When cooled to almost zero temperature, helium offers a very versatile subject for the experimental study of quantum matter. The two stable isotopes of helium, He-3, and He-4, and their mixtures, are the only macroscopic condensed matter systems that do not solidify at normal pressure even upon cooling to the absolute zero temperature. The cause for this is the large zero point energy compared to the interatomic bonds of the light noble gas. At extremely low temperatures the properties of the chemically identical isotopes differ considerably due to differences in quantum statistics. An especially interesting system is the dilute phase of the mixture of the isotopes, in which He-3 atoms form a rarefied fermi gas, whose properties can be continuously adjusted by varying the pressure and concentration, while the bosonic He-4 component remains in the background in the superfluid state. Also the He-3 component of the dilute mixture has been theoretically predicted to undergo a superfluid transition at very low temperature. \nThis thesis presents new methods for the experimental study of helium mixtures at very low temperatures, as well as results on measurements on the properties of helium fluids at previously unstudied temperature and pressure range. Adiabatic melting is a cooling method in which the cooling, based on the mixing of helium isotopes, is utilized in conditions where the heat capacity of the refrigerated system is falling fast, permitting a very low final temperature. In the first millikelvin-range trial of the new method, the mixture was cooled to 300 microkelvin temperature. This is not a particularly outstanding result compared to the traditional cooling methods, but the experiment was still encouraging as the limitations were found to be technical and no fundamental obstacles for improvements were discovered. The properties of the helium sample were studied by a sensitive pressure gauge, and by small immersed mechanical oscillators. Using these, the saturation solubility of the mixture was determined over the widest possible pressure range from zero to the melting pressure of the mixture. In addition the osmotic pressure of the mixture for several concentrations at the melting pressure was measured at millikelvin-range temperatures. Traditional vibrating wires and quartz tuning forks were used as the oscillators. Quartz tuning forks were found to be feasible sensors, though acoustic phenomena related to the high resonance frequency complicated the response.
When cooled to almost zero temperature, helium offers a very versatile subject for the experimental study of quantum matter. The two stable isotopes of helium, He-3, and He-4, and their mixtures, are the only macroscopic condensed matter systems that do not solidify at normal pressure even upon cooling to the absolute zero temperature. The cause for this is the large zero point energy compared to the interatomic bonds of the light noble gas. At extremely low temperatures the properties of the chemically identical isotopes differ considerably due to differences in quantum statistics. An especially interesting system is the dilute phase of the mixture of the isotopes, in which He-3 atoms form a rarefied fermi gas, whose properties can be continuously adjusted by varying the pressure and concentration, while the bosonic He-4 component remains in the background in the superfluid state. Also the He-3 component of the dilute mixture has been theoretically predicted to undergo a superfluid transition at very low temperature. \nThis thesis presents new methods for the experimental study of helium mixtures at very low temperatures, as well as results on measurements on the properties of helium fluids at previously unstudied temperature and pressure range. Adiabatic melting is a cooling method in which the cooling, based on the mixing of helium isotopes, is utilized in conditions where the heat capacity of the refrigerated system is falling fast, permitting a very low final temperature. In the first millikelvin-range trial of the new method, the mixture was cooled to 300 microkelvin temperature. This is not a particularly outstanding result compared to the traditional cooling methods, but the experiment was still encouraging as the limitations were found to be technical and no fundamental obstacles for improvements were discovered. The properties of the helium sample were studied by a sensitive pressure gauge, and by small immersed mechanical oscillators. Using these, the saturation solubility of the mixture was determined over the widest possible pressure range from zero to the melting pressure of the mixture. In addition the osmotic pressure of the mixture for several concentrations at the melting pressure was measured at millikelvin-range temperatures. Traditional vibrating wires and quartz tuning forks were used as the oscillators. Quartz tuning forks were found to be feasible sensors, though acoustic phenomena related to the high resonance frequency complicated the response.
This thesis describes experimental work on dilute mixtures of ³He in 4He, mainly at millikelvin temperatures. The isotopic helium mixture has the unique property of remaining a miscible liquid down to the absolute zero temperature. In the mK regime, it consists of two very different components: perfectly superfluid 4He, and a weakly interacting degenerate Fermi liquid of ³He, predicted by theory to undergo transition to the superfluid state at an extremely low temperature. To discover that transition, new ways of cooling helium mixtures need to be developed, as it is not likely that the conventional method of nuclear demagnetization of copper can be improved to reach helium temperatures notably below the temperatures of order 0.1 mK attained so far. \n Adiabatic melting of 4He in the presence of liquid ³He is probably the most promising method of cooling helium mixtures to microkelvin temperatures. It produces helium mixture colder than the initial temperature as a direct consequence of the mixing of the isotopes. The starting configuration is attainable by pressurizing liquid helium mixture to its solidification pressure at a temperature below some tens of mK, as only 4He then enters the solid phase. This thesis describes an experiment in which the method of adiabatic melting was, for the first time, realized at sub-millikelvin temperatures, where the superfluidity of the pure ³He phase enables, in principle, a drastic decrease of temperature. In the experiments, cooling from initial temperatures between 0.3 and 0.9 mK was detected, temperature reduction remaining below a factor of two for recognized reasons of a technical rather than fundamental nature. \n A capacitive differential pressure transducer, constructed for the experiment, was used for high accuracy measurements of the temperature dependence of the melting pressure of helium mixtures with several ³He concentrations. The melting pressure is suitable for thermometry and carries information on the interactions of ³He particles in the mixture. Also, the response of a quartz tuning fork immersed in helium was studied. Its sensitivity to the properties of the surrounding fluid was utilized to determine the saturation concentration of dilute ³He across the entire accessible pressure range. The tuning fork was found to exhibit a complex pattern of anomalies attributed to resonant modes of second sound, or concentration waves, inside its cylindrical container.
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.
Experiments have been performed at high B/T to try to establish the existence and value of an anisotropy temperature (Ta) for pure 3He, and for 6.2% and 0.7% 3He-4He mixtures. The anisotropy of diffusion in dilute Fermi gases as the temperature T goes to zero has been predicted, though experimental evidence for such anisotropy has not been universally accepted.\n\nFinite size effects have required careful analysis of the theory of the cell for the 6.2% mixture. This alters the result as determined by the usual Leggett-Rice formula. Further investigation, beyond the scope of this thesis, is currently underway for the case of pure 3He.\n\nThe possibility of using a quartz tuning fork as a viscometer has also been investigated. It is shown that tuning forks can be used field-inpendently above 3 mK in saturated 3He-4He mixtures, and to detect the superfluid A and B-phase transitions in pure 3He. It is strongly suggested from the data that the tuning fork has great potential as a high-field viscometer; however further experiments are required to fully appreciate its useful range, in both normal and superfluids.
The goal of this chapter will be to briefly describe the remarkable properties of helium at low temperatures. After stating some of these properties we will see how they can be understood in terms of the phenomenon of Bose–Einstein condensation described in Chapter 7. We will give the main argument in two different formulations, once using the quasi-particle method of Bogoliubov, and then using a Green function approach. We start with some experimental facts. Helium is a remarkable element. It was predicted to exist from observations of the Sun before it was found on Earth. It is the only element which remains a liquid at zero temperature and atmospheric pressure. Experimentally the phase diagram of 4 He is shown in Figure 10.1. Helium I is a normal fluid and has a normal gas-liquid critical point. Helium II is a mixture of a normal fluid and a superfluid. The superfluid is characterized by the vanishing of its viscosity. Helium I and helium II are separated by a line known as the λ -transition line. At T λ = 2.18 K, P λ = 2.29 Pa, helium I, helium II, and helium gas coexist. The specific heat of liquid helium along the vapor transition line forms a logarithmic discontinuity shown in Figure 10.2. The form of this diagram resembles the Greek letter λ and is the reason for calling the transition a λ -transition. The lack of viscosity of helium II leads to some remarkable experimental consequences, one of which we briefly describe. Let two containers A and B be linked by a thin capillary through which only a fluid with zero (or very low) viscosity can pass freely.
This chapter describes a system of interacting bosons at very low temperatures. For helium, the forces are relatively weak, while, because of its low mass, the zero-point oscillations of the individual atoms are large. The low temperature phase is called He II; the high temperature phase, He I. Indications of the existence of He II were already present in the early experiments of Kamerlingh Onnes. The "superfluidity" of He II was discovered independently, and essentially, simultaneously, by Kapitza and Allen and Misener, by studying the flow of liquid helium through a thin capillary. In the two-fluid model, superfluid He II is regarded as being composed of two fluids which are simultaneously present and mutually interpenetrating. The superfluid component is the condensate, the single condensed quantum state of the Bose liquid. The existence of superfluid flow through a narrow capillary is built into the theory.
This thesis presents studies of quantum degenerate atomic gases of fermionic 6Li and bosonic 7Li. Degeneracy is reached by evaporative cooling of 7Li in a strongly confining magnetic trap. Since at low temperatures direct evaporative cooling is not possible for a polarized fermionic gas, 6Li is sympathetically cooled by thermal contact with 7Li. In a first series of experiments both isotopes are trapped in their low-field seeking higher hyperfine states. A Fermi degeneracy of is achieved for 105 fermions. For more than ~300 atoms, the 7Li condensate collapses, due to the attractive interatomic interaction in this state. This limits the degeneracy reached for both species. To overcome this limit, in a second series of experiments 7Li and 6Li atoms are transferred to their low field seeking lower hyperfine states, where the boson-boson interaction is repulsive but weak. The inter-isotope collisions are used to thermalize the mixture. A 7Li Bose-Einstein condensate (BEC) of 104 atoms immersed in a Fermi sea is produced. The BEC is quasi-one-dimensional and the thermal fraction can be negligible. The measured degeneracies are . The temperature is measured using the bosonic thermal fraction, which vanishes at the lowest temperatures, limiting our measurement sensitivity. In a third series of experiments, the bosons are transferred into an optical trap and their internal state is changed to , the lowest energy state. A Feshbach resonance is detected and used to produce a BEC with tunable atomic interactions. When the effective interaction between atoms is tuned to be small and attractive, we observe the formation of a matter-wave bright soliton. Propagation of the soliton without spreading over a macroscopic distance of 1.1~mm is observed.