperatures below $$0.5\,\mathrm {mK}$$0.5mK. 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 $$\left( 90\pm 20\right) \,\upmu {\mathrm {K}}\approx \frac{T_{c}}{\left( 29\pm 5\right) }$$90±20μK≈Tc29±5 ($$T_{c}$$Tc of pure $$^{3}\hbox {He}$$3He). We did not observe any indication of superfluidity of the $$^{3}\hbox {He}$$3He component in the isotope mixture. The performance of the setup was limited by the background heat leak of the order of $$30\,\mathrm {pW}$$30pW at low melting rates, and by the heat leak caused by the flow of $$^{4}\hbox {He}$$4He in the superleak line at high melting rates up to $$500\,\upmu \mathrm {mol/s}$$500μmol/s. The optimal mixing rate between $$^{3}\hbox {He}$$3He and $$^{4}\hbox {He}$$4He, with the heat leak taken into account, was found to be about $$100..150\,\upmu \mathrm {mol/s}$$100..150μmol/s. We suggest improvements to the experimental design to reduce the ultimate achievable temperature further.