Static Stern-Gerlach effect in magnetic force microscopy

The Stern-Gerlach ~SG! effect, one of the cornerstones of a quantum mechanics, still attracts much attention. ~See, for example, Refs. @1–7#.! The SG apparatus clearly demonstrates the quantization of angular momentum and it can also demonstrate the mysterious puzzles of quantum measurement, macroscopic quantum superposition ~Schrödinger-cat! states, and decoherence. The SG effect was used to measure the spin state of a single electron in a Penning trap @8# and the spin state of a single hydrogen-like ion in a Penning trap @9#. So far, all experimental and theoretical versions of the SG apparatus exploit the influence of the spin state on the characteristics of the classical motion of a particle. In this paper, we discuss the static SG effect, in which the spin state influences the equilibrium position of a classical system. Implementation of the static SG apparatus can be used to understand the puzzles of a quantum measurement, and it also can find applications in quantum computation. Our idea is similar to Ref. @1# in which the magneticresonance force microscopy ~MRFM! was proposed as a new method for performing a SG measurement. During the last decade remarkable progress has been achieved in building ultra-thin cantilevers. ~See, for example, Refs. @10–12#.! In this connection, we explore the possibility of detecting static SG effect using the latest ultra-thin cantilevers.