This doctoral thesis consists of experimental studies on rotating superfluid helium-3 at millikelvin temperatures. Superfluid 3He provides an example of ordered systems where quantum phenomena are visible on a macroscopic scale. The order parameter is described by a 3x3 complex matrix leading to different superfluid phases with different properties. The A and B phases support topologically different kinds of defects, most notably vortex lines. Vortex lines are most easily created and studied in uniform rotation. Because of quantum nature, the circulation around the vortices is quantized in units of κ0 = h/2m3.\n\nIn superfluid 3He nuclear magnetic resonance (NMR) provides a means to distinguish between different types of vortices and count them one by one. During the course of this work the sensitivity of the NMR spectrometer was improved by an order of magnitude, which enabled the direct measurement of the circulation of a vortex in the A phase that carries two circulation quanta (2κ0). Up to now the circulation of the known quantized vortex types in other quantum fluids, which include superfluid 4He, superconductors, and Bose-Einstein -condensates, has been singly quantized.\n\nOther NMR experiments reported in the thesis are: (1) The first qualitative measurements of vortex annihilation in the A and B phases of 3He. These measurements tell the lowest rotation velocity that stabilizes an array of vortex lines with a given number of vortices, and how it depends on the type of the defect. (2) Studies of vortex arrays with both singly and doubly quantized A phase vortex lines coexisting in the experimental container. 3He-A provides a unique system in which this kind of arrangement can be done. (3) In order to improve the vortex detection sensitivity in the B phase even further, the response of different nonlinear spin precession modes to superfluid-normal fluid counterflow was studied. A new mode, where the orbital angular momentum is oriented transverse to the external magnetic field, was found.
This doctoral thesis consists of experimental studies on rotating superfluid helium-3 at millikelvin temperatures. Superfluid 3He provides an example of ordered systems where quantum phenomena are visible on a macroscopic scale. The order parameter is described by a 3x3 complex matrix leading to different superfluid phases with different properties. The A and B phases support topologically different kinds of defects, most notably vortex lines. Vortex lines are most easily created and studied in uniform rotation. Because of quantum nature, the circulation around the vortices is quantized in units of κ0 = h/2m3.\n\nIn superfluid 3He nuclear magnetic resonance (NMR) provides a means to distinguish between different types of vortices and count them one by one. During the course of this work the sensitivity of the NMR spectrometer was improved by an order of magnitude, which enabled the direct measurement of the circulation of a vortex in the A phase that carries two circulation quanta (2κ0). Up to now the circulation of the known quantized vortex types in other quantum fluids, which include superfluid 4He, superconductors, and Bose-Einstein -condensates, has been singly quantized.\n\nOther NMR experiments reported in the thesis are: (1) The first qualitative measurements of vortex annihilation in the A and B phases of 3He. These measurements tell the lowest rotation velocity that stabilizes an array of vortex lines with a given number of vortices, and how it depends on the type of the defect. (2) Studies of vortex arrays with both singly and doubly quantized A phase vortex lines coexisting in the experimental container. 3He-A provides a unique system in which this kind of arrangement can be done. (3) In order to improve the vortex detection sensitivity in the B phase even further, the response of different nonlinear spin precession modes to superfluid-normal fluid counterflow was studied. A new mode, where the orbital angular momentum is oriented transverse to the external magnetic field, was found.
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 -…
Since its realization in dilute bosonic atomic gases [], [], Bose-Einstein condensation of alkali atoms and hydrogen has been produced and studied extensively in the laboratory [], and has permitted an intriguing glimpse into the macroscopic quantum world. In view of potential applications [], [], [], the study of quantized vortices, which are well-known signatures of superfluidity, is one of the key issues. In fact, bulk superfluids are distinguished from normal fluids by their ability to support dissipationless flow. Such persistent currents are intimately related to the existence of quantized vortices, which are localized phase singularities with integer topological charge []. The superfluid vortex is an example of a topological defect that is well known in superconductors [] and in liquid helium []. The occurrence of quantized vortices in superfluids has been the focus of fundamental theoretical and experimental work []. Different research groups have obtained quantized vortices in Bose-Einstein condensates (BECs) experimentally, e.g., the JILA group [], [], the ENS group [] and the MIT group [], []. Currently, there are at least two typical ways to generate quantized vortices from a BEC ground state: (i) impose a laser beam rotating with an angular velocity on the magnetic trap holding the atoms to create a harmonic anisotropic potential [], [], []; or (ii) add to the stationary magnetic trap a narrow, moving Gaussian potential, representing a far-blue detuned laser [], [], [], [], [], [].
This paper provides a brief description of recent experiments measuring the fluid circulation in 3He. In the B phase, the circulation around a 16 ~m diameter wire is found to be quantized in units of h/2m~. Possible future experiments are also described. It is widely believed that quantized circulation is a fundamental property of any superfluid system [1]. The fluid circulation must be quantized in units of h/nm, where m is the mass of the individual atoms in the fluid and n is an integer that depends on the microscopic process responsible for the macroscopic quantum state. For the case of 4He, the interacting atoms experience a Bose condensation into the superfluid state and n = 1. This fact has been demonstrated in several different types of experiments [1].
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.
Quantized vorticity is a property of quantum fluids that has been widely studied in various types of superfluids, either with or without spin [77],[86],[87] and Chapter 6. Superfluids with a two component (spinor) order parameter are characterized by a different type of vortex than those found in conventional scalar superfluids [99]-[102]. This new type of vortex is the so called half quantum vortex (HQV). HQVs have lower energy with respect to full vortices and constitute the elementary excitations of spinor superfluids. When circumventing their core, the phase and the polarization vector experience a ±π rotation. In this sense, HQV can be understood as a half phase vortex combined with a half polarization vortex [99]. In 4He superfluids, the HQV cannot be formed as the spin degree of freedom is absent. However, in 3He [99],[100] or in triplet superconductors [101],[102], the order parameter has two or more components, so that the formation of HQV is possible. So far, experiments have not presented any direct evidence for HQV in 3He [103], while more reliable indications of existence of HQV have been reported in cuprate superconductors [104].
The spin superfluidity -- superfluidity in the magnetic subsystem of a condensed matter -- is manifested as the spontaneous phase-coherent precession of spins first discovered in 1984 in ^3He-B. This superfluid current of spins -- spin supercurrent -- is one more representative of superfluid currents known or discussed in other systems, such as the superfluid current of mass and atoms in superfluid ^4He; superfluid current of electric charge in superconductors; superfluid current of hypercharge in Standard Model of particle physics; superfluid baryonic current and current of chiral charge in quark matter; etc. Spin superfluidity can be described in terms of the Bose condensation of spin waves -- magnons. We discuss different states of magnon superfluidity with different types of spin-orbit coupling: in bulk ^3He-B; magnetically traped "Q-balls" at very low temperatures; in ^3He-A and ^3He-B immerged in deformed aerogel; etc. Some effects in normal ^3He can also be treated as a magnetic BEC of fermi liquid. A very similar phenomena can be observed also in a magnetic systems with dinamical frequensy shift, like MnC03. We will discuss the main experimental signatures of magnons superfluidity: (i) spin supercurrent, which transports the magnetization on a macroscopic distance more than 1 cm long; (ii) spin current Josephson effect which shows interference between two condensates; (iii) spin current vortex -- a topological defect which is an analog of a quantized vortex in superfluids, of an Abrikosov vortex in superconductors, and cosmic strings in relativistic theories; (iv) Goldstone modes related to the broken U(1) symmetry -- phonons in the spin-superfluid magnon gas; etc. For recent review see Yu. M. Bunkov and G. E. Volovik J. Phys. Cond. Matter. 22, 164210 (2010)