  We study a model of a magnetic resonance force microscope (MRFM) based on the
cyclic adiabatic inversion technique as a high-resolution tool to detect single
electron spins. We investigate the quantum dynamics of spin and cantilever in
the presence of coupling to an environment. To obtain the reduced dynamics of
the combined system of spin and cantilever, we use the Feynman-Vernon influence
functional and get results valid at any temperature as well as at arbitrary
system-bath coupling strength. We propose that the MRFM can be used as a
quantum measurement device, i.e., not only to detect the modulus of the spin
but also its direction.
