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arXiv:quant-ph/0210006 · Physical Review A

Transient dynamics in magnetic force microscopy for a single-spin measurement

G. P. Berman, F. Borgonovi, Gustavo V. López, V. I. Tsifrinovich

Published Jul 9, 2003• 7 citations
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Abstract

We analyze a single-spin measurement using a transient process in magnetic force microscopy which could increase the maximum operating temperature by a factor of Q (the quality factor of the cantilever) in comparison with the static Stern-Gerlach effect. We obtain an exact solution of the master equation, which confirms this result. We also discuss the conditions required to create a macroscopic quantum superposition in the cantilever.

DOI
10.1103/physreva.68.012102

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We analyze a single-spin measurement using a transient process in magnetic force microscopy which could increase the maximum operating temperature by a factor of Q (the quality factor of the cantilever) in comparison with the static Stern-Gerlach effect. We obtain an exact solution of the master equation, which confirms this result. We also discuss the conditions required to create a macroscopic quantum superposition in the cantilever.
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A promising technique for measuring single electron spins is magnetic resonance force microscopy (MRFM), in which a microcantilever with a permanent magnetic tip is resonantly driven by a single oscillating spin. The most effective experimental technique is the oscillating cantilever-driven adiabatic reversals (OSCAR) protocol, in which the signal takes the form of a frequency shift. If the quality factor of the cantilever is high enough, this signal will be amplified over time to the point where it can be detected by optical or other techniques. An important requirement, however, is that this measurement process occurs on a time scale that is short compared to any noise which disturbs the orientation of the measured spin. We describe a model of spin noise for the MRFM system and show how this noise is transformed to become time dependent in going to the usual rotating frame. We simplify the description of the cantilever-spin system by approximating the cantilever wave function as a Gaussian wave packet and show that the resulting approximation closely matches the full quantum behavior. We then examine the problem of detecting the signal for a cantilever with thermal noise and spin with spin noise, deriving a condition for this to be a useful measurement.
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.
We review the quantum theory of a single-spin magnetic resonance force microscopy (MRFM). We concentrate on the novel technique called oscillating cantilever-driven adiabatic reversals (OSCARs), which has been used for a single-spin detection. First we describe the quantum dynamics of the cantilever-spin system using simple estimates in the spirit of the mean field approximation. Then we present the results of our computer simulations of the Schro/spl uml/dinger equation for the wave function of the cantilever-spin system and of the master equation for the density matrix of the system. We demonstrate that the cantilever behaves like a quasi-classical measurement device which detects the spin projection along the effective magnetic field. We show that the OSCAR technique provides continuous monitoring of the single spin, which could be used to detect the mysterious quantum collapses of the wave function of the cantilever-spin system.