Performance of adiabatic melting as a method to pursue the lowest possible temperature in $^3$He and $^3$He-$^4$He mixture at the $^4$He crystallization pressure

TL;DR

This study explores a novel adiabatic melting method to reach ultra-low temperatures below 100 microkelvin using helium isotopes, analyzing its performance, limitations, and potential improvements.

Contribution

The paper introduces a detailed experimental setup and computational model for adiabatic melting at ultra-low temperatures, extending the achievable cooling limits with helium mixtures.

Findings

Achieved temperatures down to approximately 90 microkelvin.

Identified heat leaks as primary performance limitations.

Optimal helium mixing rate around 100-150 micromoles per second.

Abstract

We studied a novel cooling method, in which $^3$He and $^4$He are mixed at the $^4$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 $\left(90\pm20\right)\,\mathrm{\mu K\approx}\frac{T_{c}}{\left(29\pm5\right)}$ ($T_{c}$ of pure $^3$He). We did not observe any indication of superfluidity of the $^3$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 $^4$He in the superleak line at high melting rates up to $500\,\mathrm{\mu mol/s}$. The optimal mixing rate between $^3$He and $^4$He, with the heat leak taken into account, was found to be about $100..150\,\mathrm{\mu mol/s}$. We suggest improvements to the experimental design to reduce the ultimate achievable temperature further.