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

TL;DR

This paper establishes an exact mapping between the Dirac equation in (1+1)-dimensional curved spacetime and a multiphoton quantum Rabi model, enabling quantum simulation of particles in curved spacetime and revealing gravity-induced wave function squeezing.

Contribution

It introduces a novel exact mapping between Dirac equations in curved spacetime and multiphoton quantum Rabi models, facilitating quantum simulation of gravitational effects.

Findings

Zitterbewegung persists in curved spacetime

Gravity induces squeezing of the Dirac wave function

Numerical simulation of a Dirac particle falling into a black hole

Abstract

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.