Three-Tone Coherent Microwave Electromechanical Measurement of a Superfluid Helmholtz Resonator

TL;DR

This paper demonstrates a novel microwave electromechanical measurement technique for a superfluid Helmholtz resonator, achieving significantly enhanced coupling strength through a coherent interference method.

Contribution

It introduces a new coherent measurement approach for superfluid electromechanical systems, enabling detection of weak couplings in the unresolved sideband regime with improved sensitivity.

Findings

Measured vacuum electromechanical coupling strength of 23.3 μHz.

Achieved coupling strength three orders of magnitude larger than previous experiments.

Developed a two-probe optomechanically induced transparency/amplification technique.

Abstract

We demonstrate electromechanical coupling between a superfluid mechanical mode and a microwave mode formed by a patterned microfluidic chip and a 3D cavity. The electric field of the chip-cavity microwave resonator can be used to both drive and detect the motion of a pure superflow Helmholtz mode, which is dictated by geometric confinement. The coupling is characterized using a coherent measurement technique developed for measuring weak couplings deep in the sideband unresolved regime. The technique is based on two-probe optomechanically induced transparency/amplification using amplitude modulation. Instead of measuring two probe tones separately, they are interfered to retain only a signal coherent with the mechanical motion. With this method, we measure a vacuum electromechanical coupling strength of $g_0 = 2\pi \times 23.3$ $\mathrm{\mu}$Hz, three orders of magnitude larger than previous superfluid electromechanical experiments.