Non-linear Dynamics of the Trapped Quantum Vortex*

Nanomechanical resonators have recently been studied as high-sensitivity probes of fluid dynamics in superfluid helium [1, 2, 3]. When turbulence is introduced to such a system, quantum vortices may form and become trapped by the resonator, either completely surrounding the oscillating beam (a fully trapped vortex) [4] or surrounding only part of it (a partially trapped vortex). Fully trapped vortices have been studied using the model of a linear harmonic oscillator behaviour with great success [4]. However, in the presence of a partially trapped vortex, the oscillators have been found to behave non-linearly. We analysed the non-linear response of a doubly clamped nanobeam resonator submerged in helium-4 at 10 mK in the presence of a partially trapped vortex. Our analysis demonstrates that the observed non-linearities are caused by the dynamics of the vortex line.
[1]: Scientific Reports 7 4876 (2017); [2]: Phys. Rev. B 100, 020506(R) (2019); [3]: Phys. Rev. B 101 060503(R) (2020); [4]: arXiv:2007.04482 (2020)