Nonlinear behaviour of confined superfluid helium.

Superfluid Helmholtz resonators provide a versatile tool for the study of both superfluid ⁴He and ³He under microscopic confinement. They have proven to be effective at measuring the superfluid fraction [1] and enabled detection of emergent phases under confinement in superfluid ³He [2]. We extend previous experiments into the strongly driven regime where the resonance is nonlinear. The nature of the nonlinear behaviour depends on the isotope of helium, and on the phase in superfluid 3He.

For superfluid ⁴He, the nonlinearity is due to turbulence, which at relatively high temperatures closely approximates two-dimensional turbulence of discrete point vortices even though the confinement is significantly larger than the coherence length.

For the case of superfluid ³He, the coherence length is comparable to the confinement and a new phase appears [2]. Here, the qualitative nature of the nonlinearity (i.e., nonlinear dissipation vs. Duffing resonance) changes with the superfluid phase, enabling phase identification.

[1] X. Rojas and J.P. Davis, Phys. Rev. B 91, 024503 (2015)
[2] A. Shook, et al. arXiv:1908.01779