Quantum Simulations of Relativistic Quantum Physics in Circuit QED

TL;DR

This paper proposes a circuit QED-based scheme to simulate relativistic quantum phenomena such as the Dirac equation and Klein paradox, enabling exploration of these effects in controllable superconducting systems.

Contribution

It introduces a novel method to simulate relativistic quantum physics in circuit QED using microwave drives and superconducting qubits, including implementing the Foldy-Wouthuysen transformation.

Findings

Simulation of Dirac equation dynamics in circuit QED

Proposal to realize Klein paradox in superconducting circuits

Implementation of Foldy-Wouthuysen transformation in this setup

Abstract

We present a scheme for simulating relativistic quantum physics in circuit quantum electrodynamics. By using three classical microwave drives, we show that a superconducting qubit strongly-coupled to a resonator field mode can be used to simulate the dynamics of the Dirac equation and Klein paradox in all regimes. Using the same setup we also propose the implementation of the Foldy-Wouthuysen canonical transformation, after which the time derivative of the position operator becomes a constant of the motion.