Electron spin detection in the frequency domain under the interrupted Oscillating Cantilever-driven Adiabatic Reversal (iOSCAR) Protocol

Magnetic Resonance Force Microscopy (MRFM) is an emergent technology for measuring spin-induced attonewton forces using a micromachined cantilever. In the interrupted Oscillating Cantilever-driven Adiabatic Reversal (iOSCAR) method, small ensembles of electron spins are manipulated by an external radio frequency (RF) magnetic field to produce small periodic deviations in the resonant frequency of the cantilever. These deviations can be detected by frequency demodulation, followed by conventional amplitude or energy detection. In this paper, we develop optimal detectors for several signal models that have been hypothesized for measurements induced by iOSCAR spin manipulation. We show that two simple variants of the energy detector–the filtered energy detector and a hybrid filtered energy/amplitude/energy detector–are approximately asymptotically optimal for the Discrete-Time (D-T) random telegraph signal model assuming White Gaussian Noise (WGN). For the D-T random walk signal model, the filtered energy detector performs close to the optimal Likelihood Ratio Test (LRT) when the transition probabilities are symmetric.