INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND GENERAL J. Phys. A: Math. Gen. 36 (2003) 4417–4432 PII: S0305-4470(03)39284-4 Application of magnetic resonance force microscopy cyclic adiabatic inversion for a single-spin measurement G P Berman 1 , F Borgonovi 1,2,3,4 , G Chapline 1,5 , S A Gurvitz 1,6 , P C Hammel 7 , D V Pelekhov 7 , A Suter 7 and V I Tsifrinovich 8 1 Theoretical Division and CNLS, Los Alamos National Laboratory, Los Alamos, NM 177545, USA 2 Dipartimento di Matematica e Fisica, Universit` a Cattolica, via Trieste 17, 25121 Brescia, Italy 3 INFN, Sezione di Pavia, Italy 4 INFM, Unit` a di Brescia, Italy 5 Lawrence Livermore National Laboratory, Livermore, CA 94551, USA 6 Department of Particle Physics, Weizmann Institute of Sciences, Rehovot 76100, Israel 7 MST-10, Los Alamos National Laboratory, MS K764, Los Alamos, NM 87545, USA 8 IDS Department, Polytechnic University, Six Metrotech Center, Brooklyn, NY 11201, USA Received 9 July 2002, in final form 26 February 2003 Published 3 April 2003 Online at stacks.iop.org/JPhysA/36/4417 Abstract 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 Schr ¨ odinger 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 Stern–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 0305-4470/03/154417+16$30.00 © 2003 IOP Publishing Ltd Printed in the UK 4417