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.
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.
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.
For several decades, superfluid helium has provided an almost unparalleled frontier of quantum physics research, especially in topics related to macroscopic quantum phenomena. While nowadays systems studied in quantum physics are becoming increasingly artificially engineered - the quest for quantum computers and quantum technology in general being one of the driving forces of this development - traditionally both superfluid 4He and 3He have provided a natural but versatile window to their quantum nature. Superfluid 3He, the subject of this thesis, is a quantitatively understood macroscopic quantum system of considerable yet manageable mathematical complexity. In this thesis I show how such versatility translates into a variety of emergent phenomena, touching many seemingly distant fields in physics such as cosmology.
Approaching superfluid helium-3 experimentally requires sophisticated cooling and probing methodology. We have used a rotating ultra-low-temperature refrigerator, where the superfluid sample is cooled down by a nuclear demagnetisation stage and probed using nuclear magnetic resonance spectroscopy (NMR). One particularly useful NMR instrument can be constructed by trapping a Bose-Einstein condensate (BEC) of magnon quasiparticles within the superfluid. We have used such condensates in probing a variety of delicate phenomena such as other spin wave modes, including Higgs modes. We have also observed propagation of self-trapped Q-ball solitons making use of magnon BECs. These achievements required careful experimental and numerical studies of the magnon BEC. The spectrum of the magnon BEC is controlled by the profile of the external magnetic field and by the spatial variation of the superfluid order parameter. The main part of the relaxation is due to temperature dependent spin transport in the normal component of the liquid, which allows translating the magnon BEC read-out into in-situ thermometer.
As perhaps the most pubilicized topic of this thesis, I explain how we discovered half-quantum vortices in superfluid helium-3, a manifestation of the topological versatility of this system. Nobel laureate Anthony Leggett recently listed finding these vortices the most important remaining open problem in the ultra-low-temperature superfluid physics. In general, the very name of quantum physics refers to the observation that fundamental concepts such as energy and momentum are quantised in the microscopic world, that is, changes in the quantities describing a physical system can only occur in finite steps, integer multiples one quantum. Therefore finding vortices carrying only half-a-quantum of circulation is not only intriguing, but manifests deep understanding of the underlying physics and quantum physics in general.; Supranesteet ovat jo vuosikymmenien ajan olleet kvanttifysiikan tutkimuksen kapeassa karjessa, erityisesti mita tulee makroskooppisten kvantti-ilmioiden tutkimiseen. Siina missa tamanhetkiset suuret virtaukset fysiikan tutkimuksessa kulkevat kohti varta vasten suunniteltuja kohdesysteemeja -…
Superconductivity and superfluidity of fermionic and bosonic systems are remarkable many-body quantum phenomena. In liquid helium and dilute gases, Bose and Fermi superfluidity has been observed separately, but producing a mixture in which both the fermionic and the bosonic components are superfluid is challenging. Here we report on the observation of such a mixture with dilute gases of two lithium isotopes, lithium-6 and lithium-7. We probe the collective dynamics of this system by exciting center-of-mass oscillations that exhibit extremely low damping below a certain critical velocity. Using high-precision spectroscopy of these modes, we observe coherent energy exchange and measure the coupling between the two superfluids. Our observations can be captured theoretically using a sum-rule approach that we interpret in terms of two coupled oscillators.
The last five years have seen a burst of activity leading to the current view that 3He atoms dissolved in superfluid liquid 4He show remarkable resemblance to a weakly-interacting Fermi gas. This is because the solvent 4He, having vanishingly small entropy, specific heat, viscosity and magnetic susceptibility, behaves almost as if it were a massive vacuum, in which 3He atoms float. So at last a real Fermi ‘gas’ is available and can readily be cooled to temperatures well below its Fermi degeneracy temperature. This model of solute 3He, with its weaknesses and strengths, is the basis of this article.
For several decades, superfluid helium has provided an almost unparalleled frontier of quantum physics research, especially in topics related to macroscopic quantum phenomena. While nowadays systems studied in quantum physics are becoming increasingly artificially engineered - the quest for quantum computers and quantum technology in general being one of the driving forces of this development - traditionally both superfluid 4He and 3He have provided a natural but versatile window to their quantum nature. Superfluid 3He, the subject of this thesis, is a quantitatively understood macroscopic quantum system of considerable yet manageable mathematical complexity. In this thesis I show how such versatility translates into a variety of emergent phenomena, touching many seemingly distant fields in physics such as cosmology. Approaching superfluid helium-3 experimentally requires sophisticated cooling and probing methodology. We have used a rotating ultra-low-temperature refrigerator, where the superfluid sample is cooled down by a nuclear demagnetisation stage and probed using nuclear magnetic resonance spectroscopy (NMR). One particularly useful NMR instrument can be constructed by trapping a Bose-Einstein condensate (BEC) of magnon quasiparticles within the superfluid. We have used such condensates in probing a variety of delicate phenomena such as other spin wave modes, including Higgs modes. We have also observed propagation of self-trapped Q-ball solitons making use of magnon BECs. These achievements required careful experimental and numerical studies of the magnon BEC. The spectrum of the magnon BEC is controlled by the profile of the external magnetic field and by the spatial variation of the superfluid order parameter. The main part of the relaxation is due to temperature dependent spin transport in the normal component of the liquid, which allows translating the magnon BEC read-out into in-situ thermometer. As perhaps the most pubilicized topic of this thesis, I explain how we discovered half-quantum vortices in superfluid helium-3, a manifestation of the topological versatility of this system. Nobel laureate Anthony Leggett recently listed finding these vortices the most important remaining open problem in the ultra-low-temperature superfluid physics. In general, the very name of quantum physics refers to the observation that fundamental concepts such as energy and momentum are quantised in the microscopic world, that is, changes in the quantities describing a physical system can only occur in finite steps, integer multiples one quantum. Therefore finding vortices carrying only half-a-quantum of circulation is not only intriguing, but manifests deep understanding of the underlying physics and quantum physics in general.