Nondemolition measurements of a single quantum spin using Josephson oscillations

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We consider a Josephson junction containing a single localized spin 1/2 between conventional singlet superconducting electrodes. We study the spin dynamics and measurements when a dc-magnetic field B∥ z acts on the spin and the junction is embedded into a dissipative circuit. We show that when tunneling or a voltage are turned on at time t=0 the Josephson current starts to oscillate with an amplitude depending on the initial (t=0) value of the spin z-component, Sz= ± 1/2. At low temperatures, when effects of quasiparticles may be neglected, this procedure realizes a quantum-non-demolition (QND) measurement of Sz.