Persistent entanglement in two coupled SQUID rings in the quantum to classical transition - A quantum jumps approach

We explore the quantum-classical crossover of two coupled, identical, superconducting quantum interference device (SQUID) rings. The motivation for this work is based on a series of recent papers. In ~[1] we showed that the entanglement characteristics of chaotic and periodic (entrained) solutions of the Duffing oscillator 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 system. Motivated by a wish to explore more experimentally realisable systems we extended our work in [2,3] to an analysis of SQUID rings. In [3] we showed that the two systems share a common feature. That is, when the SQUID ring's trajectories appear to follow (semi) classical orbits entanglement persists. Our analysis in[3] was restricted to the quantum state diffusion unravelling of the master equation - representing unit efficiency heterodyne detection (or ambi-quadrature homodyne detection). Here we show that very similar behaviour occurs using the quantum jumps unravelling of the master equation. Quantum jumps represents a discontinuous photon counting measurement process. Hence, the results presented here imply that such persistent entanglement is independent of measurement process and that our results may well be quite general in nature.