Fermionic Superfluidity in Three- and Two-Dimensional Solutions of 3He in 4He

Hideaki Takahashi, D. S. Hirashima

T. Soda

The interaction between two 3He atoms is calculated by taking into account the backflow effect of 3He by the 4He in the 3He-4He mixture. The effect contributes solely to the P wave part of the interaction. The repulsive S wave part of the contact interaction contributes to the exchange interaction between the 3He atoms, while the direct one phonon exchange interaction contributes both to the S and P wave attractive interactions. The overall contribution to the attractive interaction is dominated by the P wave part and the superfluidity in the P wave is more predominant than in the S wave for the 5

Vladimir V. Dmitriev

Toshio Soda

The interaction between two 3He atoms is calculated by taking into account the backflow effect of 3He by the 4He in the 3He-4He mixture. The effect contributes solely to the P wave part of the interaction. The repulsive S wave part of the contact interaction contributes to the exchange interaction between the 3He atoms, while the direct one phonon exchange interaction contributes both to the S and P wave attractive interactions. The overall contribution to the attractive interaction is dominated by the P wave part and the superfluidity in the P wave is more predominant than in the S wave for the 5

T. S. Riekki

Mixture of the two stable helium isotopes, 3He and 4He, is a versatile system to study at low temperatures. It is a mixture of two fundamentally different quantum mechanical particles: fermions and bosons. Bosonic 4He component of the dilute mixture is known to become superfluid at about 2 K, while superfluidity of the dilute fermionic 3He component has not yet been observed. The transition is anticipated to occur at temperatures below 0.0001 K (i.e. 100 uK). To reach such ultra-low temperatures, new cooling methods need to be developed, one of which is the main subject of this thesis. Current, well-established, cooling methods rely on external cooling, where a metallic coolant is used to decrease temperature in a liquid helium sample. Their performance is limited by rapidly increasing thermal boundary resistance. Our novel adiabatic melting method relies on internal cooling process, where both the coolant and the sample are same helium. First, we create a phase-separation in the mixture by increasing its pressure to about 25 times the atmospheric pressure. This solidifies the 4He component, and we ideally end up with a system of pure solid 4He and pure liquid 3He. The phase-separated system is then precooled by conventional methods, after which the solid is melted. This allows 4He to mix with 3He again in heat absorbing process, resulting in a saturated mixture with about 8% molar 3He concentration. In theory, the mixing can reduce temperature by more than a factor 1000, but external heat leaks and imperfect phase-separation reduced this to the factor 5-7 in this work. We study the performance of the melting method under various conditions, such as different melting rates, various total amount of 3He, and alternate configurations of the setup. We also developed a computational model of the system, which was needed to evaluate the lowest achieved temperatures, as the mechanical oscillators used for thermometry had already become insensitive. For it, we studied the thermal coupling parameters of our system, including thermal boundary resistances and 3He thermal conductivity. The lowest resolved temperature was (90 +- 20) uK, still above the superfluid transition of the 3He component of the mixture. We also present suggestions for future improvements for the setup.