Spin detection via parametric frequency conversion in a membrane resonator

Abstract

Recent demonstrations of ultracoherent nanomechanical resonators introduce the prospect of new protocols for solid state sensing applications. Here, we propose to use two coupled ultracoherent resonator modes on a Si3N4 membrane for the detection of small nuclear spin ensembles. To this end, we employ parametric frequency conversion between nondegenerate modes. The nondegenerate modes result from coupled degenerate resonators, and the parametric conversion is mediated by periodic inversions of the nuclear spins in the presence of a magnetic scanning tip. We analyze potential noise sources and derive the achievable signal-to-noise ratio with typical experimental parameter values. Our proposal reconciles the geometric constraints of optomechanical systems with the requirements of scanning force microscopy and brings forth a new platform for spin-phonon interaction and spin imaging.

Membrane-based scanning force microscopy

“…Figure adapted from Ref. 16. (b) A first 1550 nm laser is used to detect the membrane motion and a second 980 nm laser is used to drive the membrane via radiation-pressure forces.…”

“…In future experiments, we expect to use the doublemode structures for parametric up-conversion of magnetic forces from nuclear spins [16]. In the present work we simply take advantage of the fact that the two defects allow us to spatially separate the sites for sample placement and for optical readout.…”

“…We demonstrate scanning probe operation by imaging the nanometerresolution topography of gold nanospheres and tobacco mosaic virus (TMV) particles deposited on the membrane surface. When combined with a precise optical cavity readout and novel spin-mechanics coupling protocols [16] at cryogenic temperatures, our approach is expected to enable quantum-limited scanning force microscopy with the capability to detect individual nuclear spins.…”

“…The scanning force microscope is operated in high vacuum to avoid viscous damping. Figure adapted from Ref 16…”