arXiv2011
The intention of this work is twofold, first to present a most simple system capable of simulating the intrinsic bosonic Josephson effect with photons, and second to study various outcomes deriving from inherent or external decoherence. A qubit induces an effective coupling between two externally pumped cavity modes. Without cavity losses and in the dispersive regime, intrinsic Josephson oscillations of photons between the two modes occurs. In this case, contrary to regular Markovian decoherence, the qubit purity shows a Gaussian decay and recurrence of its coherence. Due to intrinsic non-linearities, both the Josephson oscillations as well as the qubit properties display a rich collapse-revival structure, where, however, the complexity of the qubit evolution is in some sense stronger. The qubit as a meter of the photon dynamics is considered, and it is shown that qubit dephasing, originating for example from non-demolition measurements, results in an exponential destruction of the oscillations which manifests the collectiveness of the Josephson effect. Non-selective qubit measurements, on the other hand, render a Zeno effect seen in a slowing down of the Josephson oscillations. Contrary to dephasing, cavity dissipation results in a Gaussian decay of the scaled Josephson oscillations. Finally, following Ponomarev et al. [Phys. Rev. Lett. 106, 010405 (2011)] we analyze aspects of thermalization. In particular, despite similarities with the generic model studied by Ponomarev {\it et al.}, our system does not seem to thermalize.