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The recovery of classical chaotic dynamics from quantum systems has long beena subject of interest. Furthermore, recent work indicates that quantum chaosmay well be significant in quantum information processing. In this paper wediscuss the quantum to classical crossover of a superconducting quantuminference device (SQUID) ring. Such devices comprise of thick superconductingloop enclosing a Josephson weak link. These devices are currently strongcandidates for many applications in quantum technologies. The weak link bringswith it a non-linearity such that semi-classical models of this system canexhibit chaotic dynamics. For many similar systems an application of thecorrespondence principle together with the inclusion of environmental degreesof freedom through a quantum trajectories approach can be used to effectivelyrecover classical dynamics. Here we show (i) that the standard expression ofthe correspondence principle is incompatible with the ring Hamiltonian and wepresent a more pragmatic and general expression which finds application hereand (ii) that practical limitations to circuit parameters of the SQUID ringprevent arbitrarily accurate recovery of classical chaotic dynamics.

On the correspondence principle: implications from a study of the chaotic dynamics of a macroscopic quantum device