Dirac Equation in (1 + 1)-Dimensional Curved Spacetime and the Multiphoton Quantum Rabi Model

摘要

We introduce an exact mapping between the Dirac equation in (1 + 1)-dimensional curved spacetime (DCS) and a multiphoton quantum Rabi model (QRM). A background of a (1 + 1)-dimensional black hole requires a QRM with one- and two-photon terms that can be implemented in a trapped ion for the quantum simulation of Dirac particles in curved spacetime. We illustrate our proposal with a numerical analysis of the free fall of a Dirac particle into a (1 + 1)-dimensional black hole, and find that the Zitterbewegung effect, measurable via the oscillatory trajectory of the Dirac particle, persists in the presence of gravity. From the duality between the squeezing term in the multiphoton QRM and the metric coupling in the DCS, we show that gravity generates squeezing of the Dirac particle wave function.