Near-resonant nuclear spin detection with megahertz mechanical resonators

TL;DR

This paper proposes a method to detect and control nuclear spins using megahertz mechanical resonators, leveraging frequency variance measurements to enable single nuclear spin detection.

Contribution

It introduces a novel approach for nuclear spin detection via frequency variance, enabling single nuclear spin detection with existing resonator technology.

Findings

Frequency variance increases due to spin ensemble polarization fluctuations.

Analytical and numerical results support the feasibility of single nuclear spin detection.

The method can be implemented with current resonator devices.

Abstract

Mechanical resonators operating in the megahertz range have become a versatile platform for fundamental and applied quantum research. Their exceptional properties, such as low mass and high quality factor, make them also appealing for force sensing experiments. In this work, we propose a method for detecting, and ultimately controlling, nuclear spins by coupling them to megahertz resonators via a magnetic field gradient. Dynamical backaction between the sensor and an ensemble of $N$ nuclear spins produces a shift in the sensor's resonance frequency. The mean frequency shift due to the Boltzmann polarization is challenging to measure in nanoscale sample volumes. Here, we show that the fluctuating polarization of the spin ensemble results in a measurable increase of the resonator's frequency variance. On the basis of analytical as well as numerical results, we predict that the variance measurement will allow single nuclear spin detection with existing resonator devices.