Theory of Optomechanical Interactions in Superfluid He

TL;DR

This paper develops a comprehensive theoretical framework for optomechanical interactions in superfluid helium, accounting for nonlinear phonon processes and exploring conditions where multi-phonon interactions dominate over single-phonon processes.

Contribution

It introduces a general theory including nonlinear acoustic effects and analyzes multi-phonon upconversion mechanisms in superfluid helium within optical cavities.

Findings

Two-phonon upconversion can dominate when single-phonon processes are suppressed.

Quantum interference effects are significant in two-phonon transition pathways.

Large two-step processes are possible under certain cavity mode configurations.

Abstract

A general theory is presented to describe optomechanical interactions of acoustic phonons, having extremely long lifetimes in superfluid $^4$He, with optical photons in the medium placed in a suitable electromagnetic cavity. The acoustic nonlinearity in the fluid motion is included to consider processes beyond the usual linear process involving absorption or emission of one phonon at a time. We first apply our formulation to the simplest one-phonon process involving the usual resonant anti-Stokes upconversion of an incident optical mode. However, when the allowed optical cavity modes are such that there is no single-phonon mode in the superfluid which can give rise to a resonant allowed anti-Stokes mode, we must consider the possibility of two phonon upconversion. For such a case, we show that the two step two phonon process could be dominant. We present arguments for large two step process and negligible single step two phonon contribution. The two step process also shows interesting quantum interference among different transition pathways.