Quantum Lock-in Force Sensing using Optical Clock Doppler Velocimetry

TL;DR

This paper demonstrates a highly sensitive force detection method using a single trapped ion, combining Doppler shift measurements of an optical clock transition with quantum lock-in techniques to detect low-frequency forces.

Contribution

It introduces a novel approach that integrates optical clock Doppler velocimetry with quantum lock-in to enhance force sensing sensitivity at low frequencies.

Findings

Achieved force detection sensitivity of 5.3×10⁻¹⁹ N/√Hz.

Successfully measured both phase-synchronized and asynchronous forces.

Demonstrated effective detection of low-frequency forces below resonance.

Abstract

Force sensors are at the heart of different technologies such as atomic force microscopy or inertial sensing \cite{RMPforce2003, Rugar2004, YazdiIEEE}. These sensors often rely on the measurement of the displacement amplitude of mechanical oscillators under applied force. Examples for such mechanical oscillators include micro-fabricated cantilevers \cite{YazdiIEEE}, carbon nanotubes \cite{NanotubeForce} as well as single trapped ions \cite{Bollinger, Udem} . The best sensitivity is typically achieved when the force is alternating at the mechanical resonance frequency of the oscillator thus increasing its response by the mechanical quality factor. The measurement of low-frequency forces, that are below resonance, is a more difficult task as the resulting oscillation amplitudes are significantly lower. Here we use a single trapped $^{88}Sr^{+}$ ion as a force sensor. The ion is trapped in a linear harmonic trap, and is electrically driven at a frequency much lower than the trap resonance frequency. To be able to measure the small amplitude of motion we combine two powerful techniques. The force magnitude is determined by the measured periodic Doppler shift of an atomic optical clock transition and the Quantum Lock-in technique is used to coherently accumulate the phases acquired during different force half-cycles. We demonstrate force detection both when the oscillating force is phase-synchronized with the quantum lock-in sequence and when it is asynchronous and report frequency force detection sensitivity as low as $5.3\times10^{-19}\frac{\mathrm{N}}{\sqrt{\mathrm{Hz}}}$ .