Nondemolition Measurements of a Single Quantum Spin using Josephson Oscillations

Abstract

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 dcmagnetic 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.PACS numbers: 74.50.+r, 03.65.Yz Quantum measurements in mesoscopic systems by use of tunneling attracted recently great interest. One of the motivations is the challenge of the single spin detection [1][2][3]. The other motivation comes from the quantum computing where the final state (after the computation) of a qubit must be measured. The meter couples, usually, to a single observable of the qubit, e.g., σ z . If this observable commutes with the spin Hamiltonian, the QND regime is realized, i.e., the two possible eigenvalues of σ z can be measured with proper probabilities even by a weakly coupled meter. Otherwise the initial state is quickly destroyed and one can only observe the steady state properties of the qubit and the meter performing continuous measurements [4][5][6]. In the spin detecting tunneling schemes all components of the localized spin are coupled to the tunneling electrons via the exchange interaction. Thus QND measurements seem impossible.In this paper we show that in fact QND measurements of the spin projection on the direction of the applied field B z are possible with the use of spin dependent Josephson tunneling at low temperatures, when the effect of quasiparticles is negligible. In this case the amplitude of Josephson oscillations depends on the state of the spin just before the measurement. The amplitude can be measured, e.g., in a circuit containing Josephson junction with the spin, a dc-voltage source V and a resistor R, see Fig. 1. The dissipative spin-dependent current in the circuit appears when the voltage exceeds a threshold and, effectively, it measures the squared amplitude of the Josephson-current oscillations.The measurement can begin either when the voltage exceeding a threshold [12] or the tunneling in the presence of such a voltage is switched on. The first possibility appears more natural for mesoscopic circuits, while the second could be realized with the use of the STM with a superconducting tip and a molecule with spin on the superconducting substrate. As the tip approaches the molecule, tunneling is turned on. The system we consider, i.e. a spin in a Josephson junction with applied voltage, is interesting also from the general viewpoint of quantum measurements. The entanglement of the spin with the measurement apparatus is realized here by use of the non-dissipative macroscopic quantum system as an intermediate step, namely with the superconducting pha...

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