Quantum loss of synchronization in the dynamics of two spins

¹ Laboratoire de Physique des Solides, CNRS UMR 8502, Univ. Paris-Sud - F-91405 Orsay, France, EU
² Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre et Marie Curie 4 place Jussieu, F-75252 Paris, France, EU

Received: 29 March 2013
Accepted: 27 June 2013

Abstract

Motivated by the spin self-rephasing recently observed in an atomic clock, we introduce a simple dynamical model to study the competition between dephasing and synchronization. Two spins S are taken to be initially parallel and in the plane perpendicular to an inhomogeneous magnetic field Δ that tends to dephase them. In addition, the spins are coupled by exchange interaction J that tries to keep them locked. The analytical solution of the classical dynamics shows that there is a phase transition to a synchronized regime for sufficiently large exchange interaction compared to the inhomogeneity. The quantum dynamics is solved analytically in four limits —large/small and large/small S— and numerically in between. In sharp contrast to the classical case, the quantum solution features very rich S-dependent multiscale dynamics. For any finite S, there is no synchronization but a crossover around between two regimes. The synchronization transition is only recovered when , approaching the classical solution in a non-trivial way. Quantum effects therefore suppress the synchronization transition.