[Paper Review] Gravity waves on the surface of topological superfluid 3He-B

V. B. Eltsov, P. J. Heikkinen+1 more|arXiv (Cornell University)|Feb 4, 2013

Quantum, superfluid, helium dynamics3 citations

TL;DR

This study reports the first experimental observation of gravity waves on the free surface of ultracold topological superfluid 3He-B at temperatures below 0.2 mK. Using a Bose-Einstein condensate of magnon quasiparticles as a sensitive probe, the authors detect surface wave modes and observe temperature-dependent damping and enhanced relaxation of the magnon condensate due to surface oscillations, suggesting possible coupling to surface-bound Majorana fermions.

ABSTRACT

We have observed waves on the free surface of 3He-B sample at temperatures below 0.2mK. The waves are excited by vibrations of the cryostat and detected by coupling the surface to the Bose-Einstein condensate of magnon quasiparticles in the superfluid. The two lowest gravity-wave modes in our cylindrical container are identified. Damping of the waves increases with temperature linearly with the density of thermal quasiparticles, as expected. Additionally finite damping of the waves in the zero-temperature limit and enhancement of magnetic relaxation of magnon condensates by the surface waves are observed. We discuss whether the latter effects may be related to Majorana fermions bound to the surface of the topological superfluid.

Motivation & Objective

• To detect gravity waves on the free surface of topological superfluid 3He-B at ultra-low temperatures.
• To investigate the damping of surface waves as a function of temperature and quasiparticle density.
• To probe potential coupling between surface waves and surface-bound Majorana fermions via magnon condensate relaxation.

Proposed method

• A cylindrical container of 3He-B at T < 0.2 mK hosts a free surface probed by a nuclear magnetic resonance (NMR) pick-up coil.
• A Bose-Einstein condensate (BEC) of magnon quasiparticles is formed in a trap created by radial texture of the orbital anisotropy axis and axial magnetic field minimum.
• Surface wave oscillations modulate the trapping potential, shifting the precession frequency of the magnon BEC, which is detected via NMR signal analysis.
• The system uses continuous-wave NMR pumping at the m=2 level to maintain the ground-state BEC while measuring frequency shifts from surface waves.
• Relaxation times of the magnon BEC are measured after switching off pumping, with modulation induced either by surface waves or by periodic magnetic field changes.
• Band-pass filtering isolates the ground-state condensate signal, enabling precise tracking of frequency and amplitude modulations.

Experimental results

Research questions

• RQ1 Can gravity waves be experimentally observed on the free surface of 3He-B at temperatures below 0.2 mK?
• RQ2 How does the damping of surface waves scale with temperature and quasiparticle density in the superfluid?
• RQ3 Is the observed enhancement in magnon BEC relaxation due to surface wave modulation, and could it be linked to surface-bound Majorana fermions?
• RQ4 Does the finite damping observed at zero temperature suggest new relaxation mechanisms beyond thermal quasiparticles?
• RQ5 Can the magnon BEC serve as a sensitive probe for surface wave dynamics and topological surface states?

Key findings

• Gravity waves on the free surface of 3He-B were observed at temperatures below 0.2 mK, with two lowest modes identified in the cylindrical container.
• Wave damping increases linearly with temperature, consistent with damping by thermal quasiparticles, and extrapolates to a finite value in the zero-temperature limit.
• The relaxation rate of the magnon BEC increases with increasing amplitude of surface wave oscillations, indicating an additional relaxation channel.
• This enhancement is not observed when the trapping potential is modulated via the magnetic field at the same frequency, ruling out direct modulation-induced transitions as the cause.
• The observed relaxation enhancement may be linked to coupling with surface-bound Majorana fermions, though a theoretical model is required to confirm this.