Dirac particle dynamics of a superconducting circuit

The core concept of quantum simulation is the mapping of an inaccessible quantum system onto a controllable one by identifying analogous dynamics. We map the Dirac equation of relativistic quantum mechanics in 3+1 dimensions onto a multilevel superconducting Josephson circuit. Resonant drives determine the particle mass and momentum, and the quantum state represents the internal spinor dynamics which are cast in the language of multilevel quantum optics. Zitterbewegung and wave-packet dynamics are reproduced. The degeneracy of the Dirac spectrum corresponds to a degeneracy of bright and dark states within the system, and particle spin and helicity are employed to interpret the multilevel dynamics. We also simulate the Schwinger mechanism of electron-positron pair production by introducing an analogous electric field as a doubly degenerate Landau-Zener problem. All proposed measurements can be performed well within typical decoherence times. This work opens an avenue for experimental study of the Dirac equation and provides a tool for control of complex dynamics in multilevel systems.