Single-spin measurement and decoherence in magnetic-resonance force microscopy

We consider a simple version of a cyclic adiabatic inversion (CAI) technique in magnetic-resonance force microscopy (MRFM). We study the problem: What component of the spin is measured in the CAI MRFM? We show that the nondestructive detection of the cantilever vibrations provides a measurement of the spin component along the effective magnetic field. This result is based on numerical simulations of the Hamiltonian dynamics (the Schr\"odinger equation) and the numerical solution of the master equation.