Nonequilibrium phases in hybrid arrays with flux qubits and nitrogen-vacancy centers

We propose a startling hybrid quantum architecture for simulating a localization-delocalization transition. The concept is based on an array of superconducting flux qubits which are coupled to a diamond crystal containing nitrogen-vacancy centers. The underlying description is a Jaynes-Cummings lattice in the strong-coupling regime. However, in contrast to well-studied coupled cavity arrays, the interaction between lattice sites is mediated here by the qubit rather than by the oscillator degrees of freedom. Nevertheless, we point out that a transition between a localized and a delocalized phase occurs in this system as well. We demonstrate the possibility of monitoring this transition in a nonequilibrium scenario, including decoherence effects. The proposed scheme allows the monitoring of localization-delocalization transitions in Jaynes-Cummings lattices by use of currently available experimental technology. Contrary to cavity-coupled lattices, our proposed recourse to stylized qubit networks facilitates (i) investigating localization-delocalization transitions in arbitrary dimensions and (ii) tuning the intersite coupling in situ.