Models for quantum measurement of particles with higher spin

Abstract

The Curie-Weiss model for quantum measurement describes the dynamical measurement of a spin-$\frac{1}{2}$ by an apparatus consisting of an Ising magnet of many spins $\frac{1}{2}$ coupled to a thermal phonon bath. To measure the $z$-component $s=-l,-l+1,\cdots,l$ of a spin $l$, a class of models is designed along the same lines, which involve $2l$ order parameters. As required for unbiased measurement, the Hamiltonian of the magnet, its entropy and the interaction Hamiltonian possess an invariance under the permutation $s\to s+1$ mod $2l+1$. The theory is worked out for the spin-1 case, where the thermodynamics is analyzed in detail, and for spins $\frac{3}{2},2,\frac{5}{2}$ the thermodynamics and the invariance is presented.