Analog Quantum Simulation of Dirac Equation Effects using Multi-Cavity Modes in Circuit QED

Quantum simulators are controllable quantum systems employed to study other quantum systems that may be less accessible or difficult to manipulate. While research on quantum simulations has been conducted across various platforms, common challenges remain, including scalability and instability in large quantum systems. Therefore, implementing quantum simulations with minimal quantum components is crucial.

In this work, we propose a method for analog quantum simulations using multi-mode cavities in circuit QED to address the aforementioned limitations. Our approach utilizes a Rabi driven qubit coupled to high-Q cavity modes. We show that by applying cavity mode sidebands we can simulate various quantum relativistic effects arising from the Dirac equation all in the same system. Specifically, we introduce techniques for simulating the zitterbewegung phenomenon of free Dirac particles in one and two dimensions, the motion of two-dimensional Dirac particles in the presence of a magnetic field, and the Klein paradox.

We present numerical simulations and analyze the degree of agreement with theoretical predictions. Our findings aim to provide insights into the effective utilization of quantum resources for quantum simulations while advancing the understanding of relativistic quantum phenomena.