NON-LINEAR DYNAMICS, ENTANGLEMENT AND THE QUANTUM-CLASSICAL CROSSOVER OF TWO COUPLED SQUID RINGS

Hirotaka Tanaka, Shiro Saito, Hideaki Takayanagi

Lock Yue Chew

Miłosz R. Michalski

M. J. Everitt

We explore the quantum-classical crossover of two coupled, identical, superconducting quantum interference device (SQUID) rings. We note that the motivation for this work is based on a study of a similar system comprising two coupled Duffing oscillators. In that work we showed that the entanglement characteristics of chaotic and periodic (entrained) solutions differed significantly and that in the classical limit entanglement was preserved only in the chaotic-like solutions. However, Duffing oscillators are a highly idealised toy model. Motivated by a wish to explore more experimentally realisable systems we now extend our work to an analysis of two coupled SQUID rings. We observe some differences in behaviour between the system that is based on SQUID rings rather than on Duffing oscillators. However, we show that the two systems share a common feature. That is, even when the SQUID ring's trajectories appear to follow (semi) classical orbits entanglement persists.

M. J. Everitt

Aranya B. Bhattacherjee, Man Mohan

Crossover from individual Rabi dynamics to collective Josephson dynamics in two-coupled Bose–Einstein condensates is studied as a phase transition process. We obtain the critical value of the parameter Λ (ratio of the mean field energy to the tunneling matrix element) for the π-phase oscillations from the non-linear perturbation expansion of small oscillations around the saddle point of the first-order Euclidean (imaginary time) differential equations for polar and azimuthal angles θ and ϕ without approximation.