Gaussian approximation and single-spin measurement in OSCAR MRFM with spin noise

TL;DR

This paper models the detection of single electron spins using MRFM, demonstrating how Gaussian approximations and spin noise influence measurement sensitivity and establishing conditions for effective spin detection.

Contribution

It introduces a Gaussian wavepacket approximation for the cantilever-spin system and analyzes the impact of spin noise on MRFM measurement performance.

Findings

Gaussian approximation closely matches quantum behavior

Derived conditions for effective spin detection amidst noise

Analyzed the influence of thermal and spin noise on measurement

Abstract

A promising technique for measuring single electron spins is magnetic resonance force microscopy (MRFM), in which a microcantilever with a permanent magnetic tip is resonantly driven by a single oscillating spin. If the quality factor of the cantilever is high enough, this signal will be amplified over time to the point that it can be detected by optical or other techniques. An important requirement, however, is that this measurement process occur on a time scale short compared to any noise which disturbs the orientation of the measured spin. We describe a model of spin noise for the MRFM system, and show how this noise is transformed to become time-dependent in going to the usual rotating frame. We simplify the description of the cantilever-spin system by approximating the cantilever wavefunction as a Gaussian wavepacket, and show that the resulting approximation closely matches the full quantum behavior. We then examine the problem of detecting the signal for a cantilever with thermal noise and spin with spin noise, deriving a condition for this to be a useful measurement.