Acoustic modes in He I and He II in the presence of an alternating electric field

TL;DR

This paper investigates how an alternating electric field influences acoustic modes in helium I and II, revealing coupling effects, velocity modifications, and the potential for resonance phenomena leading to narrow absorption lines.

Contribution

It introduces a theoretical analysis of the coupling between electric fields and acoustic modes in helium, predicting velocity shifts and hybrid density waves with resonance behavior.

Findings

Electric field alters sound velocities in helium.

Hybrid acousto-electric density waves are generated.

Resonance effects could produce narrow electromagnetic absorption lines.

Abstract

By solving the equations of ordinary and two-fluid hydrodynamics, we study the oscillatory modes in isotropic nonpolar dielectrics He I and He II in the presence of an alternating electric field $\textbf{E}=E_{0}\textbf{i}_{z}\sin{(k_{0}z-\omega_{0} t)}$. The electric field and oscillations of the density become ``coupled,'' since the density gradient causes a spontaneous polarization $\textbf{P}_{s}$, and the electric force contains the term $(\textbf{P}_{s}\nabla)\textbf{E}$. The analysis shows that the field $\textbf{E}$ changes the velocities of first and second sounds, propagating along $\textbf{E}$, by the formula $u_{j}\approx c_{j}+\chi_{j} E_{0}^{2}$ (where $j=1, 2$; $c_{j}$ is the velocity of the $j$-th sound for $E_{0}=0$, and $\chi_{j}$ is a constant). We have found that the field $\textbf{E}$ jointly with a wave of the first (second) sound $(\omega,k)$ should create in He II hybrid acousto-electric (thermo-electric) density waves $(\omega + l \omega_{0},k + lk_{0})$, where $l=\pm 1, \pm 2, \ldots$. The amplitudes of acousto-electric waves and the quantity $|u_{1}-c_{1}|$ are negligibly small, but they should increase in the resonance way at definite $\omega$ and $\omega_{0}$. Apparently, the first resonance corresponds to the decay of a photon into two phonons with the transfer of a momentum to the whole liquid. Therefore, the spectrum of an electromagnetic signal should contain a narrow absorption line like that in the M\"{o}ssbauer effect.