Dirac particle dynamics of a superconducting circuit

TL;DR

This paper demonstrates how a superconducting circuit can simulate the Dirac equation, enabling experimental exploration of relativistic quantum phenomena like pair production within controllable quantum systems.

Contribution

It introduces a novel mapping of the Dirac equation onto a superconducting circuit, allowing simulation of relativistic quantum effects in a multi-level quantum system.

Findings

Successful simulation of Dirac particle dynamics in a superconducting circuit

Observation of the Schwinger mechanism analog in the system

All measurements feasible within typical decoherence times

Abstract

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 multi-level 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 multi-level quantum optics. The degeneracy of the Dirac spectrum corresponds to a degeneracy of bright/dark states within the system and particle spin and helicity are employed to interpret the multi-level dynamics. We 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 a new avenue for experimental study of the Dirac equation and provides a tool for control of complex dynamics in multi-level systems.