Theoretical studies of superfluid ³He

One of the greatest problems in physics is to understand interacting many-body systems. In condensed matter physics, the number of particles in the system is usually very large, which makes theoretical research quite challenging. Out of the wide spectrum of possibilities, a particularly interesting subject of research is helium. The main reason for this is the possibility to observe macroscopic quantum phenomena. This means that the laws of quantum mechanics, which are usually only important at microscopic scale, can be observed at macroscopic scale, even with naked eye.

In my doctoral research I shall study the lighter isotope of helium, ³He, at very low temperatures (< 1 mK). At these temperatures ³He is a superfluid. The research will consist of three projects.

In the first project we study superfluid phases of ³He in the presence of nematically ordered aerogel using the Ginzburg-Landau theory. Helium-3 is naturally a very pure substance. It is therefore interesting to study how impurities affect the superfluidity. Nematically ordered aerogel consists of thin strands oriented along the same axis, making it an ordered impurity. Our goal is to calculate the phase diagram, and compare it with the measured one [1]. It seems that the aerogel stabilises the polar phase, which is not a stable phase in the bulk.

In the second project we study spin dynamics of B-phase vortices. Nuclear magnetic resonance (NMR) is the main tool in experimental research of superfluid ³He. When studying vortices in the B-phase, it is possible to create a homogeneously precessing domain, where spins of the nuclei in some region precess uniformly with a large tipping angle (104°) with respect to the magnetic field. Different vortex structures are identified by measuring energy absorption [2]. We propose that vortices dissipate energy by radiating spin waves. The amount of energy radiated can be calculated using the Leggett theory. The results would seem to be in agreement with the experimental results.

In the third project we study motion of objects immersed in superfluid ³He. Vibrating wires are commonly used to study properties of quantum fluids. Recently, an experiment was made in very cold ³He with a wire which does not oscillate, but moves with a constant velocity [3]. This experiment showed an interesting phenomenon. A naive expectation is that the force exerted on the object by the liquid increases suddenly, when the velocity of the object reaches the Landau velocity v_L = Δ / p_F. This, however, was not observed, and we would like to understand why. Our idea is that the fluid flow around the wire could shield the wire from the incoming quasiparticles. Theory is based on the Fermi liquid theory of superfluidity, i.e. the quasiclassical theory.

References

1. R. Sh. Askhadullin, V. V. Dmitriev, and D. A. Krasnikhin, P. N. Martynov, A. A. Osipov, A. A. Senin, A. N. Yudin, JETP Lett. 95 , 326 (2012).
2. Y. Kondo, J. S. Korhonen, M. Krusius, V. V. Dmitriev, Y. M. Mukharsky, E. B. Sonin and G. E. Volovik, Phys. Rev. Lett. 67, 81 (1991).
3. D. I. Bradley, S. N. Fisher, A. M. Guénault, R. P. Haley, C. R. Lawson, G. R. Pickett, R. Schanen, M. Skyba, V. Tsepelin, D. E. Zmeev, Nature Phys. 12 , 1017 (2016).

Publications

• S. M. Laine and E. V. Thuneberg, Calculation of Leggett-Takagi Relaxation in Vortices of Superfluid ³He-B, J. Low Temp. Phys. 183, 222 (2016).
• S. M. Laine and E. V. Thuneberg, Spin wave radiation from vortices in ³He-B, Phys. Rev. B 98, 174516 (2018).
• J. A. Kuorelahti, S. M. Laine and E. V. Thuneberg, Models for supercritical motion in a superfluid Fermi liquid, Phys. Rev. B 98, 144512 (2018).

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