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

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 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 (90 ± 20) μK ≈ T c (29±5) (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 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 μmol/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 μmol/s. We suggest improvements to the experimental design to reduce the ultimate achievable temperature further.

Properties of fermionic systems with the path-integral ground state method

“…In particular, operators in coordinate representation have a direct estimator expression that follows from Eqs. ( 14) and (15). Once the sampling algorithm has achieved an equilibrium state, the configurations of the polymers are used to calculate a Monte Carlo ground state estimate O(τ) associated with operator Ô following the expression…”

“…They are challenging systems for experimental and theoretical studies near zero temperatures. In experiments, the quest for a doubly superfluid Bose-Fermi of the mixture continues [15], despite extraordinary technical difficulties to reach its predicted critical temperature of about 45 µK [16]. Another challenge regarding 3 He atoms occurs in experiments with neutrons, where an absorption cross-section of about 10 4 barns [17] makes observations of the intensity of the scattered neutrons extremely difficult.…”

Ground state properties of fermionic systems with the Density Matrix Projection method

“…They are challenging systems for experimental and theoretical studies near zero temperatures. In experiments, the quest for a doubly superfluid Bose-Fermi of the mixture continues (Riekki et al, 2020), despite extraordinary technical difficulties to reach its predicted critical temperature of about 45 µK (Rysti et al, 2012).…”