We demonstrate successful "dry" refrigeration of quantum fluids down to T = 0.16 mK by using copper nuclear demagnetization stage that is pre-cooled by a pulse-tube-based dilution refrigerator. This type of refrigeration delivers a flexible and simple sub-mK solution to a variety of needs including experiments with superfluid 3 He. Our central design principle was to eliminate relative vibrations between the high-field magnet and the nuclear refrigeration stage, which resulted in the minimum heat leak of Q = 4.4 nW obtained in field of 35 mT. For thermometry, we employed a quartz tuning fork immersed into liquid 3 He. We show that the fork oscillator can be considered as self-calibrating in superfluid 3 He at the crossover point from hydrodynamic into ballistic quasiparticle regime.

We have measured the melting curve of 4 He in the temperature range from 10 to 400 mK with the accuracy of about 0.5 µbar. Crystals of different quality show the expected T 4 -dependence in the range from 80 to 400 mK without any sign of the supersolid transition, and the coefficient is in excellent agreement with available data on the sound velocity in liquid 4 He and on the Debye temperature of solid 4 He. Below 80 mK we have observed a small deviation from T 4 -dependence which however cannot be attributed to the supersolid transition because instead of decrease the entropy of the solid rather remains constant, about 2.5 × 10 −6 R.

The growth anisotropy of different facets has been measured in 3He crystals at 0.55 mK using a low-temperature Fabry-Pérot interferometer and high-resolution pressure measurements. The observed linear dependence of the growth velocity on the driving force shows that facets grow due to the presence of dislocations. The values of the obtained step energies suggest that 3He has stronger coupling of the liquid-solid interface to the lattice than has been expected. The dependence of the step energy versus the step height is consistent with a quartic power law pointing out that the step-step interactions are of elastic origin.

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We have measured the melting pressure and pressure in the liquid at constant density of ultra-pure 4 He (0.3 ppb of 3 He impurities) with the accuracy of about 0.5 µbar in the temperature range from 10 to 320 mK. Our measurements show that the anomaly on the melting curve below 80 mK which we have recently observed [1] is entirely due to an anomaly in the elastic modulus of Be-Cu from which our pressure gauge is made of. We thus conclude that the melting pressure of 4 He follows the T 4 law due to phonons in the whole temperature range from 10 to 320 mK without any sign of a supersolid transition.Recent experimental results obtained by Kim and Chan [2,3] have revived great interest to the problem of supersolidity which was first discussed almost 40 years ago [4,5,6]. The supersolid state of matter is characterized by the coexistence of crystalline order and superfluidity. In helium crystals, according to Andreev and Lifshitz [4] and Chester [5], quantum delocalization of point defects (most probably -vacancies) might decrease their activation energy to zero. Bose condensation of such defects can lead then to superfluidity in a crystal, that is, supersolidity. During 1970s and 1980s many experimental groups tried to detect this possible supersolid state by various methods, but unsuccessfully (see [7] for a review).