Application of magnetic resonance force microscopy cyclic adiabatic inversion for a single-spin measurement

We consider the process of a single-spin measurement using magnetic resonance force microscopy (MRFM) with a cyclic adiabatic inversion (CAI). This technique is also important for different applications, including a measurement of a qubit state in quantum computation. The measurement takes place through the interaction of a single spin with a cantilever modelled by a quantum oscillator in a coherent state in a quasi-classical range of parameters. The entire system is treated rigorously within the framework of the Schrodinger equation. For a many-spin system our equations accurately describe conventional MRFM experiments involving CAI of the spin system. Our computer simulations of the quantum spin-cantilever dynamics show that the probability distribution for the cantilever position develops two asymmetric peaks with the total relative probabilities mainly dependent on the initial angle between the directions of the average spin and the effective magnetic field, in the rotating frame. We show that each of the peaks is correlated with the direction of the average spin (being along or opposite to the direction of the effective magnetic field). This generates two possible outcomes of a single-spin measurement, similar to the Stem-Gerlach effect. We demonstrate that the generation of the second peak can be significantly suppressed by turning on adiabatically the amplitude of the rf magnetic field. We also show that MRFM CAI can be used both for detecting a signal from a single spin, and for measuring the single-spin state by measuring the phase of the cantilever driving oscillations.