Decoupling between first sound and second sound in $^3$He - superfluid $^4$He mixtures

TL;DR

This study investigates the decoupling of first and second sound modes in dilute helium mixtures, revealing specific conditions where their coupling vanishes, which is crucial for understanding superfluid helium dynamics.

Contribution

It provides experimental evidence of decoupling conditions between first and second sound in helium mixtures, highlighting the temperature and concentration dependence of their coupling.

Findings

Decoupling occurs at specific temperatures and concentrations.

Resonance anomalies disappear when coupling terms cancel.

Coupling strength varies with temperature and helium concentration.

Abstract

Bulk superfluid helium supports two sound modes: first sound is an ordinary pressure wave, while second sound is a temperature wave, unique to inviscid superfluid systems. These sound modes do not usually exist independently, but rather variations in pressure are accompanied by variations in temperature, and vice versa. We studied the coupling between first and second sound in dilute $^3$He - superfluid $^4$He mixtures, between 1.6 K and 2.2 K, at $^3$He concentrations ranging from 0 to 11 %, under saturated vapor pressure, using a quartz tuning fork oscillator. Second sound coupled to first sound can create anomalies in the resonance response of the fork, which disappear only at very specific temperatures and concentrations, where two terms governing the coupling cancel each other, and second sound and first sound become decoupled.