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arXiv:1601.04190 · Journal of Experimental and Theoretical Physics Letters

Linear NMR in the Polar Phase of 3He in Aerogel

V. V. Zavjalov

Published Sep 1, 2018• 3 citations
arXivHTMLPDF

Abstract

3 He is an example of the system with non-trivial Cooper paring. A few different superfluid phases are known in this system. Recently the new one, the polar phase, have been observed in 3 He confined in nematically ordered aerogel. A number of various topological defects including half-quantum vortices can exist the polar phase. In this work, we present theoretical and numerical studies of linear nuclear magnetic resonance in the polar phase both in the uniform order-parameter texture and in the presence of half-quantum vortices.

DOI
10.1134/s0021364018180029

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3 He is an example of the system with non-trivial Cooper paring. A few different superfluid phases are known in this system. Recently the new one, the polar phase, have been observed in 3 He confined in nematically ordered aerogel. A number of various topological defects including half-quantum vortices can exist the polar phase. In this work, we present theoretical and numerical studies of linear nuclear magnetic resonance in the polar phase both in the uniform order-parameter texture and in the presence of half-quantum vortices.
We report theoretical results for the stability of half-quantum vortices (HQVs) in the superfluid phases of 3He^{3}\mathrm{He}3He confined in highly anisotropic Nafen aerogel. Superfluidity of 3He^{3}\mathrm{He}3He confined in Nafen is the realization of a ``nematic superfluid'' with Cooper pairs condensed into a single ppp-wave orbital aligned along the anisotropy axis of the Nafen aerogel. In addition to the nematic phase, we predict a second ``chiral'' phase that onsets at a lower transition temperature. This chiral phase spontaneously breaks time-reversal symmetry and is a topological superfluid. Both superfluid phases are equal-spin pairing condensates that host arrays of HQVs as equilibrium states of rotating superfluid 3He^{3}\mathrm{He}3He. We present results for the structure of HQVs, including magnetic and topological signatures of HQVs in both the nematic and chiral phases of 3He^{3}\mathrm{He}3He-Nafen.
Deformation of aerogel strongly modifies the orientation of the order parameter of superfluid 3He confined in aerogel. We used a radial squeezing of aerogel to keep the orbital angular momentum of the 3He Cooper pairs in the plane perpendicular to the magnetic field. We did not find strong evidence for a polar phase, with a nodal line along the equator of the Fermi surface, predicted to occur at large radial squeezing. Instead we observed 3He-A with a clear experimental evidence of the destruction of the long-range order by random anisotropy -- the Larkin-Imry-Ma effect. In 3He-B we observed and identified new modes of NMR, which are impossible to obtain in bulk 3He-B. One of these modes is characterized by a repulsive interaction between magnons, which is suitable for the magnon Bose-Einstein condensation (BEC).
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.
The influence of spin-exchange scattering centers on the triplet Cooper pairing is considered to explore the behavior of superfluid 3He in high porosity aerogel containing 3He atoms localized at the surface of silica strands. The homogeneously located and isotropically scattering system of spin-polarized ``impurity'' centers is adopted as a simple model to investigate the contribution of spin-exchange scattering chanel for quasiparticles to the formation of non-unitary superfluid A1-phase in aerogel environment. It is demonstrated that an interference between the potential and exchange parts of quasiparticle scattering against spin-polarized ``impurity'' centers can change considerably the temperature width and the spin structure of A_{1}-phase in aerogel.
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 -…
We report results of experiments with superfluid ^{3}He confined in aerogels with parallel strands which lead to anisotropic scattering of ^{3}He quasiparticles. We vary boundary conditions for the scattering by covering the strands with different numbers of atomic ^{4}He layers and observe that the superfluid phase diagram and the nature of superfluid phases strongly depend on the coverage. We assume the main reason for these phenomena is a magnetic channel of the scattering which becomes important at low coverages and can be essential in other Fermi systems with triplet pairing.